https://wiki.cs.hse.ru/api.php?action=feedcontributions&feedformat=atom&user=Vvbalakirev Wiki - Факультет компьютерных наук - Вклад [ru] 2026-09-20T23:03:41Z Вклад MediaWiki 1.43.9 https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=93572 Calculus 2 DSBA 2025/2026 2025-11-11T23:44:13Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 2 '''<br /> * [ '''Lecture 10'''] (07.11.2025) Multiple Riemann integrals: Part II.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/gnun2r1ys31ltw11cyluv/Calculus_2_Lecture_9.pdf?rlkey=m5dge8pgcn11bmvfzegy0ni1x&amp;st=l81a97dz&amp;dl=0 '''Lecture 9'''] (24.10.2025) Multiple Riemann integrals: Part I].<br /> <br /> * [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&amp;dl=0 '''Lecture 8'''] (17.10.2025) Analytic functions; differentiability classes; smooth functions; the Taylor series; the Taylor formula; criteria for analyticity; the Borel lemma; some pathological examples of smooth functions.<br /> <br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 '''Lecture 7'''] (10.10.2025) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/9z1kt1bgw7ujbrac78v5d/Calculus_2_HW_6_g241.pdf?rlkey=kn7jp6u81zaonv14tw7zjr92o&amp;st=4v21ojzt&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/mnl3dgqxb7g3psmutcezl/Calculus_2_HW_6_g246.pdf?rlkey=l2xv2p4pm1r4x9eypu7l95yxo&amp;st=a6ihzr71&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6]<br /> |- <br /> !| [https://www.dropbox.com/scl/fi/cp4ef052mrbf3vzkgn0se/Calculus_2_HW_7_g241.pdf?rlkey=98e9i80a4tpnkvmkg5y13a2x8&amp;st=8145hs2d&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] || [https://www.dropbox.com/scl/fi/ta6uj8dy428j41joltuj7/HW-7.pdf?rlkey=sxzuw64vujs154zzb49hpnz3v&amp;dl=0 HW_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/uxqxqvvffevfrxmndj7z5/Seminar-7-problems.pdf?rlkey=ni8vov4uc9jickfbccwdnkjwe&amp;dl=0 Sem_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/2qem0m9zawcy4fzxd34lu/Seminar-7-solutions.pdf?rlkey=g1s8xfyzezg8ktbms6hfq451c&amp;dl=0 Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [https://www.dropbox.com/scl/fi/g52laj6f2xbsdzoat2rl4/Calculus_2_HW_7_g246.pdf?rlkey=r1vvhd71fy0lljrl264o0f3nl&amp;st=8vjovzvq&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] <br /> |- <br /> !| [https://www.dropbox.com/scl/fi/1poymegtu4efr6v21ppvt/Calculus_2_HW_8_g241.pdf?rlkey=8wyfzeys8k1gwmdwn6bx0zbyf&amp;st=0i7iu2ke&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] || [https://www.dropbox.com/scl/fi/93xh32tzj5o0f2uogouyf/HW-8.pdf?rlkey=u58bjyb86tt0urri6o3m5b1ay&amp;dl=0 HW_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/fanjeiw51cxhjjg7kz6s4/Seminar-8-problems.pdf?rlkey=bcgs7t0po75erotiyvhzvp9rx&amp;dl=0 Sem_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/38f9xgyaohj1879gzbxfn/Seminar-8-solutions.pdf?rlkey=nnf1sjgstan4lzxnanh6vn5sa&amp;dl=0 Solutions 8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [https://www.dropbox.com/scl/fi/ozubrursz6zy4iwdyqta1/Calculus_2_HW_8_g246.pdf?rlkey=j2qhhaz8mv4i1wervl5uaznd2&amp;st=4ribpd8h&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] <br /> |- <br /> !| [https://www.dropbox.com/scl/fi/48k6ub6f2jytmf7wrktx6/Calculus_2_HW_9_g241.pdf?rlkey=s2xi61ueqngkuq5i50cfqhxf9&amp;st=x8mjehkz&amp;dl=0 HW_9] (14.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&amp;st=xiiei8ji&amp;dl=0 Sem_9] || [https://www.dropbox.com/scl/fi/flsork2rii9ll5ufhkr6t/HW-9.pdf?rlkey=a7ia97ttf1obno46ii6k1k18r&amp;dl=0 HW_9] &lt;br&gt; [ Sem_9] &lt;br&gt; [Solutions 9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [https://www.dropbox.com/scl/fi/29gh3rsrcgcejwzihlu7p/Calculus_2_HW_9_g246.pdf?rlkey=hdvx4cwtbu32iut0t16jgf93d&amp;st=uzwnsg0f&amp;dl=0 HW_9] (14.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&amp;st=xiiei8ji&amp;dl=0 Sem_9] <br /> |- <br /> |-<br /> !| [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [https://www.dropbox.com/scl/fi/pp8oybrka3wqu7lv37rn4/HW-10.pdf?rlkey=3wu73g5ecworrdcbxgr0g8cb8&amp;dl=0 HW_10] &lt;br&gt; [ Sem_10] &lt;br&gt; [Solutions 10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] <br /> |-<br /> !| [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] &lt;br&gt; [ Sem_11] &lt;br&gt; [Solutions 11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] <br /> |-<br /> !| [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] &lt;br&gt; [ Sem_12] &lt;br&gt; [Solutions 12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12]<br /> |-<br /> !| [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] &lt;br&gt; [ Sem_13] &lt;br&gt; [Solutions 13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=93571 Calculus 2 DSBA 2025/2026 2025-11-11T23:43:51Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 2 '''<br /> * [ '''Lecture 10'''] (07.11.2025) Multiple Riemann integrals: Part II.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/gnun2r1ys31ltw11cyluv/Calculus_2_Lecture_9.pdf?rlkey=m5dge8pgcn11bmvfzegy0ni1x&amp;st=l81a97dz&amp;dl=0 '''Lecture 9'''] (24.10.2025) Multiple Riemann integrals: Part I].<br /> <br /> * [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&amp;dl=0 '''Lecture 8'''] (17.10.2025) Analytic functions; differentiability classes; smooth functions; the Taylor series; the Taylor formula; criteria for analyticity; the Borel lemma; some pathological examples of smooth functions.<br /> <br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 '''Lecture 7'''] (10.10.2025) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/9z1kt1bgw7ujbrac78v5d/Calculus_2_HW_6_g241.pdf?rlkey=kn7jp6u81zaonv14tw7zjr92o&amp;st=4v21ojzt&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/mnl3dgqxb7g3psmutcezl/Calculus_2_HW_6_g246.pdf?rlkey=l2xv2p4pm1r4x9eypu7l95yxo&amp;st=a6ihzr71&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6]<br /> |- <br /> !| [https://www.dropbox.com/scl/fi/cp4ef052mrbf3vzkgn0se/Calculus_2_HW_7_g241.pdf?rlkey=98e9i80a4tpnkvmkg5y13a2x8&amp;st=8145hs2d&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] || [https://www.dropbox.com/scl/fi/ta6uj8dy428j41joltuj7/HW-7.pdf?rlkey=sxzuw64vujs154zzb49hpnz3v&amp;dl=0 HW_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/uxqxqvvffevfrxmndj7z5/Seminar-7-problems.pdf?rlkey=ni8vov4uc9jickfbccwdnkjwe&amp;dl=0 Sem_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/2qem0m9zawcy4fzxd34lu/Seminar-7-solutions.pdf?rlkey=g1s8xfyzezg8ktbms6hfq451c&amp;dl=0 Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [https://www.dropbox.com/scl/fi/g52laj6f2xbsdzoat2rl4/Calculus_2_HW_7_g246.pdf?rlkey=r1vvhd71fy0lljrl264o0f3nl&amp;st=8vjovzvq&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] <br /> |- <br /> !| [https://www.dropbox.com/scl/fi/1poymegtu4efr6v21ppvt/Calculus_2_HW_8_g241.pdf?rlkey=8wyfzeys8k1gwmdwn6bx0zbyf&amp;st=0i7iu2ke&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] || [https://www.dropbox.com/scl/fi/93xh32tzj5o0f2uogouyf/HW-8.pdf?rlkey=u58bjyb86tt0urri6o3m5b1ay&amp;dl=0 HW_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/fanjeiw51cxhjjg7kz6s4/Seminar-8-problems.pdf?rlkey=bcgs7t0po75erotiyvhzvp9rx&amp;dl=0 Sem_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/38f9xgyaohj1879gzbxfn/Seminar-8-solutions.pdf?rlkey=nnf1sjgstan4lzxnanh6vn5sa&amp;dl=0 Solutions 8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [https://www.dropbox.com/scl/fi/ozubrursz6zy4iwdyqta1/Calculus_2_HW_8_g246.pdf?rlkey=j2qhhaz8mv4i1wervl5uaznd2&amp;st=4ribpd8h&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] <br /> |- <br /> !| [https://www.dropbox.com/scl/fi/48k6ub6f2jytmf7wrktx6/Calculus_2_HW_9_g241.pdf?rlkey=s2xi61ueqngkuq5i50cfqhxf9&amp;st=x8mjehkz&amp;dl=0 HW_9] (14.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&amp;st=xiiei8ji&amp;dl=0 Sem_9] || [https://www.dropbox.com/scl/fi/flsork2rii9ll5ufhkr6t/HW-9.pdf?rlkey=a7ia97ttf1obno46ii6k1k18r&amp;dl=0 HW_9] &lt;br&gt; [ Sem_9] &lt;br&gt; [Solutions 9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [https://www.dropbox.com/scl/fi/29gh3rsrcgcejwzihlu7p/Calculus_2_HW_9_g246.pdf?rlkey=hdvx4cwtbu32iut0t16jgf93d&amp;st=uzwnsg0f&amp;dl=0 HW_9] (14.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&amp;st=xiiei8ji&amp;dl=0 Sem_9] <br /> |- <br /> |-<br /> !| [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [https://www.dropbox.com/scl/fi/pp8oybrka3wqu7lv37rn4/HW-10.pdf?rlkey=3wu73g5ecworrdcbxgr0g8cb8&amp;dl=0 HW_10] &lt;br&gt; [ Sem_10] &lt;br&gt; [Solutions 10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] <br /> |-&lt;|<br /> !| [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] &lt;br&gt; [ Sem_11] &lt;br&gt; [Solutions 11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] <br /> |-<br /> !| [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] &lt;br&gt; [ Sem_12] &lt;br&gt; [Solutions 12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12]<br /> |-<br /> !| [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] &lt;br&gt; [ Sem_13] &lt;br&gt; [Solutions 13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=93570 Calculus 2 DSBA 2025/2026 2025-11-11T23:43:30Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 2 '''<br /> * [ '''Lecture 10'''] (07.11.2025) Multiple Riemann integrals: Part II.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/gnun2r1ys31ltw11cyluv/Calculus_2_Lecture_9.pdf?rlkey=m5dge8pgcn11bmvfzegy0ni1x&amp;st=l81a97dz&amp;dl=0 '''Lecture 9'''] (24.10.2025) Multiple Riemann integrals: Part I].<br /> <br /> * [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&amp;dl=0 '''Lecture 8'''] (17.10.2025) Analytic functions; differentiability classes; smooth functions; the Taylor series; the Taylor formula; criteria for analyticity; the Borel lemma; some pathological examples of smooth functions.<br /> <br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 '''Lecture 7'''] (10.10.2025) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/9z1kt1bgw7ujbrac78v5d/Calculus_2_HW_6_g241.pdf?rlkey=kn7jp6u81zaonv14tw7zjr92o&amp;st=4v21ojzt&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/mnl3dgqxb7g3psmutcezl/Calculus_2_HW_6_g246.pdf?rlkey=l2xv2p4pm1r4x9eypu7l95yxo&amp;st=a6ihzr71&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6]<br /> |- <br /> !| [https://www.dropbox.com/scl/fi/cp4ef052mrbf3vzkgn0se/Calculus_2_HW_7_g241.pdf?rlkey=98e9i80a4tpnkvmkg5y13a2x8&amp;st=8145hs2d&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] || [https://www.dropbox.com/scl/fi/ta6uj8dy428j41joltuj7/HW-7.pdf?rlkey=sxzuw64vujs154zzb49hpnz3v&amp;dl=0 HW_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/uxqxqvvffevfrxmndj7z5/Seminar-7-problems.pdf?rlkey=ni8vov4uc9jickfbccwdnkjwe&amp;dl=0 Sem_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/2qem0m9zawcy4fzxd34lu/Seminar-7-solutions.pdf?rlkey=g1s8xfyzezg8ktbms6hfq451c&amp;dl=0 Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [https://www.dropbox.com/scl/fi/g52laj6f2xbsdzoat2rl4/Calculus_2_HW_7_g246.pdf?rlkey=r1vvhd71fy0lljrl264o0f3nl&amp;st=8vjovzvq&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] <br /> |- <br /> !| [https://www.dropbox.com/scl/fi/1poymegtu4efr6v21ppvt/Calculus_2_HW_8_g241.pdf?rlkey=8wyfzeys8k1gwmdwn6bx0zbyf&amp;st=0i7iu2ke&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] || [https://www.dropbox.com/scl/fi/93xh32tzj5o0f2uogouyf/HW-8.pdf?rlkey=u58bjyb86tt0urri6o3m5b1ay&amp;dl=0 HW_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/fanjeiw51cxhjjg7kz6s4/Seminar-8-problems.pdf?rlkey=bcgs7t0po75erotiyvhzvp9rx&amp;dl=0 Sem_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/38f9xgyaohj1879gzbxfn/Seminar-8-solutions.pdf?rlkey=nnf1sjgstan4lzxnanh6vn5sa&amp;dl=0 Solutions 8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [https://www.dropbox.com/scl/fi/ozubrursz6zy4iwdyqta1/Calculus_2_HW_8_g246.pdf?rlkey=j2qhhaz8mv4i1wervl5uaznd2&amp;st=4ribpd8h&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] <br /> |- <br /> !| [https://www.dropbox.com/scl/fi/48k6ub6f2jytmf7wrktx6/Calculus_2_HW_9_g241.pdf?rlkey=s2xi61ueqngkuq5i50cfqhxf9&amp;st=x8mjehkz&amp;dl=0 HW_9] (14.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&amp;st=xiiei8ji&amp;dl=0 Sem_9] || [https://www.dropbox.com/scl/fi/flsork2rii9ll5ufhkr6t/HW-9.pdf?rlkey=a7ia97ttf1obno46ii6k1k18r&amp;dl=0 HW_9] &lt;br&gt; [ Sem_9] &lt;br&gt; [Solutions 9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [https://www.dropbox.com/scl/fi/29gh3rsrcgcejwzihlu7p/Calculus_2_HW_9_g246.pdf?rlkey=hdvx4cwtbu32iut0t16jgf93d&amp;st=uzwnsg0f&amp;dl=0 HW_9] (14.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&amp;st=xiiei8ji&amp;dl=0 Sem_9] <br /> |- <br /> |-<br /> !| [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [https://www.dropbox.com/scl/fi/pp8oybrka3wqu7lv37rn4/HW-10.pdf?rlkey=3wu73g5ecworrdcbxgr0g8cb8&amp;dl=0 HW_10] &lt;br&gt; [ Sem_10] &lt;br&gt; [Solutions 10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] <br /> |-<br /> !| [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] &lt;br&gt; [ Sem_11] &lt;br&gt; [Solutions 11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] <br /> |-<br /> !| [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] &lt;br&gt; [ Sem_12] &lt;br&gt; [Solutions 12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12]<br /> |-<br /> !| [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] &lt;br&gt; [ Sem_13] &lt;br&gt; [Solutions 13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=93513 Calculus 2 DSBA 2025/2026 2025-11-09T22:39:50Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 2 '''<br /> * [ '''Lecture 10'''] (07.11.2025) Multiple Riemann integrals: Part II.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/gnun2r1ys31ltw11cyluv/Calculus_2_Lecture_9.pdf?rlkey=m5dge8pgcn11bmvfzegy0ni1x&amp;st=l81a97dz&amp;dl=0 '''Lecture 9'''] (24.10.2025) Multiple Riemann integrals: Part I].<br /> <br /> * [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&amp;dl=0 '''Lecture 8'''] (17.10.2025) Analytic functions; differentiability classes; smooth functions; the Taylor series; the Taylor formula; criteria for analyticity; the Borel lemma; some pathological examples of smooth functions.<br /> <br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 '''Lecture 7'''] (10.10.2025) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/9z1kt1bgw7ujbrac78v5d/Calculus_2_HW_6_g241.pdf?rlkey=kn7jp6u81zaonv14tw7zjr92o&amp;st=4v21ojzt&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/mnl3dgqxb7g3psmutcezl/Calculus_2_HW_6_g246.pdf?rlkey=l2xv2p4pm1r4x9eypu7l95yxo&amp;st=a6ihzr71&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6]<br /> |- <br /> !| [https://www.dropbox.com/scl/fi/cp4ef052mrbf3vzkgn0se/Calculus_2_HW_7_g241.pdf?rlkey=98e9i80a4tpnkvmkg5y13a2x8&amp;st=8145hs2d&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] || [https://www.dropbox.com/scl/fi/ta6uj8dy428j41joltuj7/HW-7.pdf?rlkey=sxzuw64vujs154zzb49hpnz3v&amp;dl=0 HW_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/uxqxqvvffevfrxmndj7z5/Seminar-7-problems.pdf?rlkey=ni8vov4uc9jickfbccwdnkjwe&amp;dl=0 Sem_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/2qem0m9zawcy4fzxd34lu/Seminar-7-solutions.pdf?rlkey=g1s8xfyzezg8ktbms6hfq451c&amp;dl=0 Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [https://www.dropbox.com/scl/fi/g52laj6f2xbsdzoat2rl4/Calculus_2_HW_7_g246.pdf?rlkey=r1vvhd71fy0lljrl264o0f3nl&amp;st=8vjovzvq&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] <br /> |- <br /> !| [https://www.dropbox.com/scl/fi/1poymegtu4efr6v21ppvt/Calculus_2_HW_8_g241.pdf?rlkey=8wyfzeys8k1gwmdwn6bx0zbyf&amp;st=0i7iu2ke&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] || [https://www.dropbox.com/scl/fi/93xh32tzj5o0f2uogouyf/HW-8.pdf?rlkey=u58bjyb86tt0urri6o3m5b1ay&amp;dl=0 HW_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/fanjeiw51cxhjjg7kz6s4/Seminar-8-problems.pdf?rlkey=bcgs7t0po75erotiyvhzvp9rx&amp;dl=0 Sem_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/38f9xgyaohj1879gzbxfn/Seminar-8-solutions.pdf?rlkey=nnf1sjgstan4lzxnanh6vn5sa&amp;dl=0 Solutions 8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [https://www.dropbox.com/scl/fi/ozubrursz6zy4iwdyqta1/Calculus_2_HW_8_g246.pdf?rlkey=j2qhhaz8mv4i1wervl5uaznd2&amp;st=4ribpd8h&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] <br /> |- <br /> !| [https://www.dropbox.com/scl/fi/48k6ub6f2jytmf7wrktx6/Calculus_2_HW_9_g241.pdf?rlkey=s2xi61ueqngkuq5i50cfqhxf9&amp;st=x8mjehkz&amp;dl=0 HW_9] (14.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&amp;st=xiiei8ji&amp;dl=0 Sem_9] || [https://www.dropbox.com/scl/fi/flsork2rii9ll5ufhkr6t/HW-9.pdf?rlkey=a7ia97ttf1obno46ii6k1k18r&amp;dl=0 HW_9] &lt;br&gt; [ Sem_9] &lt;br&gt; [Solutions 9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [ HW_9] (??.??.25)&lt;br&gt; [ Sem_9] || [https://www.dropbox.com/scl/fi/29gh3rsrcgcejwzihlu7p/Calculus_2_HW_9_g246.pdf?rlkey=hdvx4cwtbu32iut0t16jgf93d&amp;st=uzwnsg0f&amp;dl=0 HW_9] (14.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&amp;st=xiiei8ji&amp;dl=0 Sem_9] <br /> |- <br /> |- &lt;!--<br /> !| [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] &lt;br&gt; [ Sem_10] &lt;br&gt; [Solutions 10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] || [ HW_10] (??.??.25)&lt;br&gt; [ Sem_10] <br /> |-<br /> !| [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] &lt;br&gt; [ Sem_11] &lt;br&gt; [Solutions 11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] || [ HW_11] (??.??.25)&lt;br&gt; [ Sem_11] <br /> |-<br /> !| [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] &lt;br&gt; [ Sem_12] &lt;br&gt; [Solutions 12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12] || [ HW_12] (??.??.25)&lt;br&gt; [ Sem_12]<br /> |-<br /> !| [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] &lt;br&gt; [ Sem_13] &lt;br&gt; [Solutions 13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] || [ HW_13] (??.??.25)&lt;br&gt; [ Sem_13] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=93353 Calculus 2 DSBA 2025/2026 2025-11-01T00:48:00Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/gnun2r1ys31ltw11cyluv/Calculus_2_Lecture_9.pdf?rlkey=m5dge8pgcn11bmvfzegy0ni1x&amp;st=l81a97dz&amp;dl=0 '''Lecture 9'''] (24.10.2025) Multiple Riemann integrals: Part I].<br /> <br /> * [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&amp;dl=0 '''Lecture 8'''] (17.10.2025) Analytic functions; differentiability classes; smooth functions; the Taylor series; the Taylor formula; criteria for analyticity; the Borel lemma; some pathological examples of smooth functions.<br /> <br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 '''Lecture 7'''] (10.10.2025) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/9z1kt1bgw7ujbrac78v5d/Calculus_2_HW_6_g241.pdf?rlkey=kn7jp6u81zaonv14tw7zjr92o&amp;st=4v21ojzt&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/mnl3dgqxb7g3psmutcezl/Calculus_2_HW_6_g246.pdf?rlkey=l2xv2p4pm1r4x9eypu7l95yxo&amp;st=a6ihzr71&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6]<br /> |- <br /> !| [https://www.dropbox.com/scl/fi/cp4ef052mrbf3vzkgn0se/Calculus_2_HW_7_g241.pdf?rlkey=98e9i80a4tpnkvmkg5y13a2x8&amp;st=8145hs2d&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] || [https://www.dropbox.com/scl/fi/ta6uj8dy428j41joltuj7/HW-7.pdf?rlkey=sxzuw64vujs154zzb49hpnz3v&amp;dl=0 HW_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/uxqxqvvffevfrxmndj7z5/Seminar-7-problems.pdf?rlkey=ni8vov4uc9jickfbccwdnkjwe&amp;dl=0 Sem_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/2qem0m9zawcy4fzxd34lu/Seminar-7-solutions.pdf?rlkey=g1s8xfyzezg8ktbms6hfq451c&amp;dl=0 Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [https://www.dropbox.com/scl/fi/g52laj6f2xbsdzoat2rl4/Calculus_2_HW_7_g246.pdf?rlkey=r1vvhd71fy0lljrl264o0f3nl&amp;st=8vjovzvq&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] <br /> |- <br /> !| [https://www.dropbox.com/scl/fi/1poymegtu4efr6v21ppvt/Calculus_2_HW_8_g241.pdf?rlkey=8wyfzeys8k1gwmdwn6bx0zbyf&amp;st=0i7iu2ke&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] || [https://www.dropbox.com/scl/fi/93xh32tzj5o0f2uogouyf/HW-8.pdf?rlkey=u58bjyb86tt0urri6o3m5b1ay&amp;dl=0 HW_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/fanjeiw51cxhjjg7kz6s4/Seminar-8-problems.pdf?rlkey=bcgs7t0po75erotiyvhzvp9rx&amp;dl=0 Sem_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/38f9xgyaohj1879gzbxfn/Seminar-8-solutions.pdf?rlkey=nnf1sjgstan4lzxnanh6vn5sa&amp;dl=0 Solutions 8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [https://www.dropbox.com/scl/fi/ozubrursz6zy4iwdyqta1/Calculus_2_HW_8_g246.pdf?rlkey=j2qhhaz8mv4i1wervl5uaznd2&amp;st=4ribpd8h&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=93319 Calculus 2 DSBA 2025/2026 2025-10-27T18:48:06Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/gnun2r1ys31ltw11cyluv/Calculus_2_Lecture_9.pdf?rlkey=m5dge8pgcn11bmvfzegy0ni1x&amp;st=l81a97dz&amp;dl=0 '''Lecture 9'''] (24.10.2025) Multiple Riemann integrals: Part I].<br /> <br /> * [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&amp;dl=0 '''Lecture 8'''] (17.10.2025) Analytic functions; differentiability classes; smooth functions; the Taylor series; the Taylor formula; criteria for analyticity; the Borel lemma; some pathological examples of smooth functions.<br /> <br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 '''Lecture 7'''] (10.10.2025) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/9z1kt1bgw7ujbrac78v5d/Calculus_2_HW_6_g241.pdf?rlkey=kn7jp6u81zaonv14tw7zjr92o&amp;st=4v21ojzt&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/mnl3dgqxb7g3psmutcezl/Calculus_2_HW_6_g246.pdf?rlkey=l2xv2p4pm1r4x9eypu7l95yxo&amp;st=a6ihzr71&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6]<br /> |- <br /> !| [https://www.dropbox.com/scl/fi/cp4ef052mrbf3vzkgn0se/Calculus_2_HW_7_g241.pdf?rlkey=98e9i80a4tpnkvmkg5y13a2x8&amp;st=8145hs2d&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] || [https://www.dropbox.com/scl/fi/ta6uj8dy428j41joltuj7/HW-7.pdf?rlkey=sxzuw64vujs154zzb49hpnz3v&amp;dl=0 HW_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/uxqxqvvffevfrxmndj7z5/Seminar-7-problems.pdf?rlkey=ni8vov4uc9jickfbccwdnkjwe&amp;dl=0 Sem_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/2qem0m9zawcy4fzxd34lu/Seminar-7-solutions.pdf?rlkey=g1s8xfyzezg8ktbms6hfq451c&amp;dl=0 Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [https://www.dropbox.com/scl/fi/g52laj6f2xbsdzoat2rl4/Calculus_2_HW_7_g246.pdf?rlkey=r1vvhd71fy0lljrl264o0f3nl&amp;st=8vjovzvq&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] <br /> |- <br /> !| [https://www.dropbox.com/scl/fi/gfidjjq99l8tbjye093i1/Calculus_2_HW_8_g241.pdf?rlkey=b34dla3o5lcwzngx4ycgm0eb8&amp;st=pm79z6vf&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] || [https://youtu.be/mgUGHRLN-34?si=Nc82xq5flRrUMDkj HW_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/fanjeiw51cxhjjg7kz6s4/Seminar-8-problems.pdf?rlkey=bcgs7t0po75erotiyvhzvp9rx&amp;dl=0 Sem_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/38f9xgyaohj1879gzbxfn/Seminar-8-solutions.pdf?rlkey=nnf1sjgstan4lzxnanh6vn5sa&amp;dl=0 Solutions 8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [https://www.dropbox.com/scl/fi/ozubrursz6zy4iwdyqta1/Calculus_2_HW_8_g246.pdf?rlkey=j2qhhaz8mv4i1wervl5uaznd2&amp;st=mpml0fzd&amp;dl=0 HW_8] (02.11.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Sem_8] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=93186 Calculus 2 DSBA 2025/2026 2025-10-20T01:54:49Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&amp;dl=0 '''Lecture 8'''] (17.10.2025) Analytic functions; differentiability classes; smooth functions; the Taylor series; the Taylor formula; criteria for analyticity; the Borel lemma; some pathological examples of smooth functions.<br /> <br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 '''Lecture 7'''] (10.10.2025) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/9z1kt1bgw7ujbrac78v5d/Calculus_2_HW_6_g241.pdf?rlkey=kn7jp6u81zaonv14tw7zjr92o&amp;st=4v21ojzt&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/mnl3dgqxb7g3psmutcezl/Calculus_2_HW_6_g246.pdf?rlkey=l2xv2p4pm1r4x9eypu7l95yxo&amp;st=a6ihzr71&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6]<br /> |- <br /> !| [https://www.dropbox.com/scl/fi/cp4ef052mrbf3vzkgn0se/Calculus_2_HW_7_g241.pdf?rlkey=98e9i80a4tpnkvmkg5y13a2x8&amp;st=8145hs2d&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] || [https://www.dropbox.com/scl/fi/ta6uj8dy428j41joltuj7/HW-7.pdf?rlkey=sxzuw64vujs154zzb49hpnz3v&amp;dl=0 HW_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/uxqxqvvffevfrxmndj7z5/Seminar-7-problems.pdf?rlkey=ni8vov4uc9jickfbccwdnkjwe&amp;dl=0 Sem_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/2qem0m9zawcy4fzxd34lu/Seminar-7-solutions.pdf?rlkey=g1s8xfyzezg8ktbms6hfq451c&amp;dl=0 Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [https://www.dropbox.com/scl/fi/g52laj6f2xbsdzoat2rl4/Calculus_2_HW_7_g246.pdf?rlkey=r1vvhd71fy0lljrl264o0f3nl&amp;st=8vjovzvq&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] <br /> |- <br /> !| [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/fanjeiw51cxhjjg7kz6s4/Seminar-8-problems.pdf?rlkey=bcgs7t0po75erotiyvhzvp9rx&amp;dl=0 Sem_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/38f9xgyaohj1879gzbxfn/Seminar-8-solutions.pdf?rlkey=nnf1sjgstan4lzxnanh6vn5sa&amp;dl=0 Solutions 8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=93185 Calculus 2 DSBA 2025/2026 2025-10-20T01:54:31Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&amp;dl=0 '''Lecture 8'''] (17.10.2025) Analytic functions; differentiability classes; smooth functions; the Taylor series; the Taylor formula; criteria for analyticity; the Borel lemma; some pathological examples of smooth functions.<br /> <br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 '''Lecture 7'''] (10.10.2025) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/9z1kt1bgw7ujbrac78v5d/Calculus_2_HW_6_g241.pdf?rlkey=kn7jp6u81zaonv14tw7zjr92o&amp;st=4v21ojzt&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/mnl3dgqxb7g3psmutcezl/Calculus_2_HW_6_g246.pdf?rlkey=l2xv2p4pm1r4x9eypu7l95yxo&amp;st=a6ihzr71&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6]<br /> |- <br /> !| [https://www.dropbox.com/scl/fi/cp4ef052mrbf3vzkgn0se/Calculus_2_HW_7_g241.pdf?rlkey=98e9i80a4tpnkvmkg5y13a2x8&amp;st=8145hs2d&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] || [https://www.dropbox.com/scl/fi/ta6uj8dy428j41joltuj7/HW-7.pdf?rlkey=sxzuw64vujs154zzb49hpnz3v&amp;dl=0 HW_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/uxqxqvvffevfrxmndj7z5/Seminar-7-problems.pdf?rlkey=ni8vov4uc9jickfbccwdnkjwe&amp;dl=0 Sem_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/2qem0m9zawcy4fzxd34lu/Seminar-7-solutions.pdf?rlkey=g1s8xfyzezg8ktbms6hfq451c&amp;dl=0 Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [https://www.dropbox.com/scl/fi/g52laj6f2xbsdzoat2rl4/Calculus_2_HW_7_g246.pdf?rlkey=r1vvhd71fy0lljrl264o0f3nl&amp;st=8vjovzvq&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] <br /> |- <br /> !| [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/fanjeiw51cxhjjg7kz6s4/Seminar-8-problems.pdf?rlkey=bcgs7t0po75erotiyvhzvp9rx&amp;dl=0 Sem_8] &lt;br&gt; [https://www.dropbox.com/scl/fi/38f9xgyaohj1879gzbxfn/Seminar-8-solutions.pdf?rlkey=nnf1sjgstan4lzxnanh6vn5sa&amp;dl=0 sol8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=93184 Calculus 2 DSBA 2025/2026 2025-10-20T01:53:23Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&amp;dl=0 '''Lecture 8'''] (17.10.2025) Analytic functions; differentiability classes; smooth functions; the Taylor series; the Taylor formula; criteria for analyticity; the Borel lemma; some pathological examples of smooth functions.<br /> <br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 '''Lecture 7'''] (10.10.2025) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/9z1kt1bgw7ujbrac78v5d/Calculus_2_HW_6_g241.pdf?rlkey=kn7jp6u81zaonv14tw7zjr92o&amp;st=4v21ojzt&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/mnl3dgqxb7g3psmutcezl/Calculus_2_HW_6_g246.pdf?rlkey=l2xv2p4pm1r4x9eypu7l95yxo&amp;st=a6ihzr71&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6]<br /> |- <br /> !| [https://www.dropbox.com/scl/fi/cp4ef052mrbf3vzkgn0se/Calculus_2_HW_7_g241.pdf?rlkey=98e9i80a4tpnkvmkg5y13a2x8&amp;st=8145hs2d&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] || [https://www.dropbox.com/scl/fi/ta6uj8dy428j41joltuj7/HW-7.pdf?rlkey=sxzuw64vujs154zzb49hpnz3v&amp;dl=0 HW_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/uxqxqvvffevfrxmndj7z5/Seminar-7-problems.pdf?rlkey=ni8vov4uc9jickfbccwdnkjwe&amp;dl=0 Sem_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/2qem0m9zawcy4fzxd34lu/Seminar-7-solutions.pdf?rlkey=g1s8xfyzezg8ktbms6hfq451c&amp;dl=0 Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [https://www.dropbox.com/scl/fi/g52laj6f2xbsdzoat2rl4/Calculus_2_HW_7_g246.pdf?rlkey=r1vvhd71fy0lljrl264o0f3nl&amp;st=8vjovzvq&amp;dl=0 HW_7] (24.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Sem_7] <br /> |- <br /> !| [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] &lt;br&gt; [ Sem_8] &lt;br&gt; [] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] || [ HW_8] (??.??.25)&lt;br&gt; [ Sem_8] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=93086 Calculus 2 DSBA 2025/2026 2025-10-14T23:03:43Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 '''Lecture 7'''] (10.10.2025) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/9z1kt1bgw7ujbrac78v5d/Calculus_2_HW_6_g241.pdf?rlkey=kn7jp6u81zaonv14tw7zjr92o&amp;st=4v21ojzt&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/mnl3dgqxb7g3psmutcezl/Calculus_2_HW_6_g246.pdf?rlkey=l2xv2p4pm1r4x9eypu7l95yxo&amp;st=a6ihzr71&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6]<br /> |- <br /> !| [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [https://www.dropbox.com/scl/fi/ta6uj8dy428j41joltuj7/HW-7.pdf?rlkey=sxzuw64vujs154zzb49hpnz3v&amp;dl=0 HW_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/uxqxqvvffevfrxmndj7z5/Seminar-7-problems.pdf?rlkey=ni8vov4uc9jickfbccwdnkjwe&amp;dl=0 Sem_7] &lt;br&gt; [https://www.dropbox.com/scl/fi/2qem0m9zawcy4fzxd34lu/Seminar-7-solutions.pdf?rlkey=g1s8xfyzezg8ktbms6hfq451c&amp;dl=0 Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=93085 Calculus 2 DSBA 2025/2026 2025-10-14T23:02:44Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 '''Lecture 7'''] (10.10.2025) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/9z1kt1bgw7ujbrac78v5d/Calculus_2_HW_6_g241.pdf?rlkey=kn7jp6u81zaonv14tw7zjr92o&amp;st=4v21ojzt&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/mnl3dgqxb7g3psmutcezl/Calculus_2_HW_6_g246.pdf?rlkey=l2xv2p4pm1r4x9eypu7l95yxo&amp;st=a6ihzr71&amp;dl=0 HW_6] (17.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Sem_6]<br /> |- <br /> !| [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] &lt;br&gt; [ Sem_7] &lt;br&gt; [ Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92902 Calculus 2 DSBA 2025/2026 2025-10-07T00:17:17Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/d4q1ifgj0e3z4fcoue97h/Seminar-6-problems.pdf?rlkey=ut5s2yiiipuevkuoacbpql9se&amp;dl=0 Sem_6] &lt;br&gt; [https://www.dropbox.com/scl/fi/isbs6x7py434gzli6zavi/Seminar-6-solutions.pdf?rlkey=mce89g6e3ir1qivljyvz23ypz&amp;dl=0 Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6]<br /> |-<br /> !| [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] &lt;br&gt; [ Sem_7] &lt;br&gt; [ Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92901 Calculus 2 DSBA 2025/2026 2025-10-07T00:16:36Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-<br /> !| [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [ Sem_6] &lt;br&gt; [ Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6]<br /> |-<br /> !| [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] &lt;br&gt; [ Sem_7] &lt;br&gt; [ Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92900 Calculus 2 DSBA 2025/2026 2025-10-07T00:16:16Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-&lt;!--<br /> !| [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6] || [https://www.dropbox.com/scl/fi/oekkue76yozxsgupfibo9/HW-6.pdf?rlkey=df0n7gq23lbispy4rio6y1w12&amp;dl=0 HW_6] &lt;br&gt; [ Sem_6] &lt;br&gt; [ Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6]<br /> |-<br /> !| [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] &lt;br&gt; [ Sem_7] &lt;br&gt; [ Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92899 Calculus 2 DSBA 2025/2026 2025-10-07T00:15:50Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-&lt;!--<br /> !| [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6] || [ HW_6] &lt;br&gt; [ Sem_6] &lt;br&gt; [ Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6]<br /> |-<br /> !| [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] &lt;br&gt; [ Sem_7] &lt;br&gt; [ Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92898 Calculus 2 DSBA 2025/2026 2025-10-07T00:14:37Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [ Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-&lt;!--<br /> !| [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6] || [ HW_6] &lt;br&gt; [ Sem_6] &lt;br&gt; [ Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6]<br /> |-<br /> !| [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] &lt;br&gt; [ Sem_7] &lt;br&gt; [ Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92820 Calculus 2 DSBA 2025/2026 2025-10-03T19:35:42Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 '''Lecture 6'''] (03.10.2025) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/8c62crc3lpalbytwifhr7/Calculus_2_HW_5_g241.pdf?rlkey=3f8tb54slzmkv8xsvf33o25zu&amp;st=ffkqn5jr&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5] || [https://www.dropbox.com/scl/fi/0nwc5y12rsmq48ywz5is5/HW-5.pdf?rlkey=qa54y8ibzw2ksbgh1rk4mlbdk&amp;dl=0 HW_5] &lt;br&gt; [ Sem_5] &lt;br&gt; [ Solutions_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [ HW_5] (??.??.25)&lt;br&gt; [ Sem_5] || [https://www.dropbox.com/scl/fi/q9w0m9dyib0wlln0dq6nl/Calculus_2_HW_5_g246.pdf?rlkey=peqmq9s14hsq38n61sljuatoa&amp;st=y24ecxqz&amp;dl=0 HW_5] (10.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Sem_5]<br /> |-&lt;!--<br /> !| [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6] || [ HW_6] &lt;br&gt; [ Sem_6] &lt;br&gt; [ Solutions_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (??.??.25)&lt;br&gt; [ Sem_6] || [ HW_6] (17.10.25)&lt;br&gt; [ Sem_6]<br /> |-<br /> !| [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] &lt;br&gt; [ Sem_7] &lt;br&gt; [ Solutions_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] || [ HW_7] (??.??.25)&lt;br&gt; [ Sem_7] <br /> |- --&gt;<br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92675 Calculus 2 DSBA 2025/2026 2025-09-29T09:59:12Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 '''Lecture 5'''] (26.09.2025) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&amp;st=2lzpqhv0&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)&lt;br&gt; [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&amp;st=12fav0if&amp;dl=0 HW_4] (03.10.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Sem_4] <br /> |-<br /> !| 241 || [https://www.dropbox.com/scl/fi/a20j18evr6unm87xznnpo/Seminar-5-problems.pdf?rlkey=sh5yif4e11nhuklgx3obwkt6u&amp;dl=0 Sem_5] &lt;br&gt; [https://www.dropbox.com/scl/fi/gbmd1qvgbycqzvpptyhgo/Seminar-5-solutions.pdf?rlkey=nzl3f1gpah50eob6p5yj0b06j&amp;dl=0 Solutions_5] || 243 || 244 || 245 || 246}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92551 Calculus 2 DSBA 2025/2026 2025-09-23T22:50:38Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [ HW_3] (??.09.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [ HW_4] (??.09.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&amp;dl=0 Solutions_4] || [ HW_4] (??.09.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.09.25)&lt;br&gt; [ Sem_4] <br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92550 Calculus 2 DSBA 2025/2026 2025-09-23T22:50:17Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [ HW_3] (??.09.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [ HW_4] (??.09.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&amp;dl=0 Sem_4] &lt;br&gt; [ Solutions_4] || [ HW_4] (??.09.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.09.25)&lt;br&gt; [ Sem_4] <br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92549 Calculus 2 DSBA 2025/2026 2025-09-23T22:48:53Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 '''Lecture 4'''] (19.09.2025) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&amp;st=5l6sh20e&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [ HW_3] (??.09.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&amp;st=xcx7z9s1&amp;dl=0 HW_3] (26.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=j7mfl7q8&amp;dl=0 Sem_3] <br /> |-<br /> !| [ HW_4] (??.09.25)&lt;br&gt; [ Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&amp;dl=0 HW_4] &lt;br&gt; [ Sem_4] &lt;br&gt; [ Solutions_4] || [ HW_4] (??.09.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.??.25)&lt;br&gt; [ Sem_4] || [ HW_4] (??.09.25)&lt;br&gt; [ Sem_4] <br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92388 Calculus 2 DSBA 2025/2026 2025-09-16T18:47:00Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |-<br /> !| [ HW_3] (26.09.25)&lt;br&gt; [ Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&amp;st=8q53sw20&amp;dl=0 HW_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&amp;st=hseqkny3&amp;dl=0 Sem_3] &lt;br&gt; [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&amp;st=57k8aqw2&amp;dl=0 Solutions_3] || [ HW_3] (??.09.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (??.??.25)&lt;br&gt; [ Sem_3] || [ HW_3] (26.09.25)&lt;br&gt; [ Sem_3] <br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=92284 Calculus 2 DSBA 2025/2026 2025-09-15T01:09:10Z <p>Vvbalakirev: /* Homework */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 '''Lecture 3'''] (12.09.2025) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> {| class=&quot;wikitable&quot;<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> !| 241 || 242 || 243 || 244 || 245 || 246 <br /> |-<br /> !| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0 HW_1] (08.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0 Sem_1] &lt;br&gt; [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)&lt;br&gt; [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [ HW_1] (??.??.25)&lt;br&gt; [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 HW_1] (12.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Sem_1]<br /> |-<br /> !| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&amp;st=oaovhs69&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 HW_2] (15.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 Sem_2] &lt;br&gt; [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)&lt;br&gt; [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [ HW_2] (??.??.25)&lt;br&gt; [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&amp;st=31jdcdgi&amp;dl=0 HW_2] (19.09.25)&lt;br&gt; [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Sem_2] <br /> |}<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91986 Calculus 2 DSBA 2025/2026 2025-09-08T20:30:50Z <p>Vvbalakirev: /* Teachers and Assistants */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || Fri, 13:00 -- 14:20, N504 || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 '''HW 1'''] (release: 05.09.25; deadline: 12.09.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1'''],* [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0'''Sem 1'''], * [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 '''Solutions 1 ''']<br /> * [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 '''HW 2'''],* [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 '''Sem 2'''], *[https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 '''Solutions 2 ''']<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> * [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link'''Sem 1'''],[https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link'''HW 1''']<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 '''HW 1'''] (release: 05.09.25; deadline: 12.09.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91920 Calculus 2 DSBA 2025/2026 2025-09-07T23:56:07Z <p>Vvbalakirev: /* The homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 '''HW 1'''] (release: 05.09.25; deadline: 12.09.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1'''],* [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0'''Sem 1'''], * [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 '''Solutions 1 ''']<br /> * [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 '''HW 2'''],* [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 '''Sem 2'''], *[https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 '''Solutions 2 ''']<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> * [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link'''Sem 1'''],[https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link'''HW 1''']<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 '''HW 1'''] (release: 05.09.25; deadline: 12.09.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91919 Calculus 2 DSBA 2025/2026 2025-09-07T23:55:51Z <p>Vvbalakirev: /* The homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 '''HW 1'''] (release: 05.09.25; deadline: 12.09.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1'''],* [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0'''Sem 1'''], * [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 '''Solutions''']<br /> * [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 '''HW 2'''],* [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 '''Sem 2'''], *[https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&amp;st=etzgo47s&amp;dl=0 '''Solutions''']<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> * [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link'''Sem 1'''],[https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link'''HW 1''']<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 '''HW 1'''] (release: 05.09.25; deadline: 12.09.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91886 Calculus 2 DSBA 2025/2026 2025-09-07T10:29:57Z <p>Vvbalakirev: /* The homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 '''HW 1'''] (release: 05.09.25; deadline: 12.09.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1'''],* [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0'''Sem 1'''], * [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 '''Solutions''']<br /> * [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 '''HW 2'''],* [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 '''Sem 2'''], *<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> * [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link'''Sem 1'''],[https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link'''HW 1''']<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 '''HW 1'''] (release: 05.09.25; deadline: 12.09.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91885 Calculus 2 DSBA 2025/2026 2025-09-07T10:28:57Z <p>Vvbalakirev: /* The homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 '''Lecture 2'''] (05.09.2025) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&amp;st=qbwvqjro&amp;dl=0 '''HW 1'''] (release: 05.09.25; deadline: 12.09.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1'''],* [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0'''Sem 1'''], * [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 '''Solutions''']<br /> * [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&amp;st=st4zzc8z&amp;dl=0 ''HW 2'''],* [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&amp;st=gyrthixn&amp;dl=0 '''Sem 2'''], *<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> * [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link'''Sem 1'''],[https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link'''HW 1''']<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&amp;st=8usez3w4&amp;dl=0 '''HW 1'''] (release: 05.09.25; deadline: 12.09.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91714 Calculus 2 DSBA 2025/2026 2025-09-04T00:32:21Z <p>Vvbalakirev: /* The homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 2 '''<br /> <br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1'''],* [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0'''Sem 1'''], * [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 '''Solutions''']<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> * [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link'''Sem 1'''],[https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link'''HW 1''']<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91713 Calculus 2 DSBA 2025/2026 2025-09-04T00:32:11Z <p>Vvbalakirev: /* The homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 2 '''<br /> <br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1'''],* https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&amp;st=41v7yceh&amp;dl=0'''Sem 1'''], * [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 '''Solutions''']<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> * [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link'''Sem 1'''],[https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link'''HW 1''']<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91712 Calculus 2 DSBA 2025/2026 2025-09-04T00:31:21Z <p>Vvbalakirev: /* The homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 2 '''<br /> <br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1'''],* [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=tnuukm3l&amp;dl=0'''Sem 1'''], * [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 '''Solutions''']<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> * [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link'''Sem 1'''],[https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link'''HW 1''']<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91711 Calculus 2 DSBA 2025/2026 2025-09-04T00:31:00Z <p>Vvbalakirev: /* The homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 2 '''<br /> <br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1'''], <br /> * [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=tnuukm3l&amp;dl=0'''Sem 1'''], * [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 '''Solutions''']<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> * [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link'''Sem 1'''],[https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link'''HW 1''']<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91710 Calculus 2 DSBA 2025/2026 2025-09-04T00:30:37Z <p>Vvbalakirev: /* The homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 2 '''<br /> <br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1'''], <br /> [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=tnuukm3l&amp;dl=0'''Sem 1'''], [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 '''Solutions''']<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> * [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link'''Sem 1'''],[https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link'''HW 1''']<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91651 Calculus 2 DSBA 2025/2026 2025-09-02T20:41:02Z <p>Vvbalakirev: /* The homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 2 '''<br /> <br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1'''], * [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&amp;st=4t8e717f&amp;dl=0 '''Sem 1''']<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> * [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link'''Sem 1'''],[https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link'''HW 1''']<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=Calculus_2_DSBA_2025/2026&diff=91620 Calculus 2 DSBA 2025/2026 2025-09-02T00:20:00Z <p>Vvbalakirev: /* The homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] &lt;br&gt; ([https://t.me/vvbalakirev tg]) || Жижин Андрей &lt;br&gt; ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || || ||<br /> |-<br /> || Assistant || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Зинкин Захар &lt;br&gt; ([https://t.me/Avgustine_iw tg])<br /> || Суворова Александра &lt;br&gt; ([https://t.me/lunciare tg])<br /> || Бизина Дарья &lt;br&gt; ([https://t.me/dashulkinnnn tg])<br /> || Биктибаев Аскар &lt;br&gt; ([https://t.me/askbkt tg])<br /> || Мамакина Екатерина &lt;br&gt; ([https://t.me/katemamakina tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test ('''O''');<br /> *one in-class written test (= midterm test) ('''W''');<br /> *several quizzes ('''Q''', where '''Q''' is the average grade of all the quizzes in the course);<br /> *several homework assignments ('''H''', where '''H''' is the average grade of all the homework assignments in the course);<br /> *one written exam ('''E''').<br /> <br /> All grades (namely, '''O''', '''W''', '''Q''', '''H''', and '''E''') are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;''', '''C''', is obtained '''without rounding''' by the following formula:<br /> <br /> '''C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.'''<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', '''F''', is obtained by the following formula:<br /> <br /> '''F = Round(7/10*C + 3/10*E).'''<br /> <br /> where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> ''' &lt;span style=&quot;color:#DC143C&quot;&gt;If you notice an error or do not understand something, please describe it in the [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;'''<br /> <br /> ''' Module 2 '''<br /> <br /> <br /> ''' Module 1 '''<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 '''Lecture 1'''] (01.09.2025) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 241: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 242: ===<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&amp;st=mg9lbf8w&amp;dl=0'''HW 1''']<br /> <br /> === The homework for group 243: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 244: ===<br /> <br /> '''Module 1'''<br /> <br /> === The homework for group 245: ===<br /> <br /> '''Module 1'''<br /> === The homework for group 246: ===<br /> <br /> '''Module 1'''<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=90856 LAaG DSBA 2024/2025 2025-05-13T19:35:38Z <p>Vvbalakirev: /* Homework for group 243: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 4 '''<br /> * [https://www.dropbox.com/s/km7z6bed527pfgm/LAaG_Lecture_30.pdf?dl=0 '''Lecture 29'''] (12.05.2025) Orthogonality in Euclidian spaces; orthogonal and orthonormal sets and bases; Gram-Schmidt process; the orthogonal complement and its main properties; the projection and the rejection of a vector.<br /> <br /> * [https://www.dropbox.com/s/6wn3z42bzvrg5or/LAaG_Lecture_29.pdf?dl=0 '''Lecture 28'''] (28.04.2025) Euclidean spaces; scalar product; the norm of a vector; Cauchy–Schwarz inequality; the angle between two vectors; the Gram matrix and its main properties.<br /> <br /> * [https://www.dropbox.com/s/gkxple1prqauxoa/LAaG_Lecture_28.pdf?dl=0 '''Lecture 27'''] (21.04.2025) Quadratic forms (Part III); The Jacobi theorem; normal bases and the normal form of a quadratic form; the positive and negative indices of inertia, the signature of a quadratic form; the Sylvester law of inertia; positive (semi)-definite and negative (semi)-definite quadratic forms; the Sylvester criterion.<br /> <br /> * [https://www.dropbox.com/s/wpo6qnbxviol7u6/LAaG_Lecture_26.pdf?dl=0 '''Lecture 26'''] (14.04.2025) Quadratic forms; associated bilinear form; coordinate matrix of a quadratic form; canonical basis and canonical form of a quadratic form.<br /> <br /> * [https://www.dropbox.com/s/cfb54jzd2qdn0ze/LAaG_Lecture_25.pdf?dl=0 '''Lecture 25'''] (07.04.2025) Bilinear Forms; a coordinate matrix of a bilinear form; change-of-basis formula for bilinear forms; symmetric and skew-summetric bilinear forms. Quadratic forms; the associated bilinear form of a quadratic form.<br /> <br /> ''' Module 3 '''<br /> * [https://www.dropbox.com/s/3at8g01dkxwjn7y/LAaG_Lecture_24.pdf?dl=0 '''Lecture 24'''] (17.03.2025) Linear operators (Part IV); Jordan matrix; Jordan normal form; Jordan basis; Jordan basis theorem (without proof); Cayley-Hamilton theorem. Linear Functionals; dual space; dual basis; isomorphism between V and V*.<br /> <br /> * [https://www.dropbox.com/s/bh2gbw88rixc8e7/LAaG_Lecture_23.pdf?dl=0 '''Lecture 23'''] (10.03.2025) Linear operators (Part III); diagonalizability of a linear operator; inequality between algebraic and geometric multiplicities; criteria of diagonalizability.<br /> <br /> * [https://www.dropbox.com/s/76ydfixppp12cik/LAaG_Lecture_22.pdf?dl=0 '''Lecture 22'''] (03.03.2025) Linear operators (Part II); vector space of linear operators; the characteristic polynomial of a linear operator; algebraic and geometric multiplicity of an eigenvalue.<br /> <br /> * [https://www.dropbox.com/s/e9w3h8vqa5slwjz/LAaG_Lecture_21.pdf?dl=0 '''Lecture 21'''] (24.02.2025) Linear operators; the rank, the determinant, and the trace of a linear operator; invariant subspaces; eigenvectors and eigenvalues of a linear operator.<br /> <br /> * [https://www.dropbox.com/s/kzatlshdq6gj5zk/LAaG_Lecture_20.pdf?dl=0 '''Lecture 20'''] (17.02.2025) Linear Transformations (Part III: injectivity and surjectivity of linear transformations) injective and surjective linear transformations; isomorphisms (=linear bijections) of vector spaces; the inverse of an isomorphism; the fact that two finite dimensional vector spaces are isomorphic if and only if they both have the same dimension.<br /> <br /> * [https://www.dropbox.com/s/vczbkb79w67r4tk/LAaG_Lecture_19.pdf?dl=0 '''Lecture 19'''] (10.02.2025) Linear Transformations (Part II: matrix representation and change of basis); coordinate matrices of a linear transformation; coordinate matrix of a composition of linear transformations; change of basis.<br /> <br /> * [https://www.dropbox.com/s/is0p1nou922zynj/LAaG_Lecture_18.pdf?dl=0 '''Lecture 18'''] (03.02.2025) Linear Transformations; main properties of linear transformations; the image and the kernel of a linear transformation; singular and non-singular linear transformations; the rank and the nullity of a linear transformation.<br /> <br /> * [https://www.dropbox.com/s/td8df813s2lh38b/LAaG_Lecture_17.pdf?dl=0 '''Lecture 17'''] (27.01.2025) The rank of a matrix (Part II); we prove that the column rank equals the row rank.<br /> <br /> * [https://www.dropbox.com/s/nf44zccqg3rythp/LAaG_Lecture_16.pdf?dl=0 '''Lecture 16'''] (20.01.2025) The direct sum of subspaces; main properties of the direct sum; the rank of a matrix; column and row spaces of a matrix; column and row ranks of a matrix.<br /> <br /> * [https://www.dropbox.com/s/cl7djenawtlgp0o/LAaG_Lecture_15.pdf?dl=0 '''Lecture 15'''] (13.01.2025) Main properties of change of basis matrices; the sum, the intersection, and the direct sum of vector subspaces; the dimension of the sum of two vector subspaces.<br /> <br /> ''' Module 2 '''<br /> * [https://www.dropbox.com/s/pozm47tzgaibf4k/LAaG_Lecture_14.pdf?dl=0 '''Lecture 14'''] (16.12.2024) Vector spaces (Part III); m-element subsets of an n-dimensional vector space; extension to a basis; the dimension of a subspace of a finite dimensional vector space; ordered basis; basis matrix; change of basis matrix.<br /> <br /> * [https://www.dropbox.com/s/10v3w4efz6zi332/LAaG_Lecture_13.pdf?dl=0 '''Lecture 13'''] (09.12.2024) Vector spaces (Part II); Main theorem on linear dependence; a basis of a vector space; dimension of a vector space; finite and infinite dimensional vector spaces; some main properties of finite dimensional vector spaces.<br /> <br /> * [https://www.dropbox.com/s/snko9y9r7ccw8qk/LAaG_Lecture_12.pdf?dl=0 '''Lecture 12'''] (01.12.2024) Vector spaces (Part I); a subspace of a vector space; linear combinations; the linear span; trivial and non-trivial linear combinations; linearly dependent and linearly independent sets.<br /> <br /> * [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (25.11.2024) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br /> <br /> * [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (18.11.2024) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br /> <br /> * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (11.11.2024) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br /> <br /> * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (02.11.2024) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/iw4d8eyjayzff9kfcj33r/LAaG_HW_29_C-241.pdf?rlkey=r7mvkq3f3tipvcphvmbcs7wy9&amp;st=ftkay74b&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ew31593pflcym5wtj0een/LAaG_HW_28_C-241.pdf?rlkey=66wd02998pic8x3t24061cdbh&amp;st=q296xsgc&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sc0udwvted1nn1quz4zou/LAaG_HW_27_C-241.pdf?rlkey=s47ayfwajc9lqod48xt5tx4wa&amp;st=qd7b4y7z&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/myc8320hx3njihu24cuba/LAaG_HW_26_C-241.pdf?rlkey=23sq1u6qrb9xevdrzaoutqxca&amp;st=1jmhwafo&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/cva01p9hh7qdtagzl3kn3/LAaG_HW_25_C-241.pdf?rlkey=yal3zb4maa7zwdvqxcecssjkg&amp;st=sg8pbd9k&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/7lpp0i0xjelgq0gp35e4n/LAaG_HW_24_C-241.pdf?rlkey=a582n8pburjgu2j8510gzn83r&amp;st=2q6voag2&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/4a54pbfd61aoprnxwzu0x/LAaG_HW_23_C-241.pdf?rlkey=fe69qd7iarodjou59nsfrr6sh&amp;st=pg55d94h&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/0bwlj7nva3781wif2lht4/LAaG_HW_22_C-241.pdf?rlkey=zvnp3kg68lfgl1psi4oey1duy&amp;st=erjtper3&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/r2d0fnyhorbud4w97cw8p/LAaG_HW_21_C-241.pdf?rlkey=jge0vzkbwpun9stgsnqk1xa15&amp;st=bdihujff&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tej4f5c5io1742pc958k6/LAaG_HW_20_C-241.pdf?rlkey=j1c0yag295f53gydl5rsc2o10&amp;st=fetq10zo&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/o2624ddh1r58a3ek8v723/LAaG_HW_19_C-241.pdf?rlkey=5ztkckb96zjcydhnk7x88en29&amp;st=bg5891g6&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zpc9ji9p84zvz5mi9vws9/LAaG_HW_18_C-241.pdf?rlkey=cfv4sqgw7kvcu4wbcata3fab3&amp;st=e2c6jr7e&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vthiyr2dpqrgggx8rwc5n/LAaG_HW_17_C-241.pdf?rlkey=rfchkhjrs96c4as6z0f68005h&amp;st=agspv924&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jk1qemu09cq5pzt2mpu58/LAaG_HW_16_C-241.pdf?rlkey=565cdf9qndljixsg2hm9pgs85&amp;st=u4i6x9g4&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/e0l37mfgqhgzhc35xvv85/LAaG_HW_15_C-241.pdf?rlkey=td1du8a0w5goaf0kk1e1doh02&amp;st=dmouas60&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gfanxb92qos5yrw2rw9up/LAaG_HW_13_C-241.pdf?rlkey=3lieu7597p86akdubpgblrxv1&amp;st=tzrb0x2w&amp;dl=0 '''HW 13'''] (release: 09.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/98g4oshs0lkwzfkq7ws2o/LAaG_HW_12_C-241.pdf?rlkey=ir2gfbgas5zecrt3de03anocx&amp;st=huaalfyu&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bkwvo24thkydotpkqjv7s/LAaG_HW_11_C-241.pdf?rlkey=vw1rwyesz3cfvizb88ukwbk5c&amp;st=6lzvxcfd&amp;dl=0 '''HW 11'''] (release: 25.11.24; deadline: 02.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tz95u31aralzb00htmpfr/LAaG_HW_10_C-241.pdf?rlkey=kvbdd60wu3jaj908hve2amrb7&amp;st=kiam0tz0&amp;dl=0 '''HW 10'''] (release: 18.11.24; deadline: 25.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9icdl8t78tqqaszgnh1ex/LAaG_HW_9_C-241.pdf?rlkey=obf47jl5bm91hmrlinhymmu5a&amp;st=8pldj7gq&amp;dl=0 '''HW 9'''] (release: 11.11.24; deadline: 18.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/cuah8c9c3lm3qjxw16paw/LAaG_HW_8_C-241.pdf?rlkey=iaedxga7hdn89904yo3rirtrs&amp;st=6lvpxxgl&amp;dl=0 '''HW 8'''] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/619rsffz78buraprvzlfo/LAaG_Seminar_8.pdf?rlkey=98o6gc0rjl4h6r9djdrasfwu8&amp;st=8zetjdlw&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 243: ===<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/74v0d0eiofll1maa9jznn/LAaG_HW_29_C-246.pdf?rlkey=tkc9a738pz8ucsmoj1qa098to&amp;st=qjp6gids&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/dhn85atazelewt7hga4wm/LAaG_HW_28_C-246.pdf?rlkey=uuzzqtp8e19fwc9ed4cqity13&amp;st=cf0kk85z&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oipf5pzr862yxj8hzws0q/LAaG_HW_27_C-246.pdf?rlkey=8zm2hmvtcxaxl7gup9fhlskv4&amp;st=r2p4k1ki&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/f0ecohy3h75i4tteco78g/LAaG_HW_26_C-246.pdf?rlkey=4d2hnuddvguzw9brt08t7jfpv&amp;st=z8e70o5z&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lwvmio1folirvyij2c5te/LAaG_HW_25_C-246.pdf?rlkey=zg38wdf05opaxmuq6zfkuhsgk&amp;st=wd20mn6i&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/ais924pz2nlej2c2xggik/LAaG_HW_24_C-246.pdf?rlkey=cr3yzxr1sewhfckkas418wwlu&amp;st=cj12kvrx&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/jexjsl0jrgaui9o4nf9jl/LAaG_HW_23_C-246.pdf?rlkey=6v42cmsbukuljstxc1rw5nj2s&amp;st=3yw1rrh6&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6tnjv2kxwum90bwwklak5/LAaG_HW_22_C-246.pdf?rlkey=ml6hgg2cqnafwvhpuoe15vqsw&amp;st=xrgch4zx&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sadhn3ahnqtik4awr2tj4/LAaG_HW_21_C-246.pdf?rlkey=hs3dyl8ig4s6ygwvxyqtzgrez&amp;st=ndz29dpb&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/qurd5huy43ihn1z6a4u5g/LAaG_HW_20_C-246.pdf?rlkey=4js3uvv10nvnwxfijskwo1beg&amp;st=z6izkugw&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lit3st83vxamv4yoeux14/LAaG_HW_19_C-246.pdf?rlkey=md0jtmyyol74p3grsobpdn398&amp;st=khkc0ona&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zj4cmy6yvtb0voer5nxsz/LAaG_HW_18_C-246.pdf?rlkey=m9sfdgy428uwooyto3jc0v2n2&amp;st=3cqiogo3&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3f4p41sixiwspbws1zuyp/LAaG_HW_17_C-246.pdf?rlkey=mc9tkb24whvre9rjaa2yy4yy5&amp;st=3uly6rcr&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wwkr4nrvemckinbvlfpf4/LAaG_HW_16_C-246.pdf?rlkey=d36aqvm4sl5ymrhc9689skqmh&amp;st=ytwxjuiy&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vvxf2ix4aohlrme23iio3/LAaG_HW_15_C-246.pdf?rlkey=pz848a5pnq4x1o7192t9e3ja8&amp;st=bzl0fx87&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v60x5jr3qtp5nu1ddsywa/LAaG_HW_13_C-246.pdf?rlkey=b9zsc00sn81zfi4zlorrp1dqu&amp;st=3y4vawm7&amp;dl=0 '''HW 13'''] (release: 10.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/oqw6b4jgz5a133g1cssmw/LAaG_HW_12_C-246.pdf?rlkey=5w5gqusl520nxxzumh761y4jb&amp;st=xii5fvfc&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/z80z8a3xan9vxu4abcqah/LAaG_HW_11_C-246.pdf?rlkey=fe836n2dzg580je9n8rr2wf8e&amp;st=vts0p3p2&amp;dl=0 '''HW 11'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/klzrlfot6t4v6rfbfd02q/LAaG_HW_10_C-246.pdf?rlkey=su9akh09k4mnz4unedoqlhc90&amp;st=2ab1uvrj&amp;dl=0 '''HW 10'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6xjvw47ehtwt2ku62y9h8/LAaG_HW_9_C-246.pdf?rlkey=fjp37n3b0f3kgqivb9mtfy9tz&amp;st=6oj9hjsk&amp;dl=0 '''HW 9'''] (release: 12.11.24; deadline: 19.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/vpmwnqengjj2g9nn6zf9p/LAaG_HW_8_C-246.pdf?rlkey=7qlhr2wtmtm9lkbwf6i9coipg&amp;st=wumfffop&amp;dl=0 '''HW 8'''] (release: 07.11.24; deadline: 17.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/fupbesmknyp4bgm9sygca/LAaG_Sem_8_07_11_24_g246.pdf?rlkey=telxxvgpcx3tj70flyjye7aoc&amp;st=5dnddh72&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=90855 LAaG DSBA 2024/2025 2025-05-13T19:34:57Z <p>Vvbalakirev: /* Homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 4 '''<br /> * [https://www.dropbox.com/s/km7z6bed527pfgm/LAaG_Lecture_30.pdf?dl=0 '''Lecture 29'''] (12.05.2025) Orthogonality in Euclidian spaces; orthogonal and orthonormal sets and bases; Gram-Schmidt process; the orthogonal complement and its main properties; the projection and the rejection of a vector.<br /> <br /> * [https://www.dropbox.com/s/6wn3z42bzvrg5or/LAaG_Lecture_29.pdf?dl=0 '''Lecture 28'''] (28.04.2025) Euclidean spaces; scalar product; the norm of a vector; Cauchy–Schwarz inequality; the angle between two vectors; the Gram matrix and its main properties.<br /> <br /> * [https://www.dropbox.com/s/gkxple1prqauxoa/LAaG_Lecture_28.pdf?dl=0 '''Lecture 27'''] (21.04.2025) Quadratic forms (Part III); The Jacobi theorem; normal bases and the normal form of a quadratic form; the positive and negative indices of inertia, the signature of a quadratic form; the Sylvester law of inertia; positive (semi)-definite and negative (semi)-definite quadratic forms; the Sylvester criterion.<br /> <br /> * [https://www.dropbox.com/s/wpo6qnbxviol7u6/LAaG_Lecture_26.pdf?dl=0 '''Lecture 26'''] (14.04.2025) Quadratic forms; associated bilinear form; coordinate matrix of a quadratic form; canonical basis and canonical form of a quadratic form.<br /> <br /> * [https://www.dropbox.com/s/cfb54jzd2qdn0ze/LAaG_Lecture_25.pdf?dl=0 '''Lecture 25'''] (07.04.2025) Bilinear Forms; a coordinate matrix of a bilinear form; change-of-basis formula for bilinear forms; symmetric and skew-summetric bilinear forms. Quadratic forms; the associated bilinear form of a quadratic form.<br /> <br /> ''' Module 3 '''<br /> * [https://www.dropbox.com/s/3at8g01dkxwjn7y/LAaG_Lecture_24.pdf?dl=0 '''Lecture 24'''] (17.03.2025) Linear operators (Part IV); Jordan matrix; Jordan normal form; Jordan basis; Jordan basis theorem (without proof); Cayley-Hamilton theorem. Linear Functionals; dual space; dual basis; isomorphism between V and V*.<br /> <br /> * [https://www.dropbox.com/s/bh2gbw88rixc8e7/LAaG_Lecture_23.pdf?dl=0 '''Lecture 23'''] (10.03.2025) Linear operators (Part III); diagonalizability of a linear operator; inequality between algebraic and geometric multiplicities; criteria of diagonalizability.<br /> <br /> * [https://www.dropbox.com/s/76ydfixppp12cik/LAaG_Lecture_22.pdf?dl=0 '''Lecture 22'''] (03.03.2025) Linear operators (Part II); vector space of linear operators; the characteristic polynomial of a linear operator; algebraic and geometric multiplicity of an eigenvalue.<br /> <br /> * [https://www.dropbox.com/s/e9w3h8vqa5slwjz/LAaG_Lecture_21.pdf?dl=0 '''Lecture 21'''] (24.02.2025) Linear operators; the rank, the determinant, and the trace of a linear operator; invariant subspaces; eigenvectors and eigenvalues of a linear operator.<br /> <br /> * [https://www.dropbox.com/s/kzatlshdq6gj5zk/LAaG_Lecture_20.pdf?dl=0 '''Lecture 20'''] (17.02.2025) Linear Transformations (Part III: injectivity and surjectivity of linear transformations) injective and surjective linear transformations; isomorphisms (=linear bijections) of vector spaces; the inverse of an isomorphism; the fact that two finite dimensional vector spaces are isomorphic if and only if they both have the same dimension.<br /> <br /> * [https://www.dropbox.com/s/vczbkb79w67r4tk/LAaG_Lecture_19.pdf?dl=0 '''Lecture 19'''] (10.02.2025) Linear Transformations (Part II: matrix representation and change of basis); coordinate matrices of a linear transformation; coordinate matrix of a composition of linear transformations; change of basis.<br /> <br /> * [https://www.dropbox.com/s/is0p1nou922zynj/LAaG_Lecture_18.pdf?dl=0 '''Lecture 18'''] (03.02.2025) Linear Transformations; main properties of linear transformations; the image and the kernel of a linear transformation; singular and non-singular linear transformations; the rank and the nullity of a linear transformation.<br /> <br /> * [https://www.dropbox.com/s/td8df813s2lh38b/LAaG_Lecture_17.pdf?dl=0 '''Lecture 17'''] (27.01.2025) The rank of a matrix (Part II); we prove that the column rank equals the row rank.<br /> <br /> * [https://www.dropbox.com/s/nf44zccqg3rythp/LAaG_Lecture_16.pdf?dl=0 '''Lecture 16'''] (20.01.2025) The direct sum of subspaces; main properties of the direct sum; the rank of a matrix; column and row spaces of a matrix; column and row ranks of a matrix.<br /> <br /> * [https://www.dropbox.com/s/cl7djenawtlgp0o/LAaG_Lecture_15.pdf?dl=0 '''Lecture 15'''] (13.01.2025) Main properties of change of basis matrices; the sum, the intersection, and the direct sum of vector subspaces; the dimension of the sum of two vector subspaces.<br /> <br /> ''' Module 2 '''<br /> * [https://www.dropbox.com/s/pozm47tzgaibf4k/LAaG_Lecture_14.pdf?dl=0 '''Lecture 14'''] (16.12.2024) Vector spaces (Part III); m-element subsets of an n-dimensional vector space; extension to a basis; the dimension of a subspace of a finite dimensional vector space; ordered basis; basis matrix; change of basis matrix.<br /> <br /> * [https://www.dropbox.com/s/10v3w4efz6zi332/LAaG_Lecture_13.pdf?dl=0 '''Lecture 13'''] (09.12.2024) Vector spaces (Part II); Main theorem on linear dependence; a basis of a vector space; dimension of a vector space; finite and infinite dimensional vector spaces; some main properties of finite dimensional vector spaces.<br /> <br /> * [https://www.dropbox.com/s/snko9y9r7ccw8qk/LAaG_Lecture_12.pdf?dl=0 '''Lecture 12'''] (01.12.2024) Vector spaces (Part I); a subspace of a vector space; linear combinations; the linear span; trivial and non-trivial linear combinations; linearly dependent and linearly independent sets.<br /> <br /> * [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (25.11.2024) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br /> <br /> * [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (18.11.2024) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br /> <br /> * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (11.11.2024) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br /> <br /> * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (02.11.2024) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/iw4d8eyjayzff9kfcj33r/LAaG_HW_29_C-241.pdf?rlkey=r7mvkq3f3tipvcphvmbcs7wy9&amp;st=ftkay74b&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ew31593pflcym5wtj0een/LAaG_HW_28_C-241.pdf?rlkey=66wd02998pic8x3t24061cdbh&amp;st=q296xsgc&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sc0udwvted1nn1quz4zou/LAaG_HW_27_C-241.pdf?rlkey=s47ayfwajc9lqod48xt5tx4wa&amp;st=qd7b4y7z&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/myc8320hx3njihu24cuba/LAaG_HW_26_C-241.pdf?rlkey=23sq1u6qrb9xevdrzaoutqxca&amp;st=1jmhwafo&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/cva01p9hh7qdtagzl3kn3/LAaG_HW_25_C-241.pdf?rlkey=yal3zb4maa7zwdvqxcecssjkg&amp;st=sg8pbd9k&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/7lpp0i0xjelgq0gp35e4n/LAaG_HW_24_C-241.pdf?rlkey=a582n8pburjgu2j8510gzn83r&amp;st=2q6voag2&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/4a54pbfd61aoprnxwzu0x/LAaG_HW_23_C-241.pdf?rlkey=fe69qd7iarodjou59nsfrr6sh&amp;st=pg55d94h&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/0bwlj7nva3781wif2lht4/LAaG_HW_22_C-241.pdf?rlkey=zvnp3kg68lfgl1psi4oey1duy&amp;st=erjtper3&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/r2d0fnyhorbud4w97cw8p/LAaG_HW_21_C-241.pdf?rlkey=jge0vzkbwpun9stgsnqk1xa15&amp;st=bdihujff&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tej4f5c5io1742pc958k6/LAaG_HW_20_C-241.pdf?rlkey=j1c0yag295f53gydl5rsc2o10&amp;st=fetq10zo&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/o2624ddh1r58a3ek8v723/LAaG_HW_19_C-241.pdf?rlkey=5ztkckb96zjcydhnk7x88en29&amp;st=bg5891g6&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zpc9ji9p84zvz5mi9vws9/LAaG_HW_18_C-241.pdf?rlkey=cfv4sqgw7kvcu4wbcata3fab3&amp;st=e2c6jr7e&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vthiyr2dpqrgggx8rwc5n/LAaG_HW_17_C-241.pdf?rlkey=rfchkhjrs96c4as6z0f68005h&amp;st=agspv924&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jk1qemu09cq5pzt2mpu58/LAaG_HW_16_C-241.pdf?rlkey=565cdf9qndljixsg2hm9pgs85&amp;st=u4i6x9g4&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/e0l37mfgqhgzhc35xvv85/LAaG_HW_15_C-241.pdf?rlkey=td1du8a0w5goaf0kk1e1doh02&amp;st=dmouas60&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gfanxb92qos5yrw2rw9up/LAaG_HW_13_C-241.pdf?rlkey=3lieu7597p86akdubpgblrxv1&amp;st=tzrb0x2w&amp;dl=0 '''HW 13'''] (release: 09.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/98g4oshs0lkwzfkq7ws2o/LAaG_HW_12_C-241.pdf?rlkey=ir2gfbgas5zecrt3de03anocx&amp;st=huaalfyu&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bkwvo24thkydotpkqjv7s/LAaG_HW_11_C-241.pdf?rlkey=vw1rwyesz3cfvizb88ukwbk5c&amp;st=6lzvxcfd&amp;dl=0 '''HW 11'''] (release: 25.11.24; deadline: 02.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tz95u31aralzb00htmpfr/LAaG_HW_10_C-241.pdf?rlkey=kvbdd60wu3jaj908hve2amrb7&amp;st=kiam0tz0&amp;dl=0 '''HW 10'''] (release: 18.11.24; deadline: 25.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9icdl8t78tqqaszgnh1ex/LAaG_HW_9_C-241.pdf?rlkey=obf47jl5bm91hmrlinhymmu5a&amp;st=8pldj7gq&amp;dl=0 '''HW 9'''] (release: 11.11.24; deadline: 18.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/cuah8c9c3lm3qjxw16paw/LAaG_HW_8_C-241.pdf?rlkey=iaedxga7hdn89904yo3rirtrs&amp;st=6lvpxxgl&amp;dl=0 '''HW 8'''] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/619rsffz78buraprvzlfo/LAaG_Seminar_8.pdf?rlkey=98o6gc0rjl4h6r9djdrasfwu8&amp;st=8zetjdlw&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/74v0d0eiofll1maa9jznn/LAaG_HW_29_C-246.pdf?rlkey=tkc9a738pz8ucsmoj1qa098to&amp;st=qjp6gids&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/dhn85atazelewt7hga4wm/LAaG_HW_28_C-246.pdf?rlkey=uuzzqtp8e19fwc9ed4cqity13&amp;st=cf0kk85z&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oipf5pzr862yxj8hzws0q/LAaG_HW_27_C-246.pdf?rlkey=8zm2hmvtcxaxl7gup9fhlskv4&amp;st=r2p4k1ki&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/f0ecohy3h75i4tteco78g/LAaG_HW_26_C-246.pdf?rlkey=4d2hnuddvguzw9brt08t7jfpv&amp;st=z8e70o5z&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lwvmio1folirvyij2c5te/LAaG_HW_25_C-246.pdf?rlkey=zg38wdf05opaxmuq6zfkuhsgk&amp;st=wd20mn6i&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/ais924pz2nlej2c2xggik/LAaG_HW_24_C-246.pdf?rlkey=cr3yzxr1sewhfckkas418wwlu&amp;st=cj12kvrx&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/jexjsl0jrgaui9o4nf9jl/LAaG_HW_23_C-246.pdf?rlkey=6v42cmsbukuljstxc1rw5nj2s&amp;st=3yw1rrh6&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6tnjv2kxwum90bwwklak5/LAaG_HW_22_C-246.pdf?rlkey=ml6hgg2cqnafwvhpuoe15vqsw&amp;st=xrgch4zx&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sadhn3ahnqtik4awr2tj4/LAaG_HW_21_C-246.pdf?rlkey=hs3dyl8ig4s6ygwvxyqtzgrez&amp;st=ndz29dpb&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/qurd5huy43ihn1z6a4u5g/LAaG_HW_20_C-246.pdf?rlkey=4js3uvv10nvnwxfijskwo1beg&amp;st=z6izkugw&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lit3st83vxamv4yoeux14/LAaG_HW_19_C-246.pdf?rlkey=md0jtmyyol74p3grsobpdn398&amp;st=khkc0ona&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zj4cmy6yvtb0voer5nxsz/LAaG_HW_18_C-246.pdf?rlkey=m9sfdgy428uwooyto3jc0v2n2&amp;st=3cqiogo3&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3f4p41sixiwspbws1zuyp/LAaG_HW_17_C-246.pdf?rlkey=mc9tkb24whvre9rjaa2yy4yy5&amp;st=3uly6rcr&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wwkr4nrvemckinbvlfpf4/LAaG_HW_16_C-246.pdf?rlkey=d36aqvm4sl5ymrhc9689skqmh&amp;st=ytwxjuiy&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vvxf2ix4aohlrme23iio3/LAaG_HW_15_C-246.pdf?rlkey=pz848a5pnq4x1o7192t9e3ja8&amp;st=bzl0fx87&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v60x5jr3qtp5nu1ddsywa/LAaG_HW_13_C-246.pdf?rlkey=b9zsc00sn81zfi4zlorrp1dqu&amp;st=3y4vawm7&amp;dl=0 '''HW 13'''] (release: 10.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/oqw6b4jgz5a133g1cssmw/LAaG_HW_12_C-246.pdf?rlkey=5w5gqusl520nxxzumh761y4jb&amp;st=xii5fvfc&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/z80z8a3xan9vxu4abcqah/LAaG_HW_11_C-246.pdf?rlkey=fe836n2dzg580je9n8rr2wf8e&amp;st=vts0p3p2&amp;dl=0 '''HW 11'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/klzrlfot6t4v6rfbfd02q/LAaG_HW_10_C-246.pdf?rlkey=su9akh09k4mnz4unedoqlhc90&amp;st=2ab1uvrj&amp;dl=0 '''HW 10'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6xjvw47ehtwt2ku62y9h8/LAaG_HW_9_C-246.pdf?rlkey=fjp37n3b0f3kgqivb9mtfy9tz&amp;st=6oj9hjsk&amp;dl=0 '''HW 9'''] (release: 12.11.24; deadline: 19.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/vpmwnqengjj2g9nn6zf9p/LAaG_HW_8_C-246.pdf?rlkey=7qlhr2wtmtm9lkbwf6i9coipg&amp;st=wumfffop&amp;dl=0 '''HW 8'''] (release: 07.11.24; deadline: 17.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/fupbesmknyp4bgm9sygca/LAaG_Sem_8_07_11_24_g246.pdf?rlkey=telxxvgpcx3tj70flyjye7aoc&amp;st=5dnddh72&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=90854 LAaG DSBA 2024/2025 2025-05-13T19:34:29Z <p>Vvbalakirev: /* Homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 4 '''<br /> * [https://www.dropbox.com/s/km7z6bed527pfgm/LAaG_Lecture_30.pdf?dl=0 '''Lecture 29'''] (12.05.2025) Orthogonality in Euclidian spaces; orthogonal and orthonormal sets and bases; Gram-Schmidt process; the orthogonal complement and its main properties; the projection and the rejection of a vector.<br /> <br /> * [https://www.dropbox.com/s/6wn3z42bzvrg5or/LAaG_Lecture_29.pdf?dl=0 '''Lecture 28'''] (28.04.2025) Euclidean spaces; scalar product; the norm of a vector; Cauchy–Schwarz inequality; the angle between two vectors; the Gram matrix and its main properties.<br /> <br /> * [https://www.dropbox.com/s/gkxple1prqauxoa/LAaG_Lecture_28.pdf?dl=0 '''Lecture 27'''] (21.04.2025) Quadratic forms (Part III); The Jacobi theorem; normal bases and the normal form of a quadratic form; the positive and negative indices of inertia, the signature of a quadratic form; the Sylvester law of inertia; positive (semi)-definite and negative (semi)-definite quadratic forms; the Sylvester criterion.<br /> <br /> * [https://www.dropbox.com/s/wpo6qnbxviol7u6/LAaG_Lecture_26.pdf?dl=0 '''Lecture 26'''] (14.04.2025) Quadratic forms; associated bilinear form; coordinate matrix of a quadratic form; canonical basis and canonical form of a quadratic form.<br /> <br /> * [https://www.dropbox.com/s/cfb54jzd2qdn0ze/LAaG_Lecture_25.pdf?dl=0 '''Lecture 25'''] (07.04.2025) Bilinear Forms; a coordinate matrix of a bilinear form; change-of-basis formula for bilinear forms; symmetric and skew-summetric bilinear forms. Quadratic forms; the associated bilinear form of a quadratic form.<br /> <br /> ''' Module 3 '''<br /> * [https://www.dropbox.com/s/3at8g01dkxwjn7y/LAaG_Lecture_24.pdf?dl=0 '''Lecture 24'''] (17.03.2025) Linear operators (Part IV); Jordan matrix; Jordan normal form; Jordan basis; Jordan basis theorem (without proof); Cayley-Hamilton theorem. Linear Functionals; dual space; dual basis; isomorphism between V and V*.<br /> <br /> * [https://www.dropbox.com/s/bh2gbw88rixc8e7/LAaG_Lecture_23.pdf?dl=0 '''Lecture 23'''] (10.03.2025) Linear operators (Part III); diagonalizability of a linear operator; inequality between algebraic and geometric multiplicities; criteria of diagonalizability.<br /> <br /> * [https://www.dropbox.com/s/76ydfixppp12cik/LAaG_Lecture_22.pdf?dl=0 '''Lecture 22'''] (03.03.2025) Linear operators (Part II); vector space of linear operators; the characteristic polynomial of a linear operator; algebraic and geometric multiplicity of an eigenvalue.<br /> <br /> * [https://www.dropbox.com/s/e9w3h8vqa5slwjz/LAaG_Lecture_21.pdf?dl=0 '''Lecture 21'''] (24.02.2025) Linear operators; the rank, the determinant, and the trace of a linear operator; invariant subspaces; eigenvectors and eigenvalues of a linear operator.<br /> <br /> * [https://www.dropbox.com/s/kzatlshdq6gj5zk/LAaG_Lecture_20.pdf?dl=0 '''Lecture 20'''] (17.02.2025) Linear Transformations (Part III: injectivity and surjectivity of linear transformations) injective and surjective linear transformations; isomorphisms (=linear bijections) of vector spaces; the inverse of an isomorphism; the fact that two finite dimensional vector spaces are isomorphic if and only if they both have the same dimension.<br /> <br /> * [https://www.dropbox.com/s/vczbkb79w67r4tk/LAaG_Lecture_19.pdf?dl=0 '''Lecture 19'''] (10.02.2025) Linear Transformations (Part II: matrix representation and change of basis); coordinate matrices of a linear transformation; coordinate matrix of a composition of linear transformations; change of basis.<br /> <br /> * [https://www.dropbox.com/s/is0p1nou922zynj/LAaG_Lecture_18.pdf?dl=0 '''Lecture 18'''] (03.02.2025) Linear Transformations; main properties of linear transformations; the image and the kernel of a linear transformation; singular and non-singular linear transformations; the rank and the nullity of a linear transformation.<br /> <br /> * [https://www.dropbox.com/s/td8df813s2lh38b/LAaG_Lecture_17.pdf?dl=0 '''Lecture 17'''] (27.01.2025) The rank of a matrix (Part II); we prove that the column rank equals the row rank.<br /> <br /> * [https://www.dropbox.com/s/nf44zccqg3rythp/LAaG_Lecture_16.pdf?dl=0 '''Lecture 16'''] (20.01.2025) The direct sum of subspaces; main properties of the direct sum; the rank of a matrix; column and row spaces of a matrix; column and row ranks of a matrix.<br /> <br /> * [https://www.dropbox.com/s/cl7djenawtlgp0o/LAaG_Lecture_15.pdf?dl=0 '''Lecture 15'''] (13.01.2025) Main properties of change of basis matrices; the sum, the intersection, and the direct sum of vector subspaces; the dimension of the sum of two vector subspaces.<br /> <br /> ''' Module 2 '''<br /> * [https://www.dropbox.com/s/pozm47tzgaibf4k/LAaG_Lecture_14.pdf?dl=0 '''Lecture 14'''] (16.12.2024) Vector spaces (Part III); m-element subsets of an n-dimensional vector space; extension to a basis; the dimension of a subspace of a finite dimensional vector space; ordered basis; basis matrix; change of basis matrix.<br /> <br /> * [https://www.dropbox.com/s/10v3w4efz6zi332/LAaG_Lecture_13.pdf?dl=0 '''Lecture 13'''] (09.12.2024) Vector spaces (Part II); Main theorem on linear dependence; a basis of a vector space; dimension of a vector space; finite and infinite dimensional vector spaces; some main properties of finite dimensional vector spaces.<br /> <br /> * [https://www.dropbox.com/s/snko9y9r7ccw8qk/LAaG_Lecture_12.pdf?dl=0 '''Lecture 12'''] (01.12.2024) Vector spaces (Part I); a subspace of a vector space; linear combinations; the linear span; trivial and non-trivial linear combinations; linearly dependent and linearly independent sets.<br /> <br /> * [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (25.11.2024) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br /> <br /> * [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (18.11.2024) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br /> <br /> * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (11.11.2024) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br /> <br /> * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (02.11.2024) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/iw4d8eyjayzff9kfcj33r/LAaG_HW_29_C-241.pdf?rlkey=r7mvkq3f3tipvcphvmbcs7wy9&amp;st=ftkay74b&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ew31593pflcym5wtj0een/LAaG_HW_28_C-241.pdf?rlkey=66wd02998pic8x3t24061cdbh&amp;st=q296xsgc&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sc0udwvted1nn1quz4zou/LAaG_HW_27_C-241.pdf?rlkey=s47ayfwajc9lqod48xt5tx4wa&amp;st=qd7b4y7z&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/myc8320hx3njihu24cuba/LAaG_HW_26_C-241.pdf?rlkey=23sq1u6qrb9xevdrzaoutqxca&amp;st=1jmhwafo&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/cva01p9hh7qdtagzl3kn3/LAaG_HW_25_C-241.pdf?rlkey=yal3zb4maa7zwdvqxcecssjkg&amp;st=sg8pbd9k&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/7lpp0i0xjelgq0gp35e4n/LAaG_HW_24_C-241.pdf?rlkey=a582n8pburjgu2j8510gzn83r&amp;st=2q6voag2&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/4a54pbfd61aoprnxwzu0x/LAaG_HW_23_C-241.pdf?rlkey=fe69qd7iarodjou59nsfrr6sh&amp;st=pg55d94h&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/0bwlj7nva3781wif2lht4/LAaG_HW_22_C-241.pdf?rlkey=zvnp3kg68lfgl1psi4oey1duy&amp;st=erjtper3&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/r2d0fnyhorbud4w97cw8p/LAaG_HW_21_C-241.pdf?rlkey=jge0vzkbwpun9stgsnqk1xa15&amp;st=bdihujff&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tej4f5c5io1742pc958k6/LAaG_HW_20_C-241.pdf?rlkey=j1c0yag295f53gydl5rsc2o10&amp;st=fetq10zo&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/o2624ddh1r58a3ek8v723/LAaG_HW_19_C-241.pdf?rlkey=5ztkckb96zjcydhnk7x88en29&amp;st=bg5891g6&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zpc9ji9p84zvz5mi9vws9/LAaG_HW_18_C-241.pdf?rlkey=cfv4sqgw7kvcu4wbcata3fab3&amp;st=e2c6jr7e&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vthiyr2dpqrgggx8rwc5n/LAaG_HW_17_C-241.pdf?rlkey=rfchkhjrs96c4as6z0f68005h&amp;st=agspv924&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jk1qemu09cq5pzt2mpu58/LAaG_HW_16_C-241.pdf?rlkey=565cdf9qndljixsg2hm9pgs85&amp;st=u4i6x9g4&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/e0l37mfgqhgzhc35xvv85/LAaG_HW_15_C-241.pdf?rlkey=td1du8a0w5goaf0kk1e1doh02&amp;st=dmouas60&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gfanxb92qos5yrw2rw9up/LAaG_HW_13_C-241.pdf?rlkey=3lieu7597p86akdubpgblrxv1&amp;st=tzrb0x2w&amp;dl=0 '''HW 13'''] (release: 09.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/98g4oshs0lkwzfkq7ws2o/LAaG_HW_12_C-241.pdf?rlkey=ir2gfbgas5zecrt3de03anocx&amp;st=huaalfyu&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bkwvo24thkydotpkqjv7s/LAaG_HW_11_C-241.pdf?rlkey=vw1rwyesz3cfvizb88ukwbk5c&amp;st=6lzvxcfd&amp;dl=0 '''HW 11'''] (release: 25.11.24; deadline: 02.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tz95u31aralzb00htmpfr/LAaG_HW_10_C-241.pdf?rlkey=kvbdd60wu3jaj908hve2amrb7&amp;st=kiam0tz0&amp;dl=0 '''HW 10'''] (release: 18.11.24; deadline: 25.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9icdl8t78tqqaszgnh1ex/LAaG_HW_9_C-241.pdf?rlkey=obf47jl5bm91hmrlinhymmu5a&amp;st=8pldj7gq&amp;dl=0 '''HW 9'''] (release: 11.11.24; deadline: 18.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/cuah8c9c3lm3qjxw16paw/LAaG_HW_8_C-241.pdf?rlkey=iaedxga7hdn89904yo3rirtrs&amp;st=6lvpxxgl&amp;dl=0 '''HW 8'''] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/619rsffz78buraprvzlfo/LAaG_Seminar_8.pdf?rlkey=98o6gc0rjl4h6r9djdrasfwu8&amp;st=8zetjdlw&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/74v0d0eiofll1maa9jznn/LAaG_HW_29_C-246.pdf?rlkey=tkc9a738pz8ucsmoj1qa098to&amp;st=qjp6gids&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/dhn85atazelewt7hga4wm/LAaG_HW_28_C-246.pdf?rlkey=uuzzqtp8e19fwc9ed4cqity13&amp;st=cf0kk85z&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oipf5pzr862yxj8hzws0q/LAaG_HW_27_C-246.pdf?rlkey=8zm2hmvtcxaxl7gup9fhlskv4&amp;st=r2p4k1ki&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/f0ecohy3h75i4tteco78g/LAaG_HW_26_C-246.pdf?rlkey=4d2hnuddvguzw9brt08t7jfpv&amp;st=z8e70o5z&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lwvmio1folirvyij2c5te/LAaG_HW_25_C-246.pdf?rlkey=zg38wdf05opaxmuq6zfkuhsgk&amp;st=wd20mn6i&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/ais924pz2nlej2c2xggik/LAaG_HW_24_C-246.pdf?rlkey=cr3yzxr1sewhfckkas418wwlu&amp;st=cj12kvrx&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/jexjsl0jrgaui9o4nf9jl/LAaG_HW_23_C-246.pdf?rlkey=6v42cmsbukuljstxc1rw5nj2s&amp;st=3yw1rrh6&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6tnjv2kxwum90bwwklak5/LAaG_HW_22_C-246.pdf?rlkey=ml6hgg2cqnafwvhpuoe15vqsw&amp;st=xrgch4zx&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sadhn3ahnqtik4awr2tj4/LAaG_HW_21_C-246.pdf?rlkey=hs3dyl8ig4s6ygwvxyqtzgrez&amp;st=ndz29dpb&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/qurd5huy43ihn1z6a4u5g/LAaG_HW_20_C-246.pdf?rlkey=4js3uvv10nvnwxfijskwo1beg&amp;st=z6izkugw&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lit3st83vxamv4yoeux14/LAaG_HW_19_C-246.pdf?rlkey=md0jtmyyol74p3grsobpdn398&amp;st=khkc0ona&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zj4cmy6yvtb0voer5nxsz/LAaG_HW_18_C-246.pdf?rlkey=m9sfdgy428uwooyto3jc0v2n2&amp;st=3cqiogo3&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3f4p41sixiwspbws1zuyp/LAaG_HW_17_C-246.pdf?rlkey=mc9tkb24whvre9rjaa2yy4yy5&amp;st=3uly6rcr&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wwkr4nrvemckinbvlfpf4/LAaG_HW_16_C-246.pdf?rlkey=d36aqvm4sl5ymrhc9689skqmh&amp;st=ytwxjuiy&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vvxf2ix4aohlrme23iio3/LAaG_HW_15_C-246.pdf?rlkey=pz848a5pnq4x1o7192t9e3ja8&amp;st=bzl0fx87&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v60x5jr3qtp5nu1ddsywa/LAaG_HW_13_C-246.pdf?rlkey=b9zsc00sn81zfi4zlorrp1dqu&amp;st=3y4vawm7&amp;dl=0 '''HW 13'''] (release: 10.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/oqw6b4jgz5a133g1cssmw/LAaG_HW_12_C-246.pdf?rlkey=5w5gqusl520nxxzumh761y4jb&amp;st=xii5fvfc&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/z80z8a3xan9vxu4abcqah/LAaG_HW_11_C-246.pdf?rlkey=fe836n2dzg580je9n8rr2wf8e&amp;st=vts0p3p2&amp;dl=0 '''HW 11'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/klzrlfot6t4v6rfbfd02q/LAaG_HW_10_C-246.pdf?rlkey=su9akh09k4mnz4unedoqlhc90&amp;st=2ab1uvrj&amp;dl=0 '''HW 10'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6xjvw47ehtwt2ku62y9h8/LAaG_HW_9_C-246.pdf?rlkey=fjp37n3b0f3kgqivb9mtfy9tz&amp;st=6oj9hjsk&amp;dl=0 '''HW 9'''] (release: 12.11.24; deadline: 19.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/vpmwnqengjj2g9nn6zf9p/LAaG_HW_8_C-246.pdf?rlkey=7qlhr2wtmtm9lkbwf6i9coipg&amp;st=wumfffop&amp;dl=0 '''HW 8'''] (release: 07.11.24; deadline: 17.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/fupbesmknyp4bgm9sygca/LAaG_Sem_8_07_11_24_g246.pdf?rlkey=telxxvgpcx3tj70flyjye7aoc&amp;st=5dnddh72&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=90849 LAaG DSBA 2024/2025 2025-05-13T16:47:43Z <p>Vvbalakirev: /* Homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 4 '''<br /> * [https://www.dropbox.com/s/km7z6bed527pfgm/LAaG_Lecture_30.pdf?dl=0 '''Lecture 29'''] (12.05.2025) Orthogonality in Euclidian spaces; orthogonal and orthonormal sets and bases; Gram-Schmidt process; the orthogonal complement and its main properties; the projection and the rejection of a vector.<br /> <br /> * [https://www.dropbox.com/s/6wn3z42bzvrg5or/LAaG_Lecture_29.pdf?dl=0 '''Lecture 28'''] (28.04.2025) Euclidean spaces; scalar product; the norm of a vector; Cauchy–Schwarz inequality; the angle between two vectors; the Gram matrix and its main properties.<br /> <br /> * [https://www.dropbox.com/s/gkxple1prqauxoa/LAaG_Lecture_28.pdf?dl=0 '''Lecture 27'''] (21.04.2025) Quadratic forms (Part III); The Jacobi theorem; normal bases and the normal form of a quadratic form; the positive and negative indices of inertia, the signature of a quadratic form; the Sylvester law of inertia; positive (semi)-definite and negative (semi)-definite quadratic forms; the Sylvester criterion.<br /> <br /> * [https://www.dropbox.com/s/wpo6qnbxviol7u6/LAaG_Lecture_26.pdf?dl=0 '''Lecture 26'''] (14.04.2025) Quadratic forms; associated bilinear form; coordinate matrix of a quadratic form; canonical basis and canonical form of a quadratic form.<br /> <br /> * [https://www.dropbox.com/s/cfb54jzd2qdn0ze/LAaG_Lecture_25.pdf?dl=0 '''Lecture 25'''] (07.04.2025) Bilinear Forms; a coordinate matrix of a bilinear form; change-of-basis formula for bilinear forms; symmetric and skew-summetric bilinear forms. Quadratic forms; the associated bilinear form of a quadratic form.<br /> <br /> ''' Module 3 '''<br /> * [https://www.dropbox.com/s/3at8g01dkxwjn7y/LAaG_Lecture_24.pdf?dl=0 '''Lecture 24'''] (17.03.2025) Linear operators (Part IV); Jordan matrix; Jordan normal form; Jordan basis; Jordan basis theorem (without proof); Cayley-Hamilton theorem. Linear Functionals; dual space; dual basis; isomorphism between V and V*.<br /> <br /> * [https://www.dropbox.com/s/bh2gbw88rixc8e7/LAaG_Lecture_23.pdf?dl=0 '''Lecture 23'''] (10.03.2025) Linear operators (Part III); diagonalizability of a linear operator; inequality between algebraic and geometric multiplicities; criteria of diagonalizability.<br /> <br /> * [https://www.dropbox.com/s/76ydfixppp12cik/LAaG_Lecture_22.pdf?dl=0 '''Lecture 22'''] (03.03.2025) Linear operators (Part II); vector space of linear operators; the characteristic polynomial of a linear operator; algebraic and geometric multiplicity of an eigenvalue.<br /> <br /> * [https://www.dropbox.com/s/e9w3h8vqa5slwjz/LAaG_Lecture_21.pdf?dl=0 '''Lecture 21'''] (24.02.2025) Linear operators; the rank, the determinant, and the trace of a linear operator; invariant subspaces; eigenvectors and eigenvalues of a linear operator.<br /> <br /> * [https://www.dropbox.com/s/kzatlshdq6gj5zk/LAaG_Lecture_20.pdf?dl=0 '''Lecture 20'''] (17.02.2025) Linear Transformations (Part III: injectivity and surjectivity of linear transformations) injective and surjective linear transformations; isomorphisms (=linear bijections) of vector spaces; the inverse of an isomorphism; the fact that two finite dimensional vector spaces are isomorphic if and only if they both have the same dimension.<br /> <br /> * [https://www.dropbox.com/s/vczbkb79w67r4tk/LAaG_Lecture_19.pdf?dl=0 '''Lecture 19'''] (10.02.2025) Linear Transformations (Part II: matrix representation and change of basis); coordinate matrices of a linear transformation; coordinate matrix of a composition of linear transformations; change of basis.<br /> <br /> * [https://www.dropbox.com/s/is0p1nou922zynj/LAaG_Lecture_18.pdf?dl=0 '''Lecture 18'''] (03.02.2025) Linear Transformations; main properties of linear transformations; the image and the kernel of a linear transformation; singular and non-singular linear transformations; the rank and the nullity of a linear transformation.<br /> <br /> * [https://www.dropbox.com/s/td8df813s2lh38b/LAaG_Lecture_17.pdf?dl=0 '''Lecture 17'''] (27.01.2025) The rank of a matrix (Part II); we prove that the column rank equals the row rank.<br /> <br /> * [https://www.dropbox.com/s/nf44zccqg3rythp/LAaG_Lecture_16.pdf?dl=0 '''Lecture 16'''] (20.01.2025) The direct sum of subspaces; main properties of the direct sum; the rank of a matrix; column and row spaces of a matrix; column and row ranks of a matrix.<br /> <br /> * [https://www.dropbox.com/s/cl7djenawtlgp0o/LAaG_Lecture_15.pdf?dl=0 '''Lecture 15'''] (13.01.2025) Main properties of change of basis matrices; the sum, the intersection, and the direct sum of vector subspaces; the dimension of the sum of two vector subspaces.<br /> <br /> ''' Module 2 '''<br /> * [https://www.dropbox.com/s/pozm47tzgaibf4k/LAaG_Lecture_14.pdf?dl=0 '''Lecture 14'''] (16.12.2024) Vector spaces (Part III); m-element subsets of an n-dimensional vector space; extension to a basis; the dimension of a subspace of a finite dimensional vector space; ordered basis; basis matrix; change of basis matrix.<br /> <br /> * [https://www.dropbox.com/s/10v3w4efz6zi332/LAaG_Lecture_13.pdf?dl=0 '''Lecture 13'''] (09.12.2024) Vector spaces (Part II); Main theorem on linear dependence; a basis of a vector space; dimension of a vector space; finite and infinite dimensional vector spaces; some main properties of finite dimensional vector spaces.<br /> <br /> * [https://www.dropbox.com/s/snko9y9r7ccw8qk/LAaG_Lecture_12.pdf?dl=0 '''Lecture 12'''] (01.12.2024) Vector spaces (Part I); a subspace of a vector space; linear combinations; the linear span; trivial and non-trivial linear combinations; linearly dependent and linearly independent sets.<br /> <br /> * [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (25.11.2024) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br /> <br /> * [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (18.11.2024) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br /> <br /> * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (11.11.2024) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br /> <br /> * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (02.11.2024) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/iw4d8eyjayzff9kfcj33r/LAaG_HW_29_C-241.pdf?rlkey=r7mvkq3f3tipvcphvmbcs7wy9&amp;st=ftkay74b&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ew31593pflcym5wtj0een/LAaG_HW_28_C-241.pdf?rlkey=66wd02998pic8x3t24061cdbh&amp;st=q296xsgc&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sc0udwvted1nn1quz4zou/LAaG_HW_27_C-241.pdf?rlkey=s47ayfwajc9lqod48xt5tx4wa&amp;st=qd7b4y7z&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/myc8320hx3njihu24cuba/LAaG_HW_26_C-241.pdf?rlkey=23sq1u6qrb9xevdrzaoutqxca&amp;st=1jmhwafo&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/cva01p9hh7qdtagzl3kn3/LAaG_HW_25_C-241.pdf?rlkey=yal3zb4maa7zwdvqxcecssjkg&amp;st=sg8pbd9k&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/7lpp0i0xjelgq0gp35e4n/LAaG_HW_24_C-241.pdf?rlkey=a582n8pburjgu2j8510gzn83r&amp;st=2q6voag2&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/4a54pbfd61aoprnxwzu0x/LAaG_HW_23_C-241.pdf?rlkey=fe69qd7iarodjou59nsfrr6sh&amp;st=pg55d94h&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/0bwlj7nva3781wif2lht4/LAaG_HW_22_C-241.pdf?rlkey=zvnp3kg68lfgl1psi4oey1duy&amp;st=erjtper3&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/r2d0fnyhorbud4w97cw8p/LAaG_HW_21_C-241.pdf?rlkey=jge0vzkbwpun9stgsnqk1xa15&amp;st=bdihujff&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tej4f5c5io1742pc958k6/LAaG_HW_20_C-241.pdf?rlkey=j1c0yag295f53gydl5rsc2o10&amp;st=fetq10zo&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/o2624ddh1r58a3ek8v723/LAaG_HW_19_C-241.pdf?rlkey=5ztkckb96zjcydhnk7x88en29&amp;st=bg5891g6&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zpc9ji9p84zvz5mi9vws9/LAaG_HW_18_C-241.pdf?rlkey=cfv4sqgw7kvcu4wbcata3fab3&amp;st=e2c6jr7e&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vthiyr2dpqrgggx8rwc5n/LAaG_HW_17_C-241.pdf?rlkey=rfchkhjrs96c4as6z0f68005h&amp;st=agspv924&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jk1qemu09cq5pzt2mpu58/LAaG_HW_16_C-241.pdf?rlkey=565cdf9qndljixsg2hm9pgs85&amp;st=u4i6x9g4&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/e0l37mfgqhgzhc35xvv85/LAaG_HW_15_C-241.pdf?rlkey=td1du8a0w5goaf0kk1e1doh02&amp;st=dmouas60&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gfanxb92qos5yrw2rw9up/LAaG_HW_13_C-241.pdf?rlkey=3lieu7597p86akdubpgblrxv1&amp;st=tzrb0x2w&amp;dl=0 '''HW 13'''] (release: 09.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/98g4oshs0lkwzfkq7ws2o/LAaG_HW_12_C-241.pdf?rlkey=ir2gfbgas5zecrt3de03anocx&amp;st=huaalfyu&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bkwvo24thkydotpkqjv7s/LAaG_HW_11_C-241.pdf?rlkey=vw1rwyesz3cfvizb88ukwbk5c&amp;st=6lzvxcfd&amp;dl=0 '''HW 11'''] (release: 25.11.24; deadline: 02.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tz95u31aralzb00htmpfr/LAaG_HW_10_C-241.pdf?rlkey=kvbdd60wu3jaj908hve2amrb7&amp;st=kiam0tz0&amp;dl=0 '''HW 10'''] (release: 18.11.24; deadline: 25.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9icdl8t78tqqaszgnh1ex/LAaG_HW_9_C-241.pdf?rlkey=obf47jl5bm91hmrlinhymmu5a&amp;st=8pldj7gq&amp;dl=0 '''HW 9'''] (release: 11.11.24; deadline: 18.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/cuah8c9c3lm3qjxw16paw/LAaG_HW_8_C-241.pdf?rlkey=iaedxga7hdn89904yo3rirtrs&amp;st=6lvpxxgl&amp;dl=0 '''HW 8'''] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/619rsffz78buraprvzlfo/LAaG_Seminar_8.pdf?rlkey=98o6gc0rjl4h6r9djdrasfwu8&amp;st=8zetjdlw&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/74v0d0eiofll1maa9jznn/LAaG_HW_29_C-246.pdf?rlkey=tkc9a738pz8ucsmoj1qa098to&amp;st=qjp6gids&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/dhn85atazelewt7hga4wm/LAaG_HW_28_C-246.pdf?rlkey=uuzzqtp8e19fwc9ed4cqity13&amp;st=cf0kk85z&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oipf5pzr862yxj8hzws0q/LAaG_HW_27_C-246.pdf?rlkey=8zm2hmvtcxaxl7gup9fhlskv4&amp;st=r2p4k1ki&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/f0ecohy3h75i4tteco78g/LAaG_HW_26_C-246.pdf?rlkey=4d2hnuddvguzw9brt08t7jfpv&amp;st=z8e70o5z&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lwvmio1folirvyij2c5te/LAaG_HW_25_C-246.pdf?rlkey=zg38wdf05opaxmuq6zfkuhsgk&amp;st=wd20mn6i&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/ais924pz2nlej2c2xggik/LAaG_HW_24_C-246.pdf?rlkey=cr3yzxr1sewhfckkas418wwlu&amp;st=cj12kvrx&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/jexjsl0jrgaui9o4nf9jl/LAaG_HW_23_C-246.pdf?rlkey=6v42cmsbukuljstxc1rw5nj2s&amp;st=3yw1rrh6&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6tnjv2kxwum90bwwklak5/LAaG_HW_22_C-246.pdf?rlkey=ml6hgg2cqnafwvhpuoe15vqsw&amp;st=xrgch4zx&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sadhn3ahnqtik4awr2tj4/LAaG_HW_21_C-246.pdf?rlkey=hs3dyl8ig4s6ygwvxyqtzgrez&amp;st=ndz29dpb&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/qurd5huy43ihn1z6a4u5g/LAaG_HW_20_C-246.pdf?rlkey=4js3uvv10nvnwxfijskwo1beg&amp;st=z6izkugw&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lit3st83vxamv4yoeux14/LAaG_HW_19_C-246.pdf?rlkey=md0jtmyyol74p3grsobpdn398&amp;st=khkc0ona&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zj4cmy6yvtb0voer5nxsz/LAaG_HW_18_C-246.pdf?rlkey=m9sfdgy428uwooyto3jc0v2n2&amp;st=3cqiogo3&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3f4p41sixiwspbws1zuyp/LAaG_HW_17_C-246.pdf?rlkey=mc9tkb24whvre9rjaa2yy4yy5&amp;st=3uly6rcr&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wwkr4nrvemckinbvlfpf4/LAaG_HW_16_C-246.pdf?rlkey=d36aqvm4sl5ymrhc9689skqmh&amp;st=ytwxjuiy&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vvxf2ix4aohlrme23iio3/LAaG_HW_15_C-246.pdf?rlkey=pz848a5pnq4x1o7192t9e3ja8&amp;st=bzl0fx87&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v60x5jr3qtp5nu1ddsywa/LAaG_HW_13_C-246.pdf?rlkey=b9zsc00sn81zfi4zlorrp1dqu&amp;st=3y4vawm7&amp;dl=0 '''HW 13'''] (release: 10.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/oqw6b4jgz5a133g1cssmw/LAaG_HW_12_C-246.pdf?rlkey=5w5gqusl520nxxzumh761y4jb&amp;st=xii5fvfc&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/z80z8a3xan9vxu4abcqah/LAaG_HW_11_C-246.pdf?rlkey=fe836n2dzg580je9n8rr2wf8e&amp;st=vts0p3p2&amp;dl=0 '''HW 11'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/klzrlfot6t4v6rfbfd02q/LAaG_HW_10_C-246.pdf?rlkey=su9akh09k4mnz4unedoqlhc90&amp;st=2ab1uvrj&amp;dl=0 '''HW 10'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6xjvw47ehtwt2ku62y9h8/LAaG_HW_9_C-246.pdf?rlkey=fjp37n3b0f3kgqivb9mtfy9tz&amp;st=6oj9hjsk&amp;dl=0 '''HW 9'''] (release: 12.11.24; deadline: 19.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/vpmwnqengjj2g9nn6zf9p/LAaG_HW_8_C-246.pdf?rlkey=7qlhr2wtmtm9lkbwf6i9coipg&amp;st=wumfffop&amp;dl=0 '''HW 8'''] (release: 07.11.24; deadline: 17.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/fupbesmknyp4bgm9sygca/LAaG_Sem_8_07_11_24_g246.pdf?rlkey=telxxvgpcx3tj70flyjye7aoc&amp;st=5dnddh72&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=90848 LAaG DSBA 2024/2025 2025-05-13T16:47:32Z <p>Vvbalakirev: /* Homework for group 243: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 4 '''<br /> * [https://www.dropbox.com/s/km7z6bed527pfgm/LAaG_Lecture_30.pdf?dl=0 '''Lecture 29'''] (12.05.2025) Orthogonality in Euclidian spaces; orthogonal and orthonormal sets and bases; Gram-Schmidt process; the orthogonal complement and its main properties; the projection and the rejection of a vector.<br /> <br /> * [https://www.dropbox.com/s/6wn3z42bzvrg5or/LAaG_Lecture_29.pdf?dl=0 '''Lecture 28'''] (28.04.2025) Euclidean spaces; scalar product; the norm of a vector; Cauchy–Schwarz inequality; the angle between two vectors; the Gram matrix and its main properties.<br /> <br /> * [https://www.dropbox.com/s/gkxple1prqauxoa/LAaG_Lecture_28.pdf?dl=0 '''Lecture 27'''] (21.04.2025) Quadratic forms (Part III); The Jacobi theorem; normal bases and the normal form of a quadratic form; the positive and negative indices of inertia, the signature of a quadratic form; the Sylvester law of inertia; positive (semi)-definite and negative (semi)-definite quadratic forms; the Sylvester criterion.<br /> <br /> * [https://www.dropbox.com/s/wpo6qnbxviol7u6/LAaG_Lecture_26.pdf?dl=0 '''Lecture 26'''] (14.04.2025) Quadratic forms; associated bilinear form; coordinate matrix of a quadratic form; canonical basis and canonical form of a quadratic form.<br /> <br /> * [https://www.dropbox.com/s/cfb54jzd2qdn0ze/LAaG_Lecture_25.pdf?dl=0 '''Lecture 25'''] (07.04.2025) Bilinear Forms; a coordinate matrix of a bilinear form; change-of-basis formula for bilinear forms; symmetric and skew-summetric bilinear forms. Quadratic forms; the associated bilinear form of a quadratic form.<br /> <br /> ''' Module 3 '''<br /> * [https://www.dropbox.com/s/3at8g01dkxwjn7y/LAaG_Lecture_24.pdf?dl=0 '''Lecture 24'''] (17.03.2025) Linear operators (Part IV); Jordan matrix; Jordan normal form; Jordan basis; Jordan basis theorem (without proof); Cayley-Hamilton theorem. Linear Functionals; dual space; dual basis; isomorphism between V and V*.<br /> <br /> * [https://www.dropbox.com/s/bh2gbw88rixc8e7/LAaG_Lecture_23.pdf?dl=0 '''Lecture 23'''] (10.03.2025) Linear operators (Part III); diagonalizability of a linear operator; inequality between algebraic and geometric multiplicities; criteria of diagonalizability.<br /> <br /> * [https://www.dropbox.com/s/76ydfixppp12cik/LAaG_Lecture_22.pdf?dl=0 '''Lecture 22'''] (03.03.2025) Linear operators (Part II); vector space of linear operators; the characteristic polynomial of a linear operator; algebraic and geometric multiplicity of an eigenvalue.<br /> <br /> * [https://www.dropbox.com/s/e9w3h8vqa5slwjz/LAaG_Lecture_21.pdf?dl=0 '''Lecture 21'''] (24.02.2025) Linear operators; the rank, the determinant, and the trace of a linear operator; invariant subspaces; eigenvectors and eigenvalues of a linear operator.<br /> <br /> * [https://www.dropbox.com/s/kzatlshdq6gj5zk/LAaG_Lecture_20.pdf?dl=0 '''Lecture 20'''] (17.02.2025) Linear Transformations (Part III: injectivity and surjectivity of linear transformations) injective and surjective linear transformations; isomorphisms (=linear bijections) of vector spaces; the inverse of an isomorphism; the fact that two finite dimensional vector spaces are isomorphic if and only if they both have the same dimension.<br /> <br /> * [https://www.dropbox.com/s/vczbkb79w67r4tk/LAaG_Lecture_19.pdf?dl=0 '''Lecture 19'''] (10.02.2025) Linear Transformations (Part II: matrix representation and change of basis); coordinate matrices of a linear transformation; coordinate matrix of a composition of linear transformations; change of basis.<br /> <br /> * [https://www.dropbox.com/s/is0p1nou922zynj/LAaG_Lecture_18.pdf?dl=0 '''Lecture 18'''] (03.02.2025) Linear Transformations; main properties of linear transformations; the image and the kernel of a linear transformation; singular and non-singular linear transformations; the rank and the nullity of a linear transformation.<br /> <br /> * [https://www.dropbox.com/s/td8df813s2lh38b/LAaG_Lecture_17.pdf?dl=0 '''Lecture 17'''] (27.01.2025) The rank of a matrix (Part II); we prove that the column rank equals the row rank.<br /> <br /> * [https://www.dropbox.com/s/nf44zccqg3rythp/LAaG_Lecture_16.pdf?dl=0 '''Lecture 16'''] (20.01.2025) The direct sum of subspaces; main properties of the direct sum; the rank of a matrix; column and row spaces of a matrix; column and row ranks of a matrix.<br /> <br /> * [https://www.dropbox.com/s/cl7djenawtlgp0o/LAaG_Lecture_15.pdf?dl=0 '''Lecture 15'''] (13.01.2025) Main properties of change of basis matrices; the sum, the intersection, and the direct sum of vector subspaces; the dimension of the sum of two vector subspaces.<br /> <br /> ''' Module 2 '''<br /> * [https://www.dropbox.com/s/pozm47tzgaibf4k/LAaG_Lecture_14.pdf?dl=0 '''Lecture 14'''] (16.12.2024) Vector spaces (Part III); m-element subsets of an n-dimensional vector space; extension to a basis; the dimension of a subspace of a finite dimensional vector space; ordered basis; basis matrix; change of basis matrix.<br /> <br /> * [https://www.dropbox.com/s/10v3w4efz6zi332/LAaG_Lecture_13.pdf?dl=0 '''Lecture 13'''] (09.12.2024) Vector spaces (Part II); Main theorem on linear dependence; a basis of a vector space; dimension of a vector space; finite and infinite dimensional vector spaces; some main properties of finite dimensional vector spaces.<br /> <br /> * [https://www.dropbox.com/s/snko9y9r7ccw8qk/LAaG_Lecture_12.pdf?dl=0 '''Lecture 12'''] (01.12.2024) Vector spaces (Part I); a subspace of a vector space; linear combinations; the linear span; trivial and non-trivial linear combinations; linearly dependent and linearly independent sets.<br /> <br /> * [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (25.11.2024) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br /> <br /> * [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (18.11.2024) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br /> <br /> * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (11.11.2024) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br /> <br /> * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (02.11.2024) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/iw4d8eyjayzff9kfcj33r/LAaG_HW_29_C-241.pdf?rlkey=r7mvkq3f3tipvcphvmbcs7wy9&amp;st=ftkay74b&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ew31593pflcym5wtj0een/LAaG_HW_28_C-241.pdf?rlkey=66wd02998pic8x3t24061cdbh&amp;st=q296xsgc&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sc0udwvted1nn1quz4zou/LAaG_HW_27_C-241.pdf?rlkey=s47ayfwajc9lqod48xt5tx4wa&amp;st=qd7b4y7z&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/myc8320hx3njihu24cuba/LAaG_HW_26_C-241.pdf?rlkey=23sq1u6qrb9xevdrzaoutqxca&amp;st=1jmhwafo&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/cva01p9hh7qdtagzl3kn3/LAaG_HW_25_C-241.pdf?rlkey=yal3zb4maa7zwdvqxcecssjkg&amp;st=sg8pbd9k&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/7lpp0i0xjelgq0gp35e4n/LAaG_HW_24_C-241.pdf?rlkey=a582n8pburjgu2j8510gzn83r&amp;st=2q6voag2&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/4a54pbfd61aoprnxwzu0x/LAaG_HW_23_C-241.pdf?rlkey=fe69qd7iarodjou59nsfrr6sh&amp;st=pg55d94h&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/0bwlj7nva3781wif2lht4/LAaG_HW_22_C-241.pdf?rlkey=zvnp3kg68lfgl1psi4oey1duy&amp;st=erjtper3&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/r2d0fnyhorbud4w97cw8p/LAaG_HW_21_C-241.pdf?rlkey=jge0vzkbwpun9stgsnqk1xa15&amp;st=bdihujff&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tej4f5c5io1742pc958k6/LAaG_HW_20_C-241.pdf?rlkey=j1c0yag295f53gydl5rsc2o10&amp;st=fetq10zo&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/o2624ddh1r58a3ek8v723/LAaG_HW_19_C-241.pdf?rlkey=5ztkckb96zjcydhnk7x88en29&amp;st=bg5891g6&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zpc9ji9p84zvz5mi9vws9/LAaG_HW_18_C-241.pdf?rlkey=cfv4sqgw7kvcu4wbcata3fab3&amp;st=e2c6jr7e&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vthiyr2dpqrgggx8rwc5n/LAaG_HW_17_C-241.pdf?rlkey=rfchkhjrs96c4as6z0f68005h&amp;st=agspv924&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jk1qemu09cq5pzt2mpu58/LAaG_HW_16_C-241.pdf?rlkey=565cdf9qndljixsg2hm9pgs85&amp;st=u4i6x9g4&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/e0l37mfgqhgzhc35xvv85/LAaG_HW_15_C-241.pdf?rlkey=td1du8a0w5goaf0kk1e1doh02&amp;st=dmouas60&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gfanxb92qos5yrw2rw9up/LAaG_HW_13_C-241.pdf?rlkey=3lieu7597p86akdubpgblrxv1&amp;st=tzrb0x2w&amp;dl=0 '''HW 13'''] (release: 09.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/98g4oshs0lkwzfkq7ws2o/LAaG_HW_12_C-241.pdf?rlkey=ir2gfbgas5zecrt3de03anocx&amp;st=huaalfyu&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bkwvo24thkydotpkqjv7s/LAaG_HW_11_C-241.pdf?rlkey=vw1rwyesz3cfvizb88ukwbk5c&amp;st=6lzvxcfd&amp;dl=0 '''HW 11'''] (release: 25.11.24; deadline: 02.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tz95u31aralzb00htmpfr/LAaG_HW_10_C-241.pdf?rlkey=kvbdd60wu3jaj908hve2amrb7&amp;st=kiam0tz0&amp;dl=0 '''HW 10'''] (release: 18.11.24; deadline: 25.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9icdl8t78tqqaszgnh1ex/LAaG_HW_9_C-241.pdf?rlkey=obf47jl5bm91hmrlinhymmu5a&amp;st=8pldj7gq&amp;dl=0 '''HW 9'''] (release: 11.11.24; deadline: 18.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/cuah8c9c3lm3qjxw16paw/LAaG_HW_8_C-241.pdf?rlkey=iaedxga7hdn89904yo3rirtrs&amp;st=6lvpxxgl&amp;dl=0 '''HW 8'''] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/619rsffz78buraprvzlfo/LAaG_Seminar_8.pdf?rlkey=98o6gc0rjl4h6r9djdrasfwu8&amp;st=8zetjdlw&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> <br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/74v0d0eiofll1maa9jznn/LAaG_HW_29_C-246.pdf?rlkey=tkc9a738pz8ucsmoj1qa098to&amp;st=qjp6gids&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/dhn85atazelewt7hga4wm/LAaG_HW_28_C-246.pdf?rlkey=uuzzqtp8e19fwc9ed4cqity13&amp;st=cf0kk85z&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oipf5pzr862yxj8hzws0q/LAaG_HW_27_C-246.pdf?rlkey=8zm2hmvtcxaxl7gup9fhlskv4&amp;st=r2p4k1ki&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/f0ecohy3h75i4tteco78g/LAaG_HW_26_C-246.pdf?rlkey=4d2hnuddvguzw9brt08t7jfpv&amp;st=z8e70o5z&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lwvmio1folirvyij2c5te/LAaG_HW_25_C-246.pdf?rlkey=zg38wdf05opaxmuq6zfkuhsgk&amp;st=wd20mn6i&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/ais924pz2nlej2c2xggik/LAaG_HW_24_C-246.pdf?rlkey=cr3yzxr1sewhfckkas418wwlu&amp;st=cj12kvrx&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/jexjsl0jrgaui9o4nf9jl/LAaG_HW_23_C-246.pdf?rlkey=6v42cmsbukuljstxc1rw5nj2s&amp;st=3yw1rrh6&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6tnjv2kxwum90bwwklak5/LAaG_HW_22_C-246.pdf?rlkey=ml6hgg2cqnafwvhpuoe15vqsw&amp;st=xrgch4zx&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sadhn3ahnqtik4awr2tj4/LAaG_HW_21_C-246.pdf?rlkey=hs3dyl8ig4s6ygwvxyqtzgrez&amp;st=ndz29dpb&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/qurd5huy43ihn1z6a4u5g/LAaG_HW_20_C-246.pdf?rlkey=4js3uvv10nvnwxfijskwo1beg&amp;st=z6izkugw&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lit3st83vxamv4yoeux14/LAaG_HW_19_C-246.pdf?rlkey=md0jtmyyol74p3grsobpdn398&amp;st=khkc0ona&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zj4cmy6yvtb0voer5nxsz/LAaG_HW_18_C-246.pdf?rlkey=m9sfdgy428uwooyto3jc0v2n2&amp;st=3cqiogo3&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3f4p41sixiwspbws1zuyp/LAaG_HW_17_C-246.pdf?rlkey=mc9tkb24whvre9rjaa2yy4yy5&amp;st=3uly6rcr&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wwkr4nrvemckinbvlfpf4/LAaG_HW_16_C-246.pdf?rlkey=d36aqvm4sl5ymrhc9689skqmh&amp;st=ytwxjuiy&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vvxf2ix4aohlrme23iio3/LAaG_HW_15_C-246.pdf?rlkey=pz848a5pnq4x1o7192t9e3ja8&amp;st=bzl0fx87&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v60x5jr3qtp5nu1ddsywa/LAaG_HW_13_C-246.pdf?rlkey=b9zsc00sn81zfi4zlorrp1dqu&amp;st=3y4vawm7&amp;dl=0 '''HW 13'''] (release: 10.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/oqw6b4jgz5a133g1cssmw/LAaG_HW_12_C-246.pdf?rlkey=5w5gqusl520nxxzumh761y4jb&amp;st=xii5fvfc&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/z80z8a3xan9vxu4abcqah/LAaG_HW_11_C-246.pdf?rlkey=fe836n2dzg580je9n8rr2wf8e&amp;st=vts0p3p2&amp;dl=0 '''HW 11'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/klzrlfot6t4v6rfbfd02q/LAaG_HW_10_C-246.pdf?rlkey=su9akh09k4mnz4unedoqlhc90&amp;st=2ab1uvrj&amp;dl=0 '''HW 10'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6xjvw47ehtwt2ku62y9h8/LAaG_HW_9_C-246.pdf?rlkey=fjp37n3b0f3kgqivb9mtfy9tz&amp;st=6oj9hjsk&amp;dl=0 '''HW 9'''] (release: 12.11.24; deadline: 19.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/vpmwnqengjj2g9nn6zf9p/LAaG_HW_8_C-246.pdf?rlkey=7qlhr2wtmtm9lkbwf6i9coipg&amp;st=wumfffop&amp;dl=0 '''HW 8'''] (release: 07.11.24; deadline: 17.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/fupbesmknyp4bgm9sygca/LAaG_Sem_8_07_11_24_g246.pdf?rlkey=telxxvgpcx3tj70flyjye7aoc&amp;st=5dnddh72&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=90847 LAaG DSBA 2024/2025 2025-05-13T16:46:55Z <p>Vvbalakirev: /* Homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 4 '''<br /> * [https://www.dropbox.com/s/km7z6bed527pfgm/LAaG_Lecture_30.pdf?dl=0 '''Lecture 29'''] (12.05.2025) Orthogonality in Euclidian spaces; orthogonal and orthonormal sets and bases; Gram-Schmidt process; the orthogonal complement and its main properties; the projection and the rejection of a vector.<br /> <br /> * [https://www.dropbox.com/s/6wn3z42bzvrg5or/LAaG_Lecture_29.pdf?dl=0 '''Lecture 28'''] (28.04.2025) Euclidean spaces; scalar product; the norm of a vector; Cauchy–Schwarz inequality; the angle between two vectors; the Gram matrix and its main properties.<br /> <br /> * [https://www.dropbox.com/s/gkxple1prqauxoa/LAaG_Lecture_28.pdf?dl=0 '''Lecture 27'''] (21.04.2025) Quadratic forms (Part III); The Jacobi theorem; normal bases and the normal form of a quadratic form; the positive and negative indices of inertia, the signature of a quadratic form; the Sylvester law of inertia; positive (semi)-definite and negative (semi)-definite quadratic forms; the Sylvester criterion.<br /> <br /> * [https://www.dropbox.com/s/wpo6qnbxviol7u6/LAaG_Lecture_26.pdf?dl=0 '''Lecture 26'''] (14.04.2025) Quadratic forms; associated bilinear form; coordinate matrix of a quadratic form; canonical basis and canonical form of a quadratic form.<br /> <br /> * [https://www.dropbox.com/s/cfb54jzd2qdn0ze/LAaG_Lecture_25.pdf?dl=0 '''Lecture 25'''] (07.04.2025) Bilinear Forms; a coordinate matrix of a bilinear form; change-of-basis formula for bilinear forms; symmetric and skew-summetric bilinear forms. Quadratic forms; the associated bilinear form of a quadratic form.<br /> <br /> ''' Module 3 '''<br /> * [https://www.dropbox.com/s/3at8g01dkxwjn7y/LAaG_Lecture_24.pdf?dl=0 '''Lecture 24'''] (17.03.2025) Linear operators (Part IV); Jordan matrix; Jordan normal form; Jordan basis; Jordan basis theorem (without proof); Cayley-Hamilton theorem. Linear Functionals; dual space; dual basis; isomorphism between V and V*.<br /> <br /> * [https://www.dropbox.com/s/bh2gbw88rixc8e7/LAaG_Lecture_23.pdf?dl=0 '''Lecture 23'''] (10.03.2025) Linear operators (Part III); diagonalizability of a linear operator; inequality between algebraic and geometric multiplicities; criteria of diagonalizability.<br /> <br /> * [https://www.dropbox.com/s/76ydfixppp12cik/LAaG_Lecture_22.pdf?dl=0 '''Lecture 22'''] (03.03.2025) Linear operators (Part II); vector space of linear operators; the characteristic polynomial of a linear operator; algebraic and geometric multiplicity of an eigenvalue.<br /> <br /> * [https://www.dropbox.com/s/e9w3h8vqa5slwjz/LAaG_Lecture_21.pdf?dl=0 '''Lecture 21'''] (24.02.2025) Linear operators; the rank, the determinant, and the trace of a linear operator; invariant subspaces; eigenvectors and eigenvalues of a linear operator.<br /> <br /> * [https://www.dropbox.com/s/kzatlshdq6gj5zk/LAaG_Lecture_20.pdf?dl=0 '''Lecture 20'''] (17.02.2025) Linear Transformations (Part III: injectivity and surjectivity of linear transformations) injective and surjective linear transformations; isomorphisms (=linear bijections) of vector spaces; the inverse of an isomorphism; the fact that two finite dimensional vector spaces are isomorphic if and only if they both have the same dimension.<br /> <br /> * [https://www.dropbox.com/s/vczbkb79w67r4tk/LAaG_Lecture_19.pdf?dl=0 '''Lecture 19'''] (10.02.2025) Linear Transformations (Part II: matrix representation and change of basis); coordinate matrices of a linear transformation; coordinate matrix of a composition of linear transformations; change of basis.<br /> <br /> * [https://www.dropbox.com/s/is0p1nou922zynj/LAaG_Lecture_18.pdf?dl=0 '''Lecture 18'''] (03.02.2025) Linear Transformations; main properties of linear transformations; the image and the kernel of a linear transformation; singular and non-singular linear transformations; the rank and the nullity of a linear transformation.<br /> <br /> * [https://www.dropbox.com/s/td8df813s2lh38b/LAaG_Lecture_17.pdf?dl=0 '''Lecture 17'''] (27.01.2025) The rank of a matrix (Part II); we prove that the column rank equals the row rank.<br /> <br /> * [https://www.dropbox.com/s/nf44zccqg3rythp/LAaG_Lecture_16.pdf?dl=0 '''Lecture 16'''] (20.01.2025) The direct sum of subspaces; main properties of the direct sum; the rank of a matrix; column and row spaces of a matrix; column and row ranks of a matrix.<br /> <br /> * [https://www.dropbox.com/s/cl7djenawtlgp0o/LAaG_Lecture_15.pdf?dl=0 '''Lecture 15'''] (13.01.2025) Main properties of change of basis matrices; the sum, the intersection, and the direct sum of vector subspaces; the dimension of the sum of two vector subspaces.<br /> <br /> ''' Module 2 '''<br /> * [https://www.dropbox.com/s/pozm47tzgaibf4k/LAaG_Lecture_14.pdf?dl=0 '''Lecture 14'''] (16.12.2024) Vector spaces (Part III); m-element subsets of an n-dimensional vector space; extension to a basis; the dimension of a subspace of a finite dimensional vector space; ordered basis; basis matrix; change of basis matrix.<br /> <br /> * [https://www.dropbox.com/s/10v3w4efz6zi332/LAaG_Lecture_13.pdf?dl=0 '''Lecture 13'''] (09.12.2024) Vector spaces (Part II); Main theorem on linear dependence; a basis of a vector space; dimension of a vector space; finite and infinite dimensional vector spaces; some main properties of finite dimensional vector spaces.<br /> <br /> * [https://www.dropbox.com/s/snko9y9r7ccw8qk/LAaG_Lecture_12.pdf?dl=0 '''Lecture 12'''] (01.12.2024) Vector spaces (Part I); a subspace of a vector space; linear combinations; the linear span; trivial and non-trivial linear combinations; linearly dependent and linearly independent sets.<br /> <br /> * [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (25.11.2024) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br /> <br /> * [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (18.11.2024) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br /> <br /> * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (11.11.2024) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br /> <br /> * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (02.11.2024) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/iw4d8eyjayzff9kfcj33r/LAaG_HW_29_C-241.pdf?rlkey=r7mvkq3f3tipvcphvmbcs7wy9&amp;st=ftkay74b&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ew31593pflcym5wtj0een/LAaG_HW_28_C-241.pdf?rlkey=66wd02998pic8x3t24061cdbh&amp;st=q296xsgc&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sc0udwvted1nn1quz4zou/LAaG_HW_27_C-241.pdf?rlkey=s47ayfwajc9lqod48xt5tx4wa&amp;st=qd7b4y7z&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/myc8320hx3njihu24cuba/LAaG_HW_26_C-241.pdf?rlkey=23sq1u6qrb9xevdrzaoutqxca&amp;st=1jmhwafo&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/cva01p9hh7qdtagzl3kn3/LAaG_HW_25_C-241.pdf?rlkey=yal3zb4maa7zwdvqxcecssjkg&amp;st=sg8pbd9k&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/7lpp0i0xjelgq0gp35e4n/LAaG_HW_24_C-241.pdf?rlkey=a582n8pburjgu2j8510gzn83r&amp;st=2q6voag2&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/4a54pbfd61aoprnxwzu0x/LAaG_HW_23_C-241.pdf?rlkey=fe69qd7iarodjou59nsfrr6sh&amp;st=pg55d94h&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/0bwlj7nva3781wif2lht4/LAaG_HW_22_C-241.pdf?rlkey=zvnp3kg68lfgl1psi4oey1duy&amp;st=erjtper3&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/r2d0fnyhorbud4w97cw8p/LAaG_HW_21_C-241.pdf?rlkey=jge0vzkbwpun9stgsnqk1xa15&amp;st=bdihujff&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tej4f5c5io1742pc958k6/LAaG_HW_20_C-241.pdf?rlkey=j1c0yag295f53gydl5rsc2o10&amp;st=fetq10zo&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/o2624ddh1r58a3ek8v723/LAaG_HW_19_C-241.pdf?rlkey=5ztkckb96zjcydhnk7x88en29&amp;st=bg5891g6&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zpc9ji9p84zvz5mi9vws9/LAaG_HW_18_C-241.pdf?rlkey=cfv4sqgw7kvcu4wbcata3fab3&amp;st=e2c6jr7e&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vthiyr2dpqrgggx8rwc5n/LAaG_HW_17_C-241.pdf?rlkey=rfchkhjrs96c4as6z0f68005h&amp;st=agspv924&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jk1qemu09cq5pzt2mpu58/LAaG_HW_16_C-241.pdf?rlkey=565cdf9qndljixsg2hm9pgs85&amp;st=u4i6x9g4&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/e0l37mfgqhgzhc35xvv85/LAaG_HW_15_C-241.pdf?rlkey=td1du8a0w5goaf0kk1e1doh02&amp;st=dmouas60&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gfanxb92qos5yrw2rw9up/LAaG_HW_13_C-241.pdf?rlkey=3lieu7597p86akdubpgblrxv1&amp;st=tzrb0x2w&amp;dl=0 '''HW 13'''] (release: 09.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/98g4oshs0lkwzfkq7ws2o/LAaG_HW_12_C-241.pdf?rlkey=ir2gfbgas5zecrt3de03anocx&amp;st=huaalfyu&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bkwvo24thkydotpkqjv7s/LAaG_HW_11_C-241.pdf?rlkey=vw1rwyesz3cfvizb88ukwbk5c&amp;st=6lzvxcfd&amp;dl=0 '''HW 11'''] (release: 25.11.24; deadline: 02.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tz95u31aralzb00htmpfr/LAaG_HW_10_C-241.pdf?rlkey=kvbdd60wu3jaj908hve2amrb7&amp;st=kiam0tz0&amp;dl=0 '''HW 10'''] (release: 18.11.24; deadline: 25.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9icdl8t78tqqaszgnh1ex/LAaG_HW_9_C-241.pdf?rlkey=obf47jl5bm91hmrlinhymmu5a&amp;st=8pldj7gq&amp;dl=0 '''HW 9'''] (release: 11.11.24; deadline: 18.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/cuah8c9c3lm3qjxw16paw/LAaG_HW_8_C-241.pdf?rlkey=iaedxga7hdn89904yo3rirtrs&amp;st=6lvpxxgl&amp;dl=0 '''HW 8'''] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/619rsffz78buraprvzlfo/LAaG_Seminar_8.pdf?rlkey=98o6gc0rjl4h6r9djdrasfwu8&amp;st=8zetjdlw&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> <br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/74v0d0eiofll1maa9jznn/LAaG_HW_29_C-246.pdf?rlkey=tkc9a738pz8ucsmoj1qa098to&amp;st=qjp6gids&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/dhn85atazelewt7hga4wm/LAaG_HW_28_C-246.pdf?rlkey=uuzzqtp8e19fwc9ed4cqity13&amp;st=cf0kk85z&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oipf5pzr862yxj8hzws0q/LAaG_HW_27_C-246.pdf?rlkey=8zm2hmvtcxaxl7gup9fhlskv4&amp;st=r2p4k1ki&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/f0ecohy3h75i4tteco78g/LAaG_HW_26_C-246.pdf?rlkey=4d2hnuddvguzw9brt08t7jfpv&amp;st=z8e70o5z&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lwvmio1folirvyij2c5te/LAaG_HW_25_C-246.pdf?rlkey=zg38wdf05opaxmuq6zfkuhsgk&amp;st=wd20mn6i&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/ais924pz2nlej2c2xggik/LAaG_HW_24_C-246.pdf?rlkey=cr3yzxr1sewhfckkas418wwlu&amp;st=cj12kvrx&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/jexjsl0jrgaui9o4nf9jl/LAaG_HW_23_C-246.pdf?rlkey=6v42cmsbukuljstxc1rw5nj2s&amp;st=3yw1rrh6&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6tnjv2kxwum90bwwklak5/LAaG_HW_22_C-246.pdf?rlkey=ml6hgg2cqnafwvhpuoe15vqsw&amp;st=xrgch4zx&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sadhn3ahnqtik4awr2tj4/LAaG_HW_21_C-246.pdf?rlkey=hs3dyl8ig4s6ygwvxyqtzgrez&amp;st=ndz29dpb&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/qurd5huy43ihn1z6a4u5g/LAaG_HW_20_C-246.pdf?rlkey=4js3uvv10nvnwxfijskwo1beg&amp;st=z6izkugw&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lit3st83vxamv4yoeux14/LAaG_HW_19_C-246.pdf?rlkey=md0jtmyyol74p3grsobpdn398&amp;st=khkc0ona&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zj4cmy6yvtb0voer5nxsz/LAaG_HW_18_C-246.pdf?rlkey=m9sfdgy428uwooyto3jc0v2n2&amp;st=3cqiogo3&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3f4p41sixiwspbws1zuyp/LAaG_HW_17_C-246.pdf?rlkey=mc9tkb24whvre9rjaa2yy4yy5&amp;st=3uly6rcr&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wwkr4nrvemckinbvlfpf4/LAaG_HW_16_C-246.pdf?rlkey=d36aqvm4sl5ymrhc9689skqmh&amp;st=ytwxjuiy&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vvxf2ix4aohlrme23iio3/LAaG_HW_15_C-246.pdf?rlkey=pz848a5pnq4x1o7192t9e3ja8&amp;st=bzl0fx87&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v60x5jr3qtp5nu1ddsywa/LAaG_HW_13_C-246.pdf?rlkey=b9zsc00sn81zfi4zlorrp1dqu&amp;st=3y4vawm7&amp;dl=0 '''HW 13'''] (release: 10.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/oqw6b4jgz5a133g1cssmw/LAaG_HW_12_C-246.pdf?rlkey=5w5gqusl520nxxzumh761y4jb&amp;st=xii5fvfc&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/z80z8a3xan9vxu4abcqah/LAaG_HW_11_C-246.pdf?rlkey=fe836n2dzg580je9n8rr2wf8e&amp;st=vts0p3p2&amp;dl=0 '''HW 11'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/klzrlfot6t4v6rfbfd02q/LAaG_HW_10_C-246.pdf?rlkey=su9akh09k4mnz4unedoqlhc90&amp;st=2ab1uvrj&amp;dl=0 '''HW 10'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6xjvw47ehtwt2ku62y9h8/LAaG_HW_9_C-246.pdf?rlkey=fjp37n3b0f3kgqivb9mtfy9tz&amp;st=6oj9hjsk&amp;dl=0 '''HW 9'''] (release: 12.11.24; deadline: 19.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/vpmwnqengjj2g9nn6zf9p/LAaG_HW_8_C-246.pdf?rlkey=7qlhr2wtmtm9lkbwf6i9coipg&amp;st=wumfffop&amp;dl=0 '''HW 8'''] (release: 07.11.24; deadline: 17.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/fupbesmknyp4bgm9sygca/LAaG_Sem_8_07_11_24_g246.pdf?rlkey=telxxvgpcx3tj70flyjye7aoc&amp;st=5dnddh72&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=90846 LAaG DSBA 2024/2025 2025-05-13T16:45:51Z <p>Vvbalakirev: /* Homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 4 '''<br /> * [https://www.dropbox.com/s/km7z6bed527pfgm/LAaG_Lecture_30.pdf?dl=0 '''Lecture 29'''] (12.05.2025) Orthogonality in Euclidian spaces; orthogonal and orthonormal sets and bases; Gram-Schmidt process; the orthogonal complement and its main properties; the projection and the rejection of a vector.<br /> <br /> * [https://www.dropbox.com/s/6wn3z42bzvrg5or/LAaG_Lecture_29.pdf?dl=0 '''Lecture 28'''] (28.04.2025) Euclidean spaces; scalar product; the norm of a vector; Cauchy–Schwarz inequality; the angle between two vectors; the Gram matrix and its main properties.<br /> <br /> * [https://www.dropbox.com/s/gkxple1prqauxoa/LAaG_Lecture_28.pdf?dl=0 '''Lecture 27'''] (21.04.2025) Quadratic forms (Part III); The Jacobi theorem; normal bases and the normal form of a quadratic form; the positive and negative indices of inertia, the signature of a quadratic form; the Sylvester law of inertia; positive (semi)-definite and negative (semi)-definite quadratic forms; the Sylvester criterion.<br /> <br /> * [https://www.dropbox.com/s/wpo6qnbxviol7u6/LAaG_Lecture_26.pdf?dl=0 '''Lecture 26'''] (14.04.2025) Quadratic forms; associated bilinear form; coordinate matrix of a quadratic form; canonical basis and canonical form of a quadratic form.<br /> <br /> * [https://www.dropbox.com/s/cfb54jzd2qdn0ze/LAaG_Lecture_25.pdf?dl=0 '''Lecture 25'''] (07.04.2025) Bilinear Forms; a coordinate matrix of a bilinear form; change-of-basis formula for bilinear forms; symmetric and skew-summetric bilinear forms. Quadratic forms; the associated bilinear form of a quadratic form.<br /> <br /> ''' Module 3 '''<br /> * [https://www.dropbox.com/s/3at8g01dkxwjn7y/LAaG_Lecture_24.pdf?dl=0 '''Lecture 24'''] (17.03.2025) Linear operators (Part IV); Jordan matrix; Jordan normal form; Jordan basis; Jordan basis theorem (without proof); Cayley-Hamilton theorem. Linear Functionals; dual space; dual basis; isomorphism between V and V*.<br /> <br /> * [https://www.dropbox.com/s/bh2gbw88rixc8e7/LAaG_Lecture_23.pdf?dl=0 '''Lecture 23'''] (10.03.2025) Linear operators (Part III); diagonalizability of a linear operator; inequality between algebraic and geometric multiplicities; criteria of diagonalizability.<br /> <br /> * [https://www.dropbox.com/s/76ydfixppp12cik/LAaG_Lecture_22.pdf?dl=0 '''Lecture 22'''] (03.03.2025) Linear operators (Part II); vector space of linear operators; the characteristic polynomial of a linear operator; algebraic and geometric multiplicity of an eigenvalue.<br /> <br /> * [https://www.dropbox.com/s/e9w3h8vqa5slwjz/LAaG_Lecture_21.pdf?dl=0 '''Lecture 21'''] (24.02.2025) Linear operators; the rank, the determinant, and the trace of a linear operator; invariant subspaces; eigenvectors and eigenvalues of a linear operator.<br /> <br /> * [https://www.dropbox.com/s/kzatlshdq6gj5zk/LAaG_Lecture_20.pdf?dl=0 '''Lecture 20'''] (17.02.2025) Linear Transformations (Part III: injectivity and surjectivity of linear transformations) injective and surjective linear transformations; isomorphisms (=linear bijections) of vector spaces; the inverse of an isomorphism; the fact that two finite dimensional vector spaces are isomorphic if and only if they both have the same dimension.<br /> <br /> * [https://www.dropbox.com/s/vczbkb79w67r4tk/LAaG_Lecture_19.pdf?dl=0 '''Lecture 19'''] (10.02.2025) Linear Transformations (Part II: matrix representation and change of basis); coordinate matrices of a linear transformation; coordinate matrix of a composition of linear transformations; change of basis.<br /> <br /> * [https://www.dropbox.com/s/is0p1nou922zynj/LAaG_Lecture_18.pdf?dl=0 '''Lecture 18'''] (03.02.2025) Linear Transformations; main properties of linear transformations; the image and the kernel of a linear transformation; singular and non-singular linear transformations; the rank and the nullity of a linear transformation.<br /> <br /> * [https://www.dropbox.com/s/td8df813s2lh38b/LAaG_Lecture_17.pdf?dl=0 '''Lecture 17'''] (27.01.2025) The rank of a matrix (Part II); we prove that the column rank equals the row rank.<br /> <br /> * [https://www.dropbox.com/s/nf44zccqg3rythp/LAaG_Lecture_16.pdf?dl=0 '''Lecture 16'''] (20.01.2025) The direct sum of subspaces; main properties of the direct sum; the rank of a matrix; column and row spaces of a matrix; column and row ranks of a matrix.<br /> <br /> * [https://www.dropbox.com/s/cl7djenawtlgp0o/LAaG_Lecture_15.pdf?dl=0 '''Lecture 15'''] (13.01.2025) Main properties of change of basis matrices; the sum, the intersection, and the direct sum of vector subspaces; the dimension of the sum of two vector subspaces.<br /> <br /> ''' Module 2 '''<br /> * [https://www.dropbox.com/s/pozm47tzgaibf4k/LAaG_Lecture_14.pdf?dl=0 '''Lecture 14'''] (16.12.2024) Vector spaces (Part III); m-element subsets of an n-dimensional vector space; extension to a basis; the dimension of a subspace of a finite dimensional vector space; ordered basis; basis matrix; change of basis matrix.<br /> <br /> * [https://www.dropbox.com/s/10v3w4efz6zi332/LAaG_Lecture_13.pdf?dl=0 '''Lecture 13'''] (09.12.2024) Vector spaces (Part II); Main theorem on linear dependence; a basis of a vector space; dimension of a vector space; finite and infinite dimensional vector spaces; some main properties of finite dimensional vector spaces.<br /> <br /> * [https://www.dropbox.com/s/snko9y9r7ccw8qk/LAaG_Lecture_12.pdf?dl=0 '''Lecture 12'''] (01.12.2024) Vector spaces (Part I); a subspace of a vector space; linear combinations; the linear span; trivial and non-trivial linear combinations; linearly dependent and linearly independent sets.<br /> <br /> * [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (25.11.2024) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br /> <br /> * [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (18.11.2024) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br /> <br /> * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (11.11.2024) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br /> <br /> * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (02.11.2024) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/iw4d8eyjayzff9kfcj33r/LAaG_HW_29_C-241.pdf?rlkey=r7mvkq3f3tipvcphvmbcs7wy9&amp;st=ftkay74b&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ew31593pflcym5wtj0een/LAaG_HW_28_C-241.pdf?rlkey=66wd02998pic8x3t24061cdbh&amp;st=q296xsgc&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sc0udwvted1nn1quz4zou/LAaG_HW_27_C-241.pdf?rlkey=s47ayfwajc9lqod48xt5tx4wa&amp;st=qd7b4y7z&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/myc8320hx3njihu24cuba/LAaG_HW_26_C-241.pdf?rlkey=23sq1u6qrb9xevdrzaoutqxca&amp;st=1jmhwafo&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/cva01p9hh7qdtagzl3kn3/LAaG_HW_25_C-241.pdf?rlkey=yal3zb4maa7zwdvqxcecssjkg&amp;st=sg8pbd9k&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/7lpp0i0xjelgq0gp35e4n/LAaG_HW_24_C-241.pdf?rlkey=a582n8pburjgu2j8510gzn83r&amp;st=2q6voag2&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/4a54pbfd61aoprnxwzu0x/LAaG_HW_23_C-241.pdf?rlkey=fe69qd7iarodjou59nsfrr6sh&amp;st=pg55d94h&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/0bwlj7nva3781wif2lht4/LAaG_HW_22_C-241.pdf?rlkey=zvnp3kg68lfgl1psi4oey1duy&amp;st=erjtper3&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/r2d0fnyhorbud4w97cw8p/LAaG_HW_21_C-241.pdf?rlkey=jge0vzkbwpun9stgsnqk1xa15&amp;st=bdihujff&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tej4f5c5io1742pc958k6/LAaG_HW_20_C-241.pdf?rlkey=j1c0yag295f53gydl5rsc2o10&amp;st=fetq10zo&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/o2624ddh1r58a3ek8v723/LAaG_HW_19_C-241.pdf?rlkey=5ztkckb96zjcydhnk7x88en29&amp;st=bg5891g6&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zpc9ji9p84zvz5mi9vws9/LAaG_HW_18_C-241.pdf?rlkey=cfv4sqgw7kvcu4wbcata3fab3&amp;st=e2c6jr7e&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vthiyr2dpqrgggx8rwc5n/LAaG_HW_17_C-241.pdf?rlkey=rfchkhjrs96c4as6z0f68005h&amp;st=agspv924&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jk1qemu09cq5pzt2mpu58/LAaG_HW_16_C-241.pdf?rlkey=565cdf9qndljixsg2hm9pgs85&amp;st=u4i6x9g4&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/e0l37mfgqhgzhc35xvv85/LAaG_HW_15_C-241.pdf?rlkey=td1du8a0w5goaf0kk1e1doh02&amp;st=dmouas60&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gfanxb92qos5yrw2rw9up/LAaG_HW_13_C-241.pdf?rlkey=3lieu7597p86akdubpgblrxv1&amp;st=tzrb0x2w&amp;dl=0 '''HW 13'''] (release: 09.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/98g4oshs0lkwzfkq7ws2o/LAaG_HW_12_C-241.pdf?rlkey=ir2gfbgas5zecrt3de03anocx&amp;st=huaalfyu&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bkwvo24thkydotpkqjv7s/LAaG_HW_11_C-241.pdf?rlkey=vw1rwyesz3cfvizb88ukwbk5c&amp;st=6lzvxcfd&amp;dl=0 '''HW 11'''] (release: 25.11.24; deadline: 02.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tz95u31aralzb00htmpfr/LAaG_HW_10_C-241.pdf?rlkey=kvbdd60wu3jaj908hve2amrb7&amp;st=kiam0tz0&amp;dl=0 '''HW 10'''] (release: 18.11.24; deadline: 25.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9icdl8t78tqqaszgnh1ex/LAaG_HW_9_C-241.pdf?rlkey=obf47jl5bm91hmrlinhymmu5a&amp;st=8pldj7gq&amp;dl=0 '''HW 9'''] (release: 11.11.24; deadline: 18.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/cuah8c9c3lm3qjxw16paw/LAaG_HW_8_C-241.pdf?rlkey=iaedxga7hdn89904yo3rirtrs&amp;st=6lvpxxgl&amp;dl=0 '''HW 8'''] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/619rsffz78buraprvzlfo/LAaG_Seminar_8.pdf?rlkey=98o6gc0rjl4h6r9djdrasfwu8&amp;st=8zetjdlw&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> <br /> === Homework for group 242: ===<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/0nqi1gu8h1amuwb1hkn5y/242_3-Homework-25.pdf?rlkey=0t74jclc1s3u4ky0ifi9es87x&amp;st=o87f0h5q&amp;dl=0'''HW 25''']<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/74v0d0eiofll1maa9jznn/LAaG_HW_29_C-246.pdf?rlkey=tkc9a738pz8ucsmoj1qa098to&amp;st=qjp6gids&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/dhn85atazelewt7hga4wm/LAaG_HW_28_C-246.pdf?rlkey=uuzzqtp8e19fwc9ed4cqity13&amp;st=cf0kk85z&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oipf5pzr862yxj8hzws0q/LAaG_HW_27_C-246.pdf?rlkey=8zm2hmvtcxaxl7gup9fhlskv4&amp;st=r2p4k1ki&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/f0ecohy3h75i4tteco78g/LAaG_HW_26_C-246.pdf?rlkey=4d2hnuddvguzw9brt08t7jfpv&amp;st=z8e70o5z&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lwvmio1folirvyij2c5te/LAaG_HW_25_C-246.pdf?rlkey=zg38wdf05opaxmuq6zfkuhsgk&amp;st=wd20mn6i&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/ais924pz2nlej2c2xggik/LAaG_HW_24_C-246.pdf?rlkey=cr3yzxr1sewhfckkas418wwlu&amp;st=cj12kvrx&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/jexjsl0jrgaui9o4nf9jl/LAaG_HW_23_C-246.pdf?rlkey=6v42cmsbukuljstxc1rw5nj2s&amp;st=3yw1rrh6&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6tnjv2kxwum90bwwklak5/LAaG_HW_22_C-246.pdf?rlkey=ml6hgg2cqnafwvhpuoe15vqsw&amp;st=xrgch4zx&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sadhn3ahnqtik4awr2tj4/LAaG_HW_21_C-246.pdf?rlkey=hs3dyl8ig4s6ygwvxyqtzgrez&amp;st=ndz29dpb&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/qurd5huy43ihn1z6a4u5g/LAaG_HW_20_C-246.pdf?rlkey=4js3uvv10nvnwxfijskwo1beg&amp;st=z6izkugw&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lit3st83vxamv4yoeux14/LAaG_HW_19_C-246.pdf?rlkey=md0jtmyyol74p3grsobpdn398&amp;st=khkc0ona&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zj4cmy6yvtb0voer5nxsz/LAaG_HW_18_C-246.pdf?rlkey=m9sfdgy428uwooyto3jc0v2n2&amp;st=3cqiogo3&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3f4p41sixiwspbws1zuyp/LAaG_HW_17_C-246.pdf?rlkey=mc9tkb24whvre9rjaa2yy4yy5&amp;st=3uly6rcr&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wwkr4nrvemckinbvlfpf4/LAaG_HW_16_C-246.pdf?rlkey=d36aqvm4sl5ymrhc9689skqmh&amp;st=ytwxjuiy&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vvxf2ix4aohlrme23iio3/LAaG_HW_15_C-246.pdf?rlkey=pz848a5pnq4x1o7192t9e3ja8&amp;st=bzl0fx87&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v60x5jr3qtp5nu1ddsywa/LAaG_HW_13_C-246.pdf?rlkey=b9zsc00sn81zfi4zlorrp1dqu&amp;st=3y4vawm7&amp;dl=0 '''HW 13'''] (release: 10.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/oqw6b4jgz5a133g1cssmw/LAaG_HW_12_C-246.pdf?rlkey=5w5gqusl520nxxzumh761y4jb&amp;st=xii5fvfc&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/z80z8a3xan9vxu4abcqah/LAaG_HW_11_C-246.pdf?rlkey=fe836n2dzg580je9n8rr2wf8e&amp;st=vts0p3p2&amp;dl=0 '''HW 11'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/klzrlfot6t4v6rfbfd02q/LAaG_HW_10_C-246.pdf?rlkey=su9akh09k4mnz4unedoqlhc90&amp;st=2ab1uvrj&amp;dl=0 '''HW 10'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6xjvw47ehtwt2ku62y9h8/LAaG_HW_9_C-246.pdf?rlkey=fjp37n3b0f3kgqivb9mtfy9tz&amp;st=6oj9hjsk&amp;dl=0 '''HW 9'''] (release: 12.11.24; deadline: 19.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/vpmwnqengjj2g9nn6zf9p/LAaG_HW_8_C-246.pdf?rlkey=7qlhr2wtmtm9lkbwf6i9coipg&amp;st=wumfffop&amp;dl=0 '''HW 8'''] (release: 07.11.24; deadline: 17.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/fupbesmknyp4bgm9sygca/LAaG_Sem_8_07_11_24_g246.pdf?rlkey=telxxvgpcx3tj70flyjye7aoc&amp;st=5dnddh72&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=90845 LAaG DSBA 2024/2025 2025-05-13T16:44:02Z <p>Vvbalakirev: /* Homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 4 '''<br /> * [https://www.dropbox.com/s/km7z6bed527pfgm/LAaG_Lecture_30.pdf?dl=0 '''Lecture 29'''] (12.05.2025) Orthogonality in Euclidian spaces; orthogonal and orthonormal sets and bases; Gram-Schmidt process; the orthogonal complement and its main properties; the projection and the rejection of a vector.<br /> <br /> * [https://www.dropbox.com/s/6wn3z42bzvrg5or/LAaG_Lecture_29.pdf?dl=0 '''Lecture 28'''] (28.04.2025) Euclidean spaces; scalar product; the norm of a vector; Cauchy–Schwarz inequality; the angle between two vectors; the Gram matrix and its main properties.<br /> <br /> * [https://www.dropbox.com/s/gkxple1prqauxoa/LAaG_Lecture_28.pdf?dl=0 '''Lecture 27'''] (21.04.2025) Quadratic forms (Part III); The Jacobi theorem; normal bases and the normal form of a quadratic form; the positive and negative indices of inertia, the signature of a quadratic form; the Sylvester law of inertia; positive (semi)-definite and negative (semi)-definite quadratic forms; the Sylvester criterion.<br /> <br /> * [https://www.dropbox.com/s/wpo6qnbxviol7u6/LAaG_Lecture_26.pdf?dl=0 '''Lecture 26'''] (14.04.2025) Quadratic forms; associated bilinear form; coordinate matrix of a quadratic form; canonical basis and canonical form of a quadratic form.<br /> <br /> * [https://www.dropbox.com/s/cfb54jzd2qdn0ze/LAaG_Lecture_25.pdf?dl=0 '''Lecture 25'''] (07.04.2025) Bilinear Forms; a coordinate matrix of a bilinear form; change-of-basis formula for bilinear forms; symmetric and skew-summetric bilinear forms. Quadratic forms; the associated bilinear form of a quadratic form.<br /> <br /> ''' Module 3 '''<br /> * [https://www.dropbox.com/s/3at8g01dkxwjn7y/LAaG_Lecture_24.pdf?dl=0 '''Lecture 24'''] (17.03.2025) Linear operators (Part IV); Jordan matrix; Jordan normal form; Jordan basis; Jordan basis theorem (without proof); Cayley-Hamilton theorem. Linear Functionals; dual space; dual basis; isomorphism between V and V*.<br /> <br /> * [https://www.dropbox.com/s/bh2gbw88rixc8e7/LAaG_Lecture_23.pdf?dl=0 '''Lecture 23'''] (10.03.2025) Linear operators (Part III); diagonalizability of a linear operator; inequality between algebraic and geometric multiplicities; criteria of diagonalizability.<br /> <br /> * [https://www.dropbox.com/s/76ydfixppp12cik/LAaG_Lecture_22.pdf?dl=0 '''Lecture 22'''] (03.03.2025) Linear operators (Part II); vector space of linear operators; the characteristic polynomial of a linear operator; algebraic and geometric multiplicity of an eigenvalue.<br /> <br /> * [https://www.dropbox.com/s/e9w3h8vqa5slwjz/LAaG_Lecture_21.pdf?dl=0 '''Lecture 21'''] (24.02.2025) Linear operators; the rank, the determinant, and the trace of a linear operator; invariant subspaces; eigenvectors and eigenvalues of a linear operator.<br /> <br /> * [https://www.dropbox.com/s/kzatlshdq6gj5zk/LAaG_Lecture_20.pdf?dl=0 '''Lecture 20'''] (17.02.2025) Linear Transformations (Part III: injectivity and surjectivity of linear transformations) injective and surjective linear transformations; isomorphisms (=linear bijections) of vector spaces; the inverse of an isomorphism; the fact that two finite dimensional vector spaces are isomorphic if and only if they both have the same dimension.<br /> <br /> * [https://www.dropbox.com/s/vczbkb79w67r4tk/LAaG_Lecture_19.pdf?dl=0 '''Lecture 19'''] (10.02.2025) Linear Transformations (Part II: matrix representation and change of basis); coordinate matrices of a linear transformation; coordinate matrix of a composition of linear transformations; change of basis.<br /> <br /> * [https://www.dropbox.com/s/is0p1nou922zynj/LAaG_Lecture_18.pdf?dl=0 '''Lecture 18'''] (03.02.2025) Linear Transformations; main properties of linear transformations; the image and the kernel of a linear transformation; singular and non-singular linear transformations; the rank and the nullity of a linear transformation.<br /> <br /> * [https://www.dropbox.com/s/td8df813s2lh38b/LAaG_Lecture_17.pdf?dl=0 '''Lecture 17'''] (27.01.2025) The rank of a matrix (Part II); we prove that the column rank equals the row rank.<br /> <br /> * [https://www.dropbox.com/s/nf44zccqg3rythp/LAaG_Lecture_16.pdf?dl=0 '''Lecture 16'''] (20.01.2025) The direct sum of subspaces; main properties of the direct sum; the rank of a matrix; column and row spaces of a matrix; column and row ranks of a matrix.<br /> <br /> * [https://www.dropbox.com/s/cl7djenawtlgp0o/LAaG_Lecture_15.pdf?dl=0 '''Lecture 15'''] (13.01.2025) Main properties of change of basis matrices; the sum, the intersection, and the direct sum of vector subspaces; the dimension of the sum of two vector subspaces.<br /> <br /> ''' Module 2 '''<br /> * [https://www.dropbox.com/s/pozm47tzgaibf4k/LAaG_Lecture_14.pdf?dl=0 '''Lecture 14'''] (16.12.2024) Vector spaces (Part III); m-element subsets of an n-dimensional vector space; extension to a basis; the dimension of a subspace of a finite dimensional vector space; ordered basis; basis matrix; change of basis matrix.<br /> <br /> * [https://www.dropbox.com/s/10v3w4efz6zi332/LAaG_Lecture_13.pdf?dl=0 '''Lecture 13'''] (09.12.2024) Vector spaces (Part II); Main theorem on linear dependence; a basis of a vector space; dimension of a vector space; finite and infinite dimensional vector spaces; some main properties of finite dimensional vector spaces.<br /> <br /> * [https://www.dropbox.com/s/snko9y9r7ccw8qk/LAaG_Lecture_12.pdf?dl=0 '''Lecture 12'''] (01.12.2024) Vector spaces (Part I); a subspace of a vector space; linear combinations; the linear span; trivial and non-trivial linear combinations; linearly dependent and linearly independent sets.<br /> <br /> * [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (25.11.2024) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br /> <br /> * [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (18.11.2024) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br /> <br /> * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (11.11.2024) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br /> <br /> * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (02.11.2024) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/iw4d8eyjayzff9kfcj33r/LAaG_HW_29_C-241.pdf?rlkey=r7mvkq3f3tipvcphvmbcs7wy9&amp;st=ftkay74b&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ew31593pflcym5wtj0een/LAaG_HW_28_C-241.pdf?rlkey=66wd02998pic8x3t24061cdbh&amp;st=q296xsgc&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sc0udwvted1nn1quz4zou/LAaG_HW_27_C-241.pdf?rlkey=s47ayfwajc9lqod48xt5tx4wa&amp;st=qd7b4y7z&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/myc8320hx3njihu24cuba/LAaG_HW_26_C-241.pdf?rlkey=23sq1u6qrb9xevdrzaoutqxca&amp;st=1jmhwafo&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/cva01p9hh7qdtagzl3kn3/LAaG_HW_25_C-241.pdf?rlkey=yal3zb4maa7zwdvqxcecssjkg&amp;st=sg8pbd9k&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/7lpp0i0xjelgq0gp35e4n/LAaG_HW_24_C-241.pdf?rlkey=a582n8pburjgu2j8510gzn83r&amp;st=2q6voag2&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/4a54pbfd61aoprnxwzu0x/LAaG_HW_23_C-241.pdf?rlkey=fe69qd7iarodjou59nsfrr6sh&amp;st=pg55d94h&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/0bwlj7nva3781wif2lht4/LAaG_HW_22_C-241.pdf?rlkey=zvnp3kg68lfgl1psi4oey1duy&amp;st=erjtper3&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/r2d0fnyhorbud4w97cw8p/LAaG_HW_21_C-241.pdf?rlkey=jge0vzkbwpun9stgsnqk1xa15&amp;st=bdihujff&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tej4f5c5io1742pc958k6/LAaG_HW_20_C-241.pdf?rlkey=j1c0yag295f53gydl5rsc2o10&amp;st=fetq10zo&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/o2624ddh1r58a3ek8v723/LAaG_HW_19_C-241.pdf?rlkey=5ztkckb96zjcydhnk7x88en29&amp;st=bg5891g6&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zpc9ji9p84zvz5mi9vws9/LAaG_HW_18_C-241.pdf?rlkey=cfv4sqgw7kvcu4wbcata3fab3&amp;st=e2c6jr7e&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vthiyr2dpqrgggx8rwc5n/LAaG_HW_17_C-241.pdf?rlkey=rfchkhjrs96c4as6z0f68005h&amp;st=agspv924&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jk1qemu09cq5pzt2mpu58/LAaG_HW_16_C-241.pdf?rlkey=565cdf9qndljixsg2hm9pgs85&amp;st=u4i6x9g4&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/e0l37mfgqhgzhc35xvv85/LAaG_HW_15_C-241.pdf?rlkey=td1du8a0w5goaf0kk1e1doh02&amp;st=dmouas60&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gfanxb92qos5yrw2rw9up/LAaG_HW_13_C-241.pdf?rlkey=3lieu7597p86akdubpgblrxv1&amp;st=tzrb0x2w&amp;dl=0 '''HW 13'''] (release: 09.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/98g4oshs0lkwzfkq7ws2o/LAaG_HW_12_C-241.pdf?rlkey=ir2gfbgas5zecrt3de03anocx&amp;st=huaalfyu&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bkwvo24thkydotpkqjv7s/LAaG_HW_11_C-241.pdf?rlkey=vw1rwyesz3cfvizb88ukwbk5c&amp;st=6lzvxcfd&amp;dl=0 '''HW 11'''] (release: 25.11.24; deadline: 02.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tz95u31aralzb00htmpfr/LAaG_HW_10_C-241.pdf?rlkey=kvbdd60wu3jaj908hve2amrb7&amp;st=kiam0tz0&amp;dl=0 '''HW 10'''] (release: 18.11.24; deadline: 25.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9icdl8t78tqqaszgnh1ex/LAaG_HW_9_C-241.pdf?rlkey=obf47jl5bm91hmrlinhymmu5a&amp;st=8pldj7gq&amp;dl=0 '''HW 9'''] (release: 11.11.24; deadline: 18.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/cuah8c9c3lm3qjxw16paw/LAaG_HW_8_C-241.pdf?rlkey=iaedxga7hdn89904yo3rirtrs&amp;st=6lvpxxgl&amp;dl=0 '''HW 8'''] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/619rsffz78buraprvzlfo/LAaG_Seminar_8.pdf?rlkey=98o6gc0rjl4h6r9djdrasfwu8&amp;st=8zetjdlw&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> <br /> === Homework for group 242: ===<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/5g5bdwfwkpdsy69gguldb/242_3-Homework-26..pdf?rlkey=b2jbpqnqsegx865faqm7uwd1m&amp;st=kwidsw3q&amp;dl=0'''HW 26''']<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/74v0d0eiofll1maa9jznn/LAaG_HW_29_C-246.pdf?rlkey=tkc9a738pz8ucsmoj1qa098to&amp;st=qjp6gids&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/dhn85atazelewt7hga4wm/LAaG_HW_28_C-246.pdf?rlkey=uuzzqtp8e19fwc9ed4cqity13&amp;st=cf0kk85z&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oipf5pzr862yxj8hzws0q/LAaG_HW_27_C-246.pdf?rlkey=8zm2hmvtcxaxl7gup9fhlskv4&amp;st=r2p4k1ki&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/f0ecohy3h75i4tteco78g/LAaG_HW_26_C-246.pdf?rlkey=4d2hnuddvguzw9brt08t7jfpv&amp;st=z8e70o5z&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lwvmio1folirvyij2c5te/LAaG_HW_25_C-246.pdf?rlkey=zg38wdf05opaxmuq6zfkuhsgk&amp;st=wd20mn6i&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/ais924pz2nlej2c2xggik/LAaG_HW_24_C-246.pdf?rlkey=cr3yzxr1sewhfckkas418wwlu&amp;st=cj12kvrx&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/jexjsl0jrgaui9o4nf9jl/LAaG_HW_23_C-246.pdf?rlkey=6v42cmsbukuljstxc1rw5nj2s&amp;st=3yw1rrh6&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6tnjv2kxwum90bwwklak5/LAaG_HW_22_C-246.pdf?rlkey=ml6hgg2cqnafwvhpuoe15vqsw&amp;st=xrgch4zx&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sadhn3ahnqtik4awr2tj4/LAaG_HW_21_C-246.pdf?rlkey=hs3dyl8ig4s6ygwvxyqtzgrez&amp;st=ndz29dpb&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/qurd5huy43ihn1z6a4u5g/LAaG_HW_20_C-246.pdf?rlkey=4js3uvv10nvnwxfijskwo1beg&amp;st=z6izkugw&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lit3st83vxamv4yoeux14/LAaG_HW_19_C-246.pdf?rlkey=md0jtmyyol74p3grsobpdn398&amp;st=khkc0ona&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zj4cmy6yvtb0voer5nxsz/LAaG_HW_18_C-246.pdf?rlkey=m9sfdgy428uwooyto3jc0v2n2&amp;st=3cqiogo3&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3f4p41sixiwspbws1zuyp/LAaG_HW_17_C-246.pdf?rlkey=mc9tkb24whvre9rjaa2yy4yy5&amp;st=3uly6rcr&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wwkr4nrvemckinbvlfpf4/LAaG_HW_16_C-246.pdf?rlkey=d36aqvm4sl5ymrhc9689skqmh&amp;st=ytwxjuiy&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vvxf2ix4aohlrme23iio3/LAaG_HW_15_C-246.pdf?rlkey=pz848a5pnq4x1o7192t9e3ja8&amp;st=bzl0fx87&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v60x5jr3qtp5nu1ddsywa/LAaG_HW_13_C-246.pdf?rlkey=b9zsc00sn81zfi4zlorrp1dqu&amp;st=3y4vawm7&amp;dl=0 '''HW 13'''] (release: 10.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/oqw6b4jgz5a133g1cssmw/LAaG_HW_12_C-246.pdf?rlkey=5w5gqusl520nxxzumh761y4jb&amp;st=xii5fvfc&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/z80z8a3xan9vxu4abcqah/LAaG_HW_11_C-246.pdf?rlkey=fe836n2dzg580je9n8rr2wf8e&amp;st=vts0p3p2&amp;dl=0 '''HW 11'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/klzrlfot6t4v6rfbfd02q/LAaG_HW_10_C-246.pdf?rlkey=su9akh09k4mnz4unedoqlhc90&amp;st=2ab1uvrj&amp;dl=0 '''HW 10'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6xjvw47ehtwt2ku62y9h8/LAaG_HW_9_C-246.pdf?rlkey=fjp37n3b0f3kgqivb9mtfy9tz&amp;st=6oj9hjsk&amp;dl=0 '''HW 9'''] (release: 12.11.24; deadline: 19.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/vpmwnqengjj2g9nn6zf9p/LAaG_HW_8_C-246.pdf?rlkey=7qlhr2wtmtm9lkbwf6i9coipg&amp;st=wumfffop&amp;dl=0 '''HW 8'''] (release: 07.11.24; deadline: 17.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/fupbesmknyp4bgm9sygca/LAaG_Sem_8_07_11_24_g246.pdf?rlkey=telxxvgpcx3tj70flyjye7aoc&amp;st=5dnddh72&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=90844 LAaG DSBA 2024/2025 2025-05-13T16:42:01Z <p>Vvbalakirev: /* Homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 4 '''<br /> * [https://www.dropbox.com/s/km7z6bed527pfgm/LAaG_Lecture_30.pdf?dl=0 '''Lecture 29'''] (12.05.2025) Orthogonality in Euclidian spaces; orthogonal and orthonormal sets and bases; Gram-Schmidt process; the orthogonal complement and its main properties; the projection and the rejection of a vector.<br /> <br /> * [https://www.dropbox.com/s/6wn3z42bzvrg5or/LAaG_Lecture_29.pdf?dl=0 '''Lecture 28'''] (28.04.2025) Euclidean spaces; scalar product; the norm of a vector; Cauchy–Schwarz inequality; the angle between two vectors; the Gram matrix and its main properties.<br /> <br /> * [https://www.dropbox.com/s/gkxple1prqauxoa/LAaG_Lecture_28.pdf?dl=0 '''Lecture 27'''] (21.04.2025) Quadratic forms (Part III); The Jacobi theorem; normal bases and the normal form of a quadratic form; the positive and negative indices of inertia, the signature of a quadratic form; the Sylvester law of inertia; positive (semi)-definite and negative (semi)-definite quadratic forms; the Sylvester criterion.<br /> <br /> * [https://www.dropbox.com/s/wpo6qnbxviol7u6/LAaG_Lecture_26.pdf?dl=0 '''Lecture 26'''] (14.04.2025) Quadratic forms; associated bilinear form; coordinate matrix of a quadratic form; canonical basis and canonical form of a quadratic form.<br /> <br /> * [https://www.dropbox.com/s/cfb54jzd2qdn0ze/LAaG_Lecture_25.pdf?dl=0 '''Lecture 25'''] (07.04.2025) Bilinear Forms; a coordinate matrix of a bilinear form; change-of-basis formula for bilinear forms; symmetric and skew-summetric bilinear forms. Quadratic forms; the associated bilinear form of a quadratic form.<br /> <br /> ''' Module 3 '''<br /> * [https://www.dropbox.com/s/3at8g01dkxwjn7y/LAaG_Lecture_24.pdf?dl=0 '''Lecture 24'''] (17.03.2025) Linear operators (Part IV); Jordan matrix; Jordan normal form; Jordan basis; Jordan basis theorem (without proof); Cayley-Hamilton theorem. Linear Functionals; dual space; dual basis; isomorphism between V and V*.<br /> <br /> * [https://www.dropbox.com/s/bh2gbw88rixc8e7/LAaG_Lecture_23.pdf?dl=0 '''Lecture 23'''] (10.03.2025) Linear operators (Part III); diagonalizability of a linear operator; inequality between algebraic and geometric multiplicities; criteria of diagonalizability.<br /> <br /> * [https://www.dropbox.com/s/76ydfixppp12cik/LAaG_Lecture_22.pdf?dl=0 '''Lecture 22'''] (03.03.2025) Linear operators (Part II); vector space of linear operators; the characteristic polynomial of a linear operator; algebraic and geometric multiplicity of an eigenvalue.<br /> <br /> * [https://www.dropbox.com/s/e9w3h8vqa5slwjz/LAaG_Lecture_21.pdf?dl=0 '''Lecture 21'''] (24.02.2025) Linear operators; the rank, the determinant, and the trace of a linear operator; invariant subspaces; eigenvectors and eigenvalues of a linear operator.<br /> <br /> * [https://www.dropbox.com/s/kzatlshdq6gj5zk/LAaG_Lecture_20.pdf?dl=0 '''Lecture 20'''] (17.02.2025) Linear Transformations (Part III: injectivity and surjectivity of linear transformations) injective and surjective linear transformations; isomorphisms (=linear bijections) of vector spaces; the inverse of an isomorphism; the fact that two finite dimensional vector spaces are isomorphic if and only if they both have the same dimension.<br /> <br /> * [https://www.dropbox.com/s/vczbkb79w67r4tk/LAaG_Lecture_19.pdf?dl=0 '''Lecture 19'''] (10.02.2025) Linear Transformations (Part II: matrix representation and change of basis); coordinate matrices of a linear transformation; coordinate matrix of a composition of linear transformations; change of basis.<br /> <br /> * [https://www.dropbox.com/s/is0p1nou922zynj/LAaG_Lecture_18.pdf?dl=0 '''Lecture 18'''] (03.02.2025) Linear Transformations; main properties of linear transformations; the image and the kernel of a linear transformation; singular and non-singular linear transformations; the rank and the nullity of a linear transformation.<br /> <br /> * [https://www.dropbox.com/s/td8df813s2lh38b/LAaG_Lecture_17.pdf?dl=0 '''Lecture 17'''] (27.01.2025) The rank of a matrix (Part II); we prove that the column rank equals the row rank.<br /> <br /> * [https://www.dropbox.com/s/nf44zccqg3rythp/LAaG_Lecture_16.pdf?dl=0 '''Lecture 16'''] (20.01.2025) The direct sum of subspaces; main properties of the direct sum; the rank of a matrix; column and row spaces of a matrix; column and row ranks of a matrix.<br /> <br /> * [https://www.dropbox.com/s/cl7djenawtlgp0o/LAaG_Lecture_15.pdf?dl=0 '''Lecture 15'''] (13.01.2025) Main properties of change of basis matrices; the sum, the intersection, and the direct sum of vector subspaces; the dimension of the sum of two vector subspaces.<br /> <br /> ''' Module 2 '''<br /> * [https://www.dropbox.com/s/pozm47tzgaibf4k/LAaG_Lecture_14.pdf?dl=0 '''Lecture 14'''] (16.12.2024) Vector spaces (Part III); m-element subsets of an n-dimensional vector space; extension to a basis; the dimension of a subspace of a finite dimensional vector space; ordered basis; basis matrix; change of basis matrix.<br /> <br /> * [https://www.dropbox.com/s/10v3w4efz6zi332/LAaG_Lecture_13.pdf?dl=0 '''Lecture 13'''] (09.12.2024) Vector spaces (Part II); Main theorem on linear dependence; a basis of a vector space; dimension of a vector space; finite and infinite dimensional vector spaces; some main properties of finite dimensional vector spaces.<br /> <br /> * [https://www.dropbox.com/s/snko9y9r7ccw8qk/LAaG_Lecture_12.pdf?dl=0 '''Lecture 12'''] (01.12.2024) Vector spaces (Part I); a subspace of a vector space; linear combinations; the linear span; trivial and non-trivial linear combinations; linearly dependent and linearly independent sets.<br /> <br /> * [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (25.11.2024) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br /> <br /> * [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (18.11.2024) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br /> <br /> * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (11.11.2024) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br /> <br /> * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (02.11.2024) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/iw4d8eyjayzff9kfcj33r/LAaG_HW_29_C-241.pdf?rlkey=r7mvkq3f3tipvcphvmbcs7wy9&amp;st=ftkay74b&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ew31593pflcym5wtj0een/LAaG_HW_28_C-241.pdf?rlkey=66wd02998pic8x3t24061cdbh&amp;st=q296xsgc&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sc0udwvted1nn1quz4zou/LAaG_HW_27_C-241.pdf?rlkey=s47ayfwajc9lqod48xt5tx4wa&amp;st=qd7b4y7z&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/myc8320hx3njihu24cuba/LAaG_HW_26_C-241.pdf?rlkey=23sq1u6qrb9xevdrzaoutqxca&amp;st=1jmhwafo&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/cva01p9hh7qdtagzl3kn3/LAaG_HW_25_C-241.pdf?rlkey=yal3zb4maa7zwdvqxcecssjkg&amp;st=sg8pbd9k&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/7lpp0i0xjelgq0gp35e4n/LAaG_HW_24_C-241.pdf?rlkey=a582n8pburjgu2j8510gzn83r&amp;st=2q6voag2&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/4a54pbfd61aoprnxwzu0x/LAaG_HW_23_C-241.pdf?rlkey=fe69qd7iarodjou59nsfrr6sh&amp;st=pg55d94h&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/0bwlj7nva3781wif2lht4/LAaG_HW_22_C-241.pdf?rlkey=zvnp3kg68lfgl1psi4oey1duy&amp;st=erjtper3&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/r2d0fnyhorbud4w97cw8p/LAaG_HW_21_C-241.pdf?rlkey=jge0vzkbwpun9stgsnqk1xa15&amp;st=bdihujff&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tej4f5c5io1742pc958k6/LAaG_HW_20_C-241.pdf?rlkey=j1c0yag295f53gydl5rsc2o10&amp;st=fetq10zo&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/o2624ddh1r58a3ek8v723/LAaG_HW_19_C-241.pdf?rlkey=5ztkckb96zjcydhnk7x88en29&amp;st=bg5891g6&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zpc9ji9p84zvz5mi9vws9/LAaG_HW_18_C-241.pdf?rlkey=cfv4sqgw7kvcu4wbcata3fab3&amp;st=e2c6jr7e&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vthiyr2dpqrgggx8rwc5n/LAaG_HW_17_C-241.pdf?rlkey=rfchkhjrs96c4as6z0f68005h&amp;st=agspv924&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jk1qemu09cq5pzt2mpu58/LAaG_HW_16_C-241.pdf?rlkey=565cdf9qndljixsg2hm9pgs85&amp;st=u4i6x9g4&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/e0l37mfgqhgzhc35xvv85/LAaG_HW_15_C-241.pdf?rlkey=td1du8a0w5goaf0kk1e1doh02&amp;st=dmouas60&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gfanxb92qos5yrw2rw9up/LAaG_HW_13_C-241.pdf?rlkey=3lieu7597p86akdubpgblrxv1&amp;st=tzrb0x2w&amp;dl=0 '''HW 13'''] (release: 09.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/98g4oshs0lkwzfkq7ws2o/LAaG_HW_12_C-241.pdf?rlkey=ir2gfbgas5zecrt3de03anocx&amp;st=huaalfyu&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bkwvo24thkydotpkqjv7s/LAaG_HW_11_C-241.pdf?rlkey=vw1rwyesz3cfvizb88ukwbk5c&amp;st=6lzvxcfd&amp;dl=0 '''HW 11'''] (release: 25.11.24; deadline: 02.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tz95u31aralzb00htmpfr/LAaG_HW_10_C-241.pdf?rlkey=kvbdd60wu3jaj908hve2amrb7&amp;st=kiam0tz0&amp;dl=0 '''HW 10'''] (release: 18.11.24; deadline: 25.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9icdl8t78tqqaszgnh1ex/LAaG_HW_9_C-241.pdf?rlkey=obf47jl5bm91hmrlinhymmu5a&amp;st=8pldj7gq&amp;dl=0 '''HW 9'''] (release: 11.11.24; deadline: 18.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/cuah8c9c3lm3qjxw16paw/LAaG_HW_8_C-241.pdf?rlkey=iaedxga7hdn89904yo3rirtrs&amp;st=6lvpxxgl&amp;dl=0 '''HW 8'''] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/619rsffz78buraprvzlfo/LAaG_Seminar_8.pdf?rlkey=98o6gc0rjl4h6r9djdrasfwu8&amp;st=8zetjdlw&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> <br /> === Homework for group 242: ===<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/28mqxu940aveolrwwve1t/242_3-Homework-27.pdf?rlkey=gpqo0hokf2qq42n68zi6zyvvk&amp;st=9pt4rad9&amp;dl=0 '''HW 27''']<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/74v0d0eiofll1maa9jznn/LAaG_HW_29_C-246.pdf?rlkey=tkc9a738pz8ucsmoj1qa098to&amp;st=qjp6gids&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/dhn85atazelewt7hga4wm/LAaG_HW_28_C-246.pdf?rlkey=uuzzqtp8e19fwc9ed4cqity13&amp;st=cf0kk85z&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oipf5pzr862yxj8hzws0q/LAaG_HW_27_C-246.pdf?rlkey=8zm2hmvtcxaxl7gup9fhlskv4&amp;st=r2p4k1ki&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/f0ecohy3h75i4tteco78g/LAaG_HW_26_C-246.pdf?rlkey=4d2hnuddvguzw9brt08t7jfpv&amp;st=z8e70o5z&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lwvmio1folirvyij2c5te/LAaG_HW_25_C-246.pdf?rlkey=zg38wdf05opaxmuq6zfkuhsgk&amp;st=wd20mn6i&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/ais924pz2nlej2c2xggik/LAaG_HW_24_C-246.pdf?rlkey=cr3yzxr1sewhfckkas418wwlu&amp;st=cj12kvrx&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/jexjsl0jrgaui9o4nf9jl/LAaG_HW_23_C-246.pdf?rlkey=6v42cmsbukuljstxc1rw5nj2s&amp;st=3yw1rrh6&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6tnjv2kxwum90bwwklak5/LAaG_HW_22_C-246.pdf?rlkey=ml6hgg2cqnafwvhpuoe15vqsw&amp;st=xrgch4zx&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sadhn3ahnqtik4awr2tj4/LAaG_HW_21_C-246.pdf?rlkey=hs3dyl8ig4s6ygwvxyqtzgrez&amp;st=ndz29dpb&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/qurd5huy43ihn1z6a4u5g/LAaG_HW_20_C-246.pdf?rlkey=4js3uvv10nvnwxfijskwo1beg&amp;st=z6izkugw&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lit3st83vxamv4yoeux14/LAaG_HW_19_C-246.pdf?rlkey=md0jtmyyol74p3grsobpdn398&amp;st=khkc0ona&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zj4cmy6yvtb0voer5nxsz/LAaG_HW_18_C-246.pdf?rlkey=m9sfdgy428uwooyto3jc0v2n2&amp;st=3cqiogo3&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3f4p41sixiwspbws1zuyp/LAaG_HW_17_C-246.pdf?rlkey=mc9tkb24whvre9rjaa2yy4yy5&amp;st=3uly6rcr&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wwkr4nrvemckinbvlfpf4/LAaG_HW_16_C-246.pdf?rlkey=d36aqvm4sl5ymrhc9689skqmh&amp;st=ytwxjuiy&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vvxf2ix4aohlrme23iio3/LAaG_HW_15_C-246.pdf?rlkey=pz848a5pnq4x1o7192t9e3ja8&amp;st=bzl0fx87&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v60x5jr3qtp5nu1ddsywa/LAaG_HW_13_C-246.pdf?rlkey=b9zsc00sn81zfi4zlorrp1dqu&amp;st=3y4vawm7&amp;dl=0 '''HW 13'''] (release: 10.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/oqw6b4jgz5a133g1cssmw/LAaG_HW_12_C-246.pdf?rlkey=5w5gqusl520nxxzumh761y4jb&amp;st=xii5fvfc&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/z80z8a3xan9vxu4abcqah/LAaG_HW_11_C-246.pdf?rlkey=fe836n2dzg580je9n8rr2wf8e&amp;st=vts0p3p2&amp;dl=0 '''HW 11'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/klzrlfot6t4v6rfbfd02q/LAaG_HW_10_C-246.pdf?rlkey=su9akh09k4mnz4unedoqlhc90&amp;st=2ab1uvrj&amp;dl=0 '''HW 10'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6xjvw47ehtwt2ku62y9h8/LAaG_HW_9_C-246.pdf?rlkey=fjp37n3b0f3kgqivb9mtfy9tz&amp;st=6oj9hjsk&amp;dl=0 '''HW 9'''] (release: 12.11.24; deadline: 19.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/vpmwnqengjj2g9nn6zf9p/LAaG_HW_8_C-246.pdf?rlkey=7qlhr2wtmtm9lkbwf6i9coipg&amp;st=wumfffop&amp;dl=0 '''HW 8'''] (release: 07.11.24; deadline: 17.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/fupbesmknyp4bgm9sygca/LAaG_Sem_8_07_11_24_g246.pdf?rlkey=telxxvgpcx3tj70flyjye7aoc&amp;st=5dnddh72&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=90843 LAaG DSBA 2024/2025 2025-05-13T16:39:56Z <p>Vvbalakirev: /* Homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 4 '''<br /> * [https://www.dropbox.com/s/km7z6bed527pfgm/LAaG_Lecture_30.pdf?dl=0 '''Lecture 29'''] (12.05.2025) Orthogonality in Euclidian spaces; orthogonal and orthonormal sets and bases; Gram-Schmidt process; the orthogonal complement and its main properties; the projection and the rejection of a vector.<br /> <br /> * [https://www.dropbox.com/s/6wn3z42bzvrg5or/LAaG_Lecture_29.pdf?dl=0 '''Lecture 28'''] (28.04.2025) Euclidean spaces; scalar product; the norm of a vector; Cauchy–Schwarz inequality; the angle between two vectors; the Gram matrix and its main properties.<br /> <br /> * [https://www.dropbox.com/s/gkxple1prqauxoa/LAaG_Lecture_28.pdf?dl=0 '''Lecture 27'''] (21.04.2025) Quadratic forms (Part III); The Jacobi theorem; normal bases and the normal form of a quadratic form; the positive and negative indices of inertia, the signature of a quadratic form; the Sylvester law of inertia; positive (semi)-definite and negative (semi)-definite quadratic forms; the Sylvester criterion.<br /> <br /> * [https://www.dropbox.com/s/wpo6qnbxviol7u6/LAaG_Lecture_26.pdf?dl=0 '''Lecture 26'''] (14.04.2025) Quadratic forms; associated bilinear form; coordinate matrix of a quadratic form; canonical basis and canonical form of a quadratic form.<br /> <br /> * [https://www.dropbox.com/s/cfb54jzd2qdn0ze/LAaG_Lecture_25.pdf?dl=0 '''Lecture 25'''] (07.04.2025) Bilinear Forms; a coordinate matrix of a bilinear form; change-of-basis formula for bilinear forms; symmetric and skew-summetric bilinear forms. Quadratic forms; the associated bilinear form of a quadratic form.<br /> <br /> ''' Module 3 '''<br /> * [https://www.dropbox.com/s/3at8g01dkxwjn7y/LAaG_Lecture_24.pdf?dl=0 '''Lecture 24'''] (17.03.2025) Linear operators (Part IV); Jordan matrix; Jordan normal form; Jordan basis; Jordan basis theorem (without proof); Cayley-Hamilton theorem. Linear Functionals; dual space; dual basis; isomorphism between V and V*.<br /> <br /> * [https://www.dropbox.com/s/bh2gbw88rixc8e7/LAaG_Lecture_23.pdf?dl=0 '''Lecture 23'''] (10.03.2025) Linear operators (Part III); diagonalizability of a linear operator; inequality between algebraic and geometric multiplicities; criteria of diagonalizability.<br /> <br /> * [https://www.dropbox.com/s/76ydfixppp12cik/LAaG_Lecture_22.pdf?dl=0 '''Lecture 22'''] (03.03.2025) Linear operators (Part II); vector space of linear operators; the characteristic polynomial of a linear operator; algebraic and geometric multiplicity of an eigenvalue.<br /> <br /> * [https://www.dropbox.com/s/e9w3h8vqa5slwjz/LAaG_Lecture_21.pdf?dl=0 '''Lecture 21'''] (24.02.2025) Linear operators; the rank, the determinant, and the trace of a linear operator; invariant subspaces; eigenvectors and eigenvalues of a linear operator.<br /> <br /> * [https://www.dropbox.com/s/kzatlshdq6gj5zk/LAaG_Lecture_20.pdf?dl=0 '''Lecture 20'''] (17.02.2025) Linear Transformations (Part III: injectivity and surjectivity of linear transformations) injective and surjective linear transformations; isomorphisms (=linear bijections) of vector spaces; the inverse of an isomorphism; the fact that two finite dimensional vector spaces are isomorphic if and only if they both have the same dimension.<br /> <br /> * [https://www.dropbox.com/s/vczbkb79w67r4tk/LAaG_Lecture_19.pdf?dl=0 '''Lecture 19'''] (10.02.2025) Linear Transformations (Part II: matrix representation and change of basis); coordinate matrices of a linear transformation; coordinate matrix of a composition of linear transformations; change of basis.<br /> <br /> * [https://www.dropbox.com/s/is0p1nou922zynj/LAaG_Lecture_18.pdf?dl=0 '''Lecture 18'''] (03.02.2025) Linear Transformations; main properties of linear transformations; the image and the kernel of a linear transformation; singular and non-singular linear transformations; the rank and the nullity of a linear transformation.<br /> <br /> * [https://www.dropbox.com/s/td8df813s2lh38b/LAaG_Lecture_17.pdf?dl=0 '''Lecture 17'''] (27.01.2025) The rank of a matrix (Part II); we prove that the column rank equals the row rank.<br /> <br /> * [https://www.dropbox.com/s/nf44zccqg3rythp/LAaG_Lecture_16.pdf?dl=0 '''Lecture 16'''] (20.01.2025) The direct sum of subspaces; main properties of the direct sum; the rank of a matrix; column and row spaces of a matrix; column and row ranks of a matrix.<br /> <br /> * [https://www.dropbox.com/s/cl7djenawtlgp0o/LAaG_Lecture_15.pdf?dl=0 '''Lecture 15'''] (13.01.2025) Main properties of change of basis matrices; the sum, the intersection, and the direct sum of vector subspaces; the dimension of the sum of two vector subspaces.<br /> <br /> ''' Module 2 '''<br /> * [https://www.dropbox.com/s/pozm47tzgaibf4k/LAaG_Lecture_14.pdf?dl=0 '''Lecture 14'''] (16.12.2024) Vector spaces (Part III); m-element subsets of an n-dimensional vector space; extension to a basis; the dimension of a subspace of a finite dimensional vector space; ordered basis; basis matrix; change of basis matrix.<br /> <br /> * [https://www.dropbox.com/s/10v3w4efz6zi332/LAaG_Lecture_13.pdf?dl=0 '''Lecture 13'''] (09.12.2024) Vector spaces (Part II); Main theorem on linear dependence; a basis of a vector space; dimension of a vector space; finite and infinite dimensional vector spaces; some main properties of finite dimensional vector spaces.<br /> <br /> * [https://www.dropbox.com/s/snko9y9r7ccw8qk/LAaG_Lecture_12.pdf?dl=0 '''Lecture 12'''] (01.12.2024) Vector spaces (Part I); a subspace of a vector space; linear combinations; the linear span; trivial and non-trivial linear combinations; linearly dependent and linearly independent sets.<br /> <br /> * [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (25.11.2024) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br /> <br /> * [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (18.11.2024) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br /> <br /> * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (11.11.2024) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br /> <br /> * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (02.11.2024) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/iw4d8eyjayzff9kfcj33r/LAaG_HW_29_C-241.pdf?rlkey=r7mvkq3f3tipvcphvmbcs7wy9&amp;st=ftkay74b&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ew31593pflcym5wtj0een/LAaG_HW_28_C-241.pdf?rlkey=66wd02998pic8x3t24061cdbh&amp;st=q296xsgc&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sc0udwvted1nn1quz4zou/LAaG_HW_27_C-241.pdf?rlkey=s47ayfwajc9lqod48xt5tx4wa&amp;st=qd7b4y7z&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/myc8320hx3njihu24cuba/LAaG_HW_26_C-241.pdf?rlkey=23sq1u6qrb9xevdrzaoutqxca&amp;st=1jmhwafo&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/cva01p9hh7qdtagzl3kn3/LAaG_HW_25_C-241.pdf?rlkey=yal3zb4maa7zwdvqxcecssjkg&amp;st=sg8pbd9k&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/7lpp0i0xjelgq0gp35e4n/LAaG_HW_24_C-241.pdf?rlkey=a582n8pburjgu2j8510gzn83r&amp;st=2q6voag2&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/4a54pbfd61aoprnxwzu0x/LAaG_HW_23_C-241.pdf?rlkey=fe69qd7iarodjou59nsfrr6sh&amp;st=pg55d94h&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/0bwlj7nva3781wif2lht4/LAaG_HW_22_C-241.pdf?rlkey=zvnp3kg68lfgl1psi4oey1duy&amp;st=erjtper3&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/r2d0fnyhorbud4w97cw8p/LAaG_HW_21_C-241.pdf?rlkey=jge0vzkbwpun9stgsnqk1xa15&amp;st=bdihujff&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tej4f5c5io1742pc958k6/LAaG_HW_20_C-241.pdf?rlkey=j1c0yag295f53gydl5rsc2o10&amp;st=fetq10zo&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/o2624ddh1r58a3ek8v723/LAaG_HW_19_C-241.pdf?rlkey=5ztkckb96zjcydhnk7x88en29&amp;st=bg5891g6&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zpc9ji9p84zvz5mi9vws9/LAaG_HW_18_C-241.pdf?rlkey=cfv4sqgw7kvcu4wbcata3fab3&amp;st=e2c6jr7e&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vthiyr2dpqrgggx8rwc5n/LAaG_HW_17_C-241.pdf?rlkey=rfchkhjrs96c4as6z0f68005h&amp;st=agspv924&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jk1qemu09cq5pzt2mpu58/LAaG_HW_16_C-241.pdf?rlkey=565cdf9qndljixsg2hm9pgs85&amp;st=u4i6x9g4&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/e0l37mfgqhgzhc35xvv85/LAaG_HW_15_C-241.pdf?rlkey=td1du8a0w5goaf0kk1e1doh02&amp;st=dmouas60&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gfanxb92qos5yrw2rw9up/LAaG_HW_13_C-241.pdf?rlkey=3lieu7597p86akdubpgblrxv1&amp;st=tzrb0x2w&amp;dl=0 '''HW 13'''] (release: 09.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/98g4oshs0lkwzfkq7ws2o/LAaG_HW_12_C-241.pdf?rlkey=ir2gfbgas5zecrt3de03anocx&amp;st=huaalfyu&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bkwvo24thkydotpkqjv7s/LAaG_HW_11_C-241.pdf?rlkey=vw1rwyesz3cfvizb88ukwbk5c&amp;st=6lzvxcfd&amp;dl=0 '''HW 11'''] (release: 25.11.24; deadline: 02.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tz95u31aralzb00htmpfr/LAaG_HW_10_C-241.pdf?rlkey=kvbdd60wu3jaj908hve2amrb7&amp;st=kiam0tz0&amp;dl=0 '''HW 10'''] (release: 18.11.24; deadline: 25.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9icdl8t78tqqaszgnh1ex/LAaG_HW_9_C-241.pdf?rlkey=obf47jl5bm91hmrlinhymmu5a&amp;st=8pldj7gq&amp;dl=0 '''HW 9'''] (release: 11.11.24; deadline: 18.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/cuah8c9c3lm3qjxw16paw/LAaG_HW_8_C-241.pdf?rlkey=iaedxga7hdn89904yo3rirtrs&amp;st=6lvpxxgl&amp;dl=0 '''HW 8'''] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/619rsffz78buraprvzlfo/LAaG_Seminar_8.pdf?rlkey=98o6gc0rjl4h6r9djdrasfwu8&amp;st=8zetjdlw&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> <br /> === Homework for group 242: ===<br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/74v0d0eiofll1maa9jznn/LAaG_HW_29_C-246.pdf?rlkey=tkc9a738pz8ucsmoj1qa098to&amp;st=qjp6gids&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/dhn85atazelewt7hga4wm/LAaG_HW_28_C-246.pdf?rlkey=uuzzqtp8e19fwc9ed4cqity13&amp;st=cf0kk85z&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oipf5pzr862yxj8hzws0q/LAaG_HW_27_C-246.pdf?rlkey=8zm2hmvtcxaxl7gup9fhlskv4&amp;st=r2p4k1ki&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/f0ecohy3h75i4tteco78g/LAaG_HW_26_C-246.pdf?rlkey=4d2hnuddvguzw9brt08t7jfpv&amp;st=z8e70o5z&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lwvmio1folirvyij2c5te/LAaG_HW_25_C-246.pdf?rlkey=zg38wdf05opaxmuq6zfkuhsgk&amp;st=wd20mn6i&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/ais924pz2nlej2c2xggik/LAaG_HW_24_C-246.pdf?rlkey=cr3yzxr1sewhfckkas418wwlu&amp;st=cj12kvrx&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/jexjsl0jrgaui9o4nf9jl/LAaG_HW_23_C-246.pdf?rlkey=6v42cmsbukuljstxc1rw5nj2s&amp;st=3yw1rrh6&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6tnjv2kxwum90bwwklak5/LAaG_HW_22_C-246.pdf?rlkey=ml6hgg2cqnafwvhpuoe15vqsw&amp;st=xrgch4zx&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sadhn3ahnqtik4awr2tj4/LAaG_HW_21_C-246.pdf?rlkey=hs3dyl8ig4s6ygwvxyqtzgrez&amp;st=ndz29dpb&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/qurd5huy43ihn1z6a4u5g/LAaG_HW_20_C-246.pdf?rlkey=4js3uvv10nvnwxfijskwo1beg&amp;st=z6izkugw&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lit3st83vxamv4yoeux14/LAaG_HW_19_C-246.pdf?rlkey=md0jtmyyol74p3grsobpdn398&amp;st=khkc0ona&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zj4cmy6yvtb0voer5nxsz/LAaG_HW_18_C-246.pdf?rlkey=m9sfdgy428uwooyto3jc0v2n2&amp;st=3cqiogo3&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3f4p41sixiwspbws1zuyp/LAaG_HW_17_C-246.pdf?rlkey=mc9tkb24whvre9rjaa2yy4yy5&amp;st=3uly6rcr&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wwkr4nrvemckinbvlfpf4/LAaG_HW_16_C-246.pdf?rlkey=d36aqvm4sl5ymrhc9689skqmh&amp;st=ytwxjuiy&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vvxf2ix4aohlrme23iio3/LAaG_HW_15_C-246.pdf?rlkey=pz848a5pnq4x1o7192t9e3ja8&amp;st=bzl0fx87&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v60x5jr3qtp5nu1ddsywa/LAaG_HW_13_C-246.pdf?rlkey=b9zsc00sn81zfi4zlorrp1dqu&amp;st=3y4vawm7&amp;dl=0 '''HW 13'''] (release: 10.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/oqw6b4jgz5a133g1cssmw/LAaG_HW_12_C-246.pdf?rlkey=5w5gqusl520nxxzumh761y4jb&amp;st=xii5fvfc&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/z80z8a3xan9vxu4abcqah/LAaG_HW_11_C-246.pdf?rlkey=fe836n2dzg580je9n8rr2wf8e&amp;st=vts0p3p2&amp;dl=0 '''HW 11'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/klzrlfot6t4v6rfbfd02q/LAaG_HW_10_C-246.pdf?rlkey=su9akh09k4mnz4unedoqlhc90&amp;st=2ab1uvrj&amp;dl=0 '''HW 10'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6xjvw47ehtwt2ku62y9h8/LAaG_HW_9_C-246.pdf?rlkey=fjp37n3b0f3kgqivb9mtfy9tz&amp;st=6oj9hjsk&amp;dl=0 '''HW 9'''] (release: 12.11.24; deadline: 19.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/vpmwnqengjj2g9nn6zf9p/LAaG_HW_8_C-246.pdf?rlkey=7qlhr2wtmtm9lkbwf6i9coipg&amp;st=wumfffop&amp;dl=0 '''HW 8'''] (release: 07.11.24; deadline: 17.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/fupbesmknyp4bgm9sygca/LAaG_Sem_8_07_11_24_g246.pdf?rlkey=telxxvgpcx3tj70flyjye7aoc&amp;st=5dnddh72&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=90842 LAaG DSBA 2024/2025 2025-05-13T16:39:41Z <p>Vvbalakirev: /* Homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 4 '''<br /> * [https://www.dropbox.com/s/km7z6bed527pfgm/LAaG_Lecture_30.pdf?dl=0 '''Lecture 29'''] (12.05.2025) Orthogonality in Euclidian spaces; orthogonal and orthonormal sets and bases; Gram-Schmidt process; the orthogonal complement and its main properties; the projection and the rejection of a vector.<br /> <br /> * [https://www.dropbox.com/s/6wn3z42bzvrg5or/LAaG_Lecture_29.pdf?dl=0 '''Lecture 28'''] (28.04.2025) Euclidean spaces; scalar product; the norm of a vector; Cauchy–Schwarz inequality; the angle between two vectors; the Gram matrix and its main properties.<br /> <br /> * [https://www.dropbox.com/s/gkxple1prqauxoa/LAaG_Lecture_28.pdf?dl=0 '''Lecture 27'''] (21.04.2025) Quadratic forms (Part III); The Jacobi theorem; normal bases and the normal form of a quadratic form; the positive and negative indices of inertia, the signature of a quadratic form; the Sylvester law of inertia; positive (semi)-definite and negative (semi)-definite quadratic forms; the Sylvester criterion.<br /> <br /> * [https://www.dropbox.com/s/wpo6qnbxviol7u6/LAaG_Lecture_26.pdf?dl=0 '''Lecture 26'''] (14.04.2025) Quadratic forms; associated bilinear form; coordinate matrix of a quadratic form; canonical basis and canonical form of a quadratic form.<br /> <br /> * [https://www.dropbox.com/s/cfb54jzd2qdn0ze/LAaG_Lecture_25.pdf?dl=0 '''Lecture 25'''] (07.04.2025) Bilinear Forms; a coordinate matrix of a bilinear form; change-of-basis formula for bilinear forms; symmetric and skew-summetric bilinear forms. Quadratic forms; the associated bilinear form of a quadratic form.<br /> <br /> ''' Module 3 '''<br /> * [https://www.dropbox.com/s/3at8g01dkxwjn7y/LAaG_Lecture_24.pdf?dl=0 '''Lecture 24'''] (17.03.2025) Linear operators (Part IV); Jordan matrix; Jordan normal form; Jordan basis; Jordan basis theorem (without proof); Cayley-Hamilton theorem. Linear Functionals; dual space; dual basis; isomorphism between V and V*.<br /> <br /> * [https://www.dropbox.com/s/bh2gbw88rixc8e7/LAaG_Lecture_23.pdf?dl=0 '''Lecture 23'''] (10.03.2025) Linear operators (Part III); diagonalizability of a linear operator; inequality between algebraic and geometric multiplicities; criteria of diagonalizability.<br /> <br /> * [https://www.dropbox.com/s/76ydfixppp12cik/LAaG_Lecture_22.pdf?dl=0 '''Lecture 22'''] (03.03.2025) Linear operators (Part II); vector space of linear operators; the characteristic polynomial of a linear operator; algebraic and geometric multiplicity of an eigenvalue.<br /> <br /> * [https://www.dropbox.com/s/e9w3h8vqa5slwjz/LAaG_Lecture_21.pdf?dl=0 '''Lecture 21'''] (24.02.2025) Linear operators; the rank, the determinant, and the trace of a linear operator; invariant subspaces; eigenvectors and eigenvalues of a linear operator.<br /> <br /> * [https://www.dropbox.com/s/kzatlshdq6gj5zk/LAaG_Lecture_20.pdf?dl=0 '''Lecture 20'''] (17.02.2025) Linear Transformations (Part III: injectivity and surjectivity of linear transformations) injective and surjective linear transformations; isomorphisms (=linear bijections) of vector spaces; the inverse of an isomorphism; the fact that two finite dimensional vector spaces are isomorphic if and only if they both have the same dimension.<br /> <br /> * [https://www.dropbox.com/s/vczbkb79w67r4tk/LAaG_Lecture_19.pdf?dl=0 '''Lecture 19'''] (10.02.2025) Linear Transformations (Part II: matrix representation and change of basis); coordinate matrices of a linear transformation; coordinate matrix of a composition of linear transformations; change of basis.<br /> <br /> * [https://www.dropbox.com/s/is0p1nou922zynj/LAaG_Lecture_18.pdf?dl=0 '''Lecture 18'''] (03.02.2025) Linear Transformations; main properties of linear transformations; the image and the kernel of a linear transformation; singular and non-singular linear transformations; the rank and the nullity of a linear transformation.<br /> <br /> * [https://www.dropbox.com/s/td8df813s2lh38b/LAaG_Lecture_17.pdf?dl=0 '''Lecture 17'''] (27.01.2025) The rank of a matrix (Part II); we prove that the column rank equals the row rank.<br /> <br /> * [https://www.dropbox.com/s/nf44zccqg3rythp/LAaG_Lecture_16.pdf?dl=0 '''Lecture 16'''] (20.01.2025) The direct sum of subspaces; main properties of the direct sum; the rank of a matrix; column and row spaces of a matrix; column and row ranks of a matrix.<br /> <br /> * [https://www.dropbox.com/s/cl7djenawtlgp0o/LAaG_Lecture_15.pdf?dl=0 '''Lecture 15'''] (13.01.2025) Main properties of change of basis matrices; the sum, the intersection, and the direct sum of vector subspaces; the dimension of the sum of two vector subspaces.<br /> <br /> ''' Module 2 '''<br /> * [https://www.dropbox.com/s/pozm47tzgaibf4k/LAaG_Lecture_14.pdf?dl=0 '''Lecture 14'''] (16.12.2024) Vector spaces (Part III); m-element subsets of an n-dimensional vector space; extension to a basis; the dimension of a subspace of a finite dimensional vector space; ordered basis; basis matrix; change of basis matrix.<br /> <br /> * [https://www.dropbox.com/s/10v3w4efz6zi332/LAaG_Lecture_13.pdf?dl=0 '''Lecture 13'''] (09.12.2024) Vector spaces (Part II); Main theorem on linear dependence; a basis of a vector space; dimension of a vector space; finite and infinite dimensional vector spaces; some main properties of finite dimensional vector spaces.<br /> <br /> * [https://www.dropbox.com/s/snko9y9r7ccw8qk/LAaG_Lecture_12.pdf?dl=0 '''Lecture 12'''] (01.12.2024) Vector spaces (Part I); a subspace of a vector space; linear combinations; the linear span; trivial and non-trivial linear combinations; linearly dependent and linearly independent sets.<br /> <br /> * [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (25.11.2024) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br /> <br /> * [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (18.11.2024) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br /> <br /> * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (11.11.2024) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br /> <br /> * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (02.11.2024) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/iw4d8eyjayzff9kfcj33r/LAaG_HW_29_C-241.pdf?rlkey=r7mvkq3f3tipvcphvmbcs7wy9&amp;st=ftkay74b&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ew31593pflcym5wtj0een/LAaG_HW_28_C-241.pdf?rlkey=66wd02998pic8x3t24061cdbh&amp;st=q296xsgc&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sc0udwvted1nn1quz4zou/LAaG_HW_27_C-241.pdf?rlkey=s47ayfwajc9lqod48xt5tx4wa&amp;st=qd7b4y7z&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/myc8320hx3njihu24cuba/LAaG_HW_26_C-241.pdf?rlkey=23sq1u6qrb9xevdrzaoutqxca&amp;st=1jmhwafo&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/cva01p9hh7qdtagzl3kn3/LAaG_HW_25_C-241.pdf?rlkey=yal3zb4maa7zwdvqxcecssjkg&amp;st=sg8pbd9k&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/7lpp0i0xjelgq0gp35e4n/LAaG_HW_24_C-241.pdf?rlkey=a582n8pburjgu2j8510gzn83r&amp;st=2q6voag2&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/4a54pbfd61aoprnxwzu0x/LAaG_HW_23_C-241.pdf?rlkey=fe69qd7iarodjou59nsfrr6sh&amp;st=pg55d94h&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/0bwlj7nva3781wif2lht4/LAaG_HW_22_C-241.pdf?rlkey=zvnp3kg68lfgl1psi4oey1duy&amp;st=erjtper3&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/r2d0fnyhorbud4w97cw8p/LAaG_HW_21_C-241.pdf?rlkey=jge0vzkbwpun9stgsnqk1xa15&amp;st=bdihujff&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tej4f5c5io1742pc958k6/LAaG_HW_20_C-241.pdf?rlkey=j1c0yag295f53gydl5rsc2o10&amp;st=fetq10zo&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/o2624ddh1r58a3ek8v723/LAaG_HW_19_C-241.pdf?rlkey=5ztkckb96zjcydhnk7x88en29&amp;st=bg5891g6&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zpc9ji9p84zvz5mi9vws9/LAaG_HW_18_C-241.pdf?rlkey=cfv4sqgw7kvcu4wbcata3fab3&amp;st=e2c6jr7e&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vthiyr2dpqrgggx8rwc5n/LAaG_HW_17_C-241.pdf?rlkey=rfchkhjrs96c4as6z0f68005h&amp;st=agspv924&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jk1qemu09cq5pzt2mpu58/LAaG_HW_16_C-241.pdf?rlkey=565cdf9qndljixsg2hm9pgs85&amp;st=u4i6x9g4&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/e0l37mfgqhgzhc35xvv85/LAaG_HW_15_C-241.pdf?rlkey=td1du8a0w5goaf0kk1e1doh02&amp;st=dmouas60&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gfanxb92qos5yrw2rw9up/LAaG_HW_13_C-241.pdf?rlkey=3lieu7597p86akdubpgblrxv1&amp;st=tzrb0x2w&amp;dl=0 '''HW 13'''] (release: 09.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/98g4oshs0lkwzfkq7ws2o/LAaG_HW_12_C-241.pdf?rlkey=ir2gfbgas5zecrt3de03anocx&amp;st=huaalfyu&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bkwvo24thkydotpkqjv7s/LAaG_HW_11_C-241.pdf?rlkey=vw1rwyesz3cfvizb88ukwbk5c&amp;st=6lzvxcfd&amp;dl=0 '''HW 11'''] (release: 25.11.24; deadline: 02.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/tz95u31aralzb00htmpfr/LAaG_HW_10_C-241.pdf?rlkey=kvbdd60wu3jaj908hve2amrb7&amp;st=kiam0tz0&amp;dl=0 '''HW 10'''] (release: 18.11.24; deadline: 25.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9icdl8t78tqqaszgnh1ex/LAaG_HW_9_C-241.pdf?rlkey=obf47jl5bm91hmrlinhymmu5a&amp;st=8pldj7gq&amp;dl=0 '''HW 9'''] (release: 11.11.24; deadline: 18.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/cuah8c9c3lm3qjxw16paw/LAaG_HW_8_C-241.pdf?rlkey=iaedxga7hdn89904yo3rirtrs&amp;st=6lvpxxgl&amp;dl=0 '''HW 8'''] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/619rsffz78buraprvzlfo/LAaG_Seminar_8.pdf?rlkey=98o6gc0rjl4h6r9djdrasfwu8&amp;st=8zetjdlw&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> <br /> === Homework for group 242: ===<br /> '''Module 4'''<br /> * https://www.dropbox.com/scl/fi/p562xkl89mig04qu9qxtp/242_3-Homework-28.pdf?rlkey=49n6amwycaivbx3j3fh3q60n6&amp;st=yt0z44d2&amp;dl=0 '''HW 28''']<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> <br /> '''Module 4'''<br /> * [https://www.dropbox.com/scl/fi/74v0d0eiofll1maa9jznn/LAaG_HW_29_C-246.pdf?rlkey=tkc9a738pz8ucsmoj1qa098to&amp;st=qjp6gids&amp;dl=0 '''HW 29'''] (release: 12.05.25; deadline: 19.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5xpmuqmleofg8hbyh77wt/LAaG_Seminar_30.pdf?rlkey=f5k43kbacz728dgtpxy293t78&amp;st=5zz28t75&amp;dl=0 Seminar_29 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/dhn85atazelewt7hga4wm/LAaG_HW_28_C-246.pdf?rlkey=uuzzqtp8e19fwc9ed4cqity13&amp;st=cf0kk85z&amp;dl=0 '''HW 28'''] (release: 29.04.25; deadline: 12.05.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/hjjmswgp898c6i4vb3liy/LAaG_Seminar_29.pdf?rlkey=ugufxdman6d871ldg5wsxi915&amp;st=zghplcd9&amp;dl=0 Seminar_28 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oipf5pzr862yxj8hzws0q/LAaG_HW_27_C-246.pdf?rlkey=8zm2hmvtcxaxl7gup9fhlskv4&amp;st=r2p4k1ki&amp;dl=0 '''HW 27'''] (release: 22.04.25; deadline: 28.04.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/f0ecohy3h75i4tteco78g/LAaG_HW_26_C-246.pdf?rlkey=4d2hnuddvguzw9brt08t7jfpv&amp;st=z8e70o5z&amp;dl=0 '''HW 26'''] (release: 14.04.25; deadline: 21.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/dit0tclcxb0dpt2ettwdk/LAaG_Seminar_26.pdf?rlkey=mkpyut1djk52q5aaat87761p9&amp;st=o2342lya&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lwvmio1folirvyij2c5te/LAaG_HW_25_C-246.pdf?rlkey=zg38wdf05opaxmuq6zfkuhsgk&amp;st=wd20mn6i&amp;dl=0 '''HW 25'''] (release: 07.04.25; deadline: 14.04.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/c3gatmg9qakitje4olaoj/LAaG_Seminar_25.pdf?rlkey=xmpd8mngs6if9znbds15r58wf&amp;st=0izgwv2g&amp;dl=0 Seminar_25 notes])&lt;/small&gt;<br /> <br /> '''Module 3'''<br /> * [https://www.dropbox.com/scl/fi/ais924pz2nlej2c2xggik/LAaG_HW_24_C-246.pdf?rlkey=cr3yzxr1sewhfckkas418wwlu&amp;st=cj12kvrx&amp;dl=0 '''HW 24'''] (release: 17.03.25; deadline: 24.03.25)<br /> <br /> * [https://www.dropbox.com/scl/fi/jexjsl0jrgaui9o4nf9jl/LAaG_HW_23_C-246.pdf?rlkey=6v42cmsbukuljstxc1rw5nj2s&amp;st=3yw1rrh6&amp;dl=0 '''HW 23'''] (release: 10.03.25; deadline: 17.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/teb6deggioeixyxpz58zk/LAaG_Seminar_23_21.pdf?rlkey=hn3ipnzk94no70tlgj3ndzq1g&amp;st=hque5vte&amp;dl=0 Seminar_23 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6tnjv2kxwum90bwwklak5/LAaG_HW_22_C-246.pdf?rlkey=ml6hgg2cqnafwvhpuoe15vqsw&amp;st=xrgch4zx&amp;dl=0 '''HW 22'''] (release: 03.03.25; deadline: 10.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/mdnw8zz4rm6k1k38496vd/LAaG_Seminar_22_21.pdf?rlkey=p2nw9g6qr2ismfko0is4cjl2z&amp;st=tiun92hn&amp;dl=0 Seminar_22 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/sadhn3ahnqtik4awr2tj4/LAaG_HW_21_C-246.pdf?rlkey=hs3dyl8ig4s6ygwvxyqtzgrez&amp;st=ndz29dpb&amp;dl=0 '''HW 21'''] (release: 24.02.25; deadline: 03.03.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/23jhss0t1xih2xra5mvc4/LAaG_Seminar_21_21.pdf?rlkey=ck9nhgb8ozjih6ofzi65ds9qx&amp;st=bgbucsb1&amp;dl=0 Seminar_21 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/qurd5huy43ihn1z6a4u5g/LAaG_HW_20_C-246.pdf?rlkey=4js3uvv10nvnwxfijskwo1beg&amp;st=z6izkugw&amp;dl=0 '''HW 20'''] (release: 17.02.25; deadline: 24.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/f9x7122gbcpszh94hlhni/LAaG_Seminar_20_21.pdf?rlkey=jq05fr6q9uq8ksi1fqq8a0yaq&amp;st=bh9s45rm&amp;dl=0 Seminar_20 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lit3st83vxamv4yoeux14/LAaG_HW_19_C-246.pdf?rlkey=md0jtmyyol74p3grsobpdn398&amp;st=khkc0ona&amp;dl=0 '''HW 19'''] (release: 10.02.25; deadline: 17.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/126dgebvg3mmtns5h6x5z/LAaG_Seminar_19_21.pdf?rlkey=0gzkiiha5kyv49brsbo6u6ykv&amp;st=gqzt33o7&amp;dl=0 Seminar_19 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/zj4cmy6yvtb0voer5nxsz/LAaG_HW_18_C-246.pdf?rlkey=m9sfdgy428uwooyto3jc0v2n2&amp;st=3cqiogo3&amp;dl=0 '''HW 18'''] (release: 03.02.25; deadline: 10.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/xs1ebar1oyuussb8rxret/LAaG_Seminar_18_21.pdf?rlkey=4u2aqauqh7cm0awdh63c3qgd6&amp;st=ympd0331&amp;dl=0 Seminar_18 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3f4p41sixiwspbws1zuyp/LAaG_HW_17_C-246.pdf?rlkey=mc9tkb24whvre9rjaa2yy4yy5&amp;st=3uly6rcr&amp;dl=0 '''HW 17'''] (release: 27.01.25; deadline: 03.02.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/uclu8m2h29zl0il7be3p4/LAaG_Seminar_17_21.pdf?rlkey=it4ij3am0e2w1oh6ikib61bt2&amp;st=9jxo12r0&amp;dl=0 Seminar_17 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wwkr4nrvemckinbvlfpf4/LAaG_HW_16_C-246.pdf?rlkey=d36aqvm4sl5ymrhc9689skqmh&amp;st=ytwxjuiy&amp;dl=0 '''HW 16'''] (release: 20.01.25; deadline: 27.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/37zf1z8cbxzszq8qter1l/LAaG_Seminar_16_21.pdf?rlkey=wgbig2cw8qq6j2l1fi7qftz8m&amp;st=igduxufe&amp;dl=0 Seminar_16 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vvxf2ix4aohlrme23iio3/LAaG_HW_15_C-246.pdf?rlkey=pz848a5pnq4x1o7192t9e3ja8&amp;st=bzl0fx87&amp;dl=0 '''HW 15'''] (release: 13.01.25; deadline: 20.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/5rpp9d4smsa8w1d3tzq1z/LAaG_Seminar_15_21.pdf?rlkey=u4z6a041gi23wzbtesalkpgrh&amp;st=ot8nrxhr&amp;dl=0 Seminar_15 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v60x5jr3qtp5nu1ddsywa/LAaG_HW_13_C-246.pdf?rlkey=b9zsc00sn81zfi4zlorrp1dqu&amp;st=3y4vawm7&amp;dl=0 '''HW 13'''] (release: 10.12.24; deadline: 13.01.25) &lt;small&gt;([https://www.dropbox.com/scl/fi/1e3geo5djpmpehgof85s3/LAaG_Seminar_13-5.pdf?rlkey=rhxxwja8obvez7r0w51yo75w0&amp;st=fvibm9jg&amp;dl=0 Seminar_13 notes])&lt;/small&gt;<br /> <br /> '''Module 2'''<br /> * [https://www.dropbox.com/scl/fi/oqw6b4jgz5a133g1cssmw/LAaG_HW_12_C-246.pdf?rlkey=5w5gqusl520nxxzumh761y4jb&amp;st=xii5fvfc&amp;dl=0 '''HW 12'''] (release: 02.12.24; deadline: 09.12.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jfooteiy7u1r2pqjig8pq/LAaG_Seminar_12.pdf?rlkey=cg0te5fgcw7u42cdvc9f0753g&amp;st=usefcrhi&amp;dl=0 Seminar_12 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/z80z8a3xan9vxu4abcqah/LAaG_HW_11_C-246.pdf?rlkey=fe836n2dzg580je9n8rr2wf8e&amp;st=vts0p3p2&amp;dl=0 '''HW 11'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/wfgqgfv0cwolvdy10c1l8/LAaG_Seminar_11.pdf?rlkey=avo95gpn6po4fnqh9llynjngo&amp;st=s31ph3ve&amp;dl=0 Seminar_11 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/klzrlfot6t4v6rfbfd02q/LAaG_HW_10_C-246.pdf?rlkey=su9akh09k4mnz4unedoqlhc90&amp;st=2ab1uvrj&amp;dl=0 '''HW 10'''] (release: 19.11.24; deadline: 26.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/a3j0gvdluufvq6410wkwk/LAaG_Seminar_10.pdf?rlkey=y2tey1a0hfz8mcqnhkb4gzjvy&amp;st=ufntncjj&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/6xjvw47ehtwt2ku62y9h8/LAaG_HW_9_C-246.pdf?rlkey=fjp37n3b0f3kgqivb9mtfy9tz&amp;st=6oj9hjsk&amp;dl=0 '''HW 9'''] (release: 12.11.24; deadline: 19.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/vpmwnqengjj2g9nn6zf9p/LAaG_HW_8_C-246.pdf?rlkey=7qlhr2wtmtm9lkbwf6i9coipg&amp;st=wumfffop&amp;dl=0 '''HW 8'''] (release: 07.11.24; deadline: 17.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/fupbesmknyp4bgm9sygca/LAaG_Sem_8_07_11_24_g246.pdf?rlkey=telxxvgpcx3tj70flyjye7aoc&amp;st=5dnddh72&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=DSBA_Algebra_2024_2025&diff=90812 DSBA Algebra 2024 2025 2025-05-06T13:00:19Z <p>Vvbalakirev: /* Problem sheets */</p> <hr /> <div>= Teachers and assistants =<br /> <br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Группа !! 241 !! 242 !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/en/org/persons/209508745 Dima Trushin] [https://t.me/DimaTrushin Telegram]<br /> |- <br /> || Teacher || [https://www.hse.ru/en/org/persons/209508745 Dima Trushin] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/en/org/persons/207901592 Vladislav Balakirev] || [https://www.hse.ru/en/org/persons/392058502 Kirill Shakhmatov] || [https://www.hse.ru/org/persons/780694072/ Aisha Nurieva] || [https://www.hse.ru/en/org/persons/305969353 Alexander Zaytsev]<br /> |-<br /> || Assistant || [https://t.me/warning172 Roman Bokhyan] || [https://t.me/Avgustine_iw Zakhar Zinkin] || [https://t.me/lunciare Sasha Suvorova] || [https://t.me/tkvlnko Taya Ibragimova] || [https://t.me/meomato Polina Doronicheva] || [https://t.me/rina_mlv Irina Milova]<br /> |}<br /> <br /> = Consultations schedule =<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! !! Teacher/Assistant !! How to contact !! When<br /> |-<br /> | &lt;center&gt;1&lt;/center&gt; || Dima Trushin || [https://t.me/DimaTrushin telegram] || Wednesday since 17:00 S812<br /> |-<br /> | &lt;center&gt;2&lt;/center&gt; || Andrew Mazhuga || [https://www.youtube.com/watch?v=dQw4w9WgXcQ&amp;ab_channel=RickAstley telegram] ||<br /> |-<br /> | &lt;center&gt;3&lt;/center&gt; || Vladislav Balakirev || || <br /> |-<br /> | &lt;center&gt;4&lt;/center&gt; || Kirill Shakhmatov || || <br /> |-<br /> | &lt;center&gt;5&lt;/center&gt; || Aisha Nurieva || ||<br /> |-<br /> | &lt;center&gt;6&lt;/center&gt; || Alexander Zaytsev || || <br /> |}<br /> <br /> = Grading system =<br /> <br /> The final grade is computed as follows<br /> <br /> F = 0,3 * H + 0,3 T + 0,4 E<br /> <br /> where H is the grade for the home assignments, T is the written test grade, and E is the final exam grade.<br /> <br /> Only the final grade is rounded in the final formula according to the standard rule.<br /> <br /> <br /> = Lecture abstracts =<br /> <br /> '''Lecture&amp;nbsp;1''' (03.04.2025). Binary operations. Associativity, neutral element, inverse element, commutativity. Definition of a group. Additive and multiplicative notations. Subgroups and cyclic subgroups. The order of an element of a group.<br /> <br /> '''Lecture&amp;nbsp;2''' (10.04.2025). Classification of cyclic groups. The subgroups of the group of integers. The subgroups of the group Z_n. Left and right cosets, examples. Normal subgroups. The Lagrange theorem and its corollaries.<br /> <br /> '''Lecture&amp;nbsp;3''' (17.04.2025). Homomorphisms and Isomorphisms of groups. Image and kernel of a homomorphism. Normal subgroups. Direct product of groups. Finite Abelian Groups. The Chinese Remainder Theorem. Structure of a finite abelian group.<br /> <br /> '''Lecture&amp;nbsp;4''' (24.04.2025). Multiplicative version of the Chinese Remainder Theorem. Structure of Z_{p^n}^*. Cryptography. Exponentiation by squaring (fast raising to a power algorithm). The discrete logarithm problem. Diffie-Hellman key exchange.<br /> <br /> = Problem sheets =<br /> <br /> The solutions should be sent to your teaching assistant before the beginning of the next seminar. If you send the solution after the deadline your grade will be multiplied by 0.7&lt;sup&gt;t&lt;/sup&gt; where t -- is the time passed after the deadline in days (not rounded). So, it is not an issue to send your work 1 or 2 hours after the deadline.<br /> <br /> '''Seminar&amp;nbsp;1''' (03.04.2024). [https://disk.yandex.ru/d/ikcTBq5kJDP1iw Problems]<br /> <br /> '''Seminar&amp;nbsp;2''' (10.04.2024). [https://disk.yandex.ru/d/0da7rDLB2b2O_w Problems]<br /> <br /> '''Seminar&amp;nbsp;3''' (17.04.2024). [https://disk.yandex.ru/i/lsR5vMFIwP9F_Q Problems]<br /> <br /> = Test =<br /> <br /> = Exam =<br /> <br /> = Results =<br /> <br /> * Homework<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1Qmhk6OuISvZGx04YgyNQKvk_qqZvR2O8d6sKyADZyNo/edit?gid=640844189#gid=640844189 241] !! [https://docs.google.com/spreadsheets/d/1Qmhk6OuISvZGx04YgyNQKvk_qqZvR2O8d6sKyADZyNo/edit?gid=1612040544#gid=1612040544 242] !! [https://docs.google.com/spreadsheets/d/1Qmhk6OuISvZGx04YgyNQKvk_qqZvR2O8d6sKyADZyNo/edit?gid=1538156963#gid=1538156963 243] !! [https://docs.google.com/spreadsheets/d/1Qmhk6OuISvZGx04YgyNQKvk_qqZvR2O8d6sKyADZyNo/edit?gid=1067620548#gid=1067620548 244] !! [https://docs.google.com/spreadsheets/d/1Qmhk6OuISvZGx04YgyNQKvk_qqZvR2O8d6sKyADZyNo/edit?gid=572193184#gid=572193184 245] !! [https://docs.google.com/spreadsheets/d/1Qmhk6OuISvZGx04YgyNQKvk_qqZvR2O8d6sKyADZyNo/edit?gid=1872255753#gid=1872255753 246]<br /> |}<br /> <br /> * Test<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246]<br /> |}<br /> <br /> * Summary Statement<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [ 241] !! [ 242] !! [ 243] !! [ 244] !! [ 245] !! [ 246]<br /> |}<br /> <br /> = Links =<br /> <br /> * Telegram [https://t.me/+h5HG-vxNOxdiNWZi channel] of the course.<br /> <br /> * [https://github.com/DimaTrushin/Algebra-DSBA/ Lecture Notes]</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=87575 LAaG DSBA 2024/2025 2024-10-30T21:56:21Z <p>Vvbalakirev: /* Teachers and Assistants */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || via telegram anytime || via telegram anytime || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=87574 LAaG DSBA 2024/2025 2024-10-30T21:53:45Z <p>Vvbalakirev: /* Homework for group 243: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || ??? || ??? || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2024/2025&diff=87573 LAaG DSBA 2024/2025 2024-10-30T21:52:50Z <p>Vvbalakirev: /* Homework for group 242: */</p> <hr /> <div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 241 (M+P+) !! 242 (P+) !! 243 !! 244 !! 245 !! 246<br /> |-<br /> || Lecturer ||colspan=&quot;6&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev tg]) || colspan=&quot;2&quot; | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||[https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] <br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || ??? || ??? || ??? || ??? || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt;<br /> |-<br /> || Assistant || Купцов Максим<br /> || Зинкин Захар<br /> || Павлов Аркадий<br /> || Бохян Роман<br /> || Дороничева Полина<br /> || Науменко Дарья<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> The course introduces students to the elements of linear algebra and analytic geometry, provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results.<br /> <br /> We will approach the subject from both a practical point of view (learning methods and acquiring computational skills<br /> relevant for problem solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts).<br /> <br /> Topics covered include: matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year.<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the academic year, the student will be formally graded on the following:<br /> *two in-class oral tests (O&lt;sub&gt;1&lt;/sub&gt; and O&lt;sub&gt;2&lt;/sub&gt;);<br /> *two in-class written tests (W&lt;sub&gt;1&lt;/sub&gt; and W&lt;sub&gt;2&lt;/sub&gt;);<br /> *several quizzes (Q&lt;sub&gt;1&lt;/sub&gt; and Q&lt;sub&gt;2&lt;/sub&gt;, where Q&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the quizzes in the i-th semester);<br /> *several homework assignments (H&lt;sub&gt;1&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;, where H&lt;sub&gt;i&lt;/sub&gt; is the average grade of all the homework assignments in the i-th semester);<br /> *two written exams (E&lt;sub&gt;1&lt;/sub&gt; and E&lt;sub&gt;2&lt;/sub&gt;).<br /> <br /> All grades (namely, O&lt;sub&gt;1&lt;/sub&gt;, O&lt;sub&gt;2&lt;/sub&gt;, W&lt;sub&gt;1&lt;/sub&gt;, W&lt;sub&gt;2&lt;/sub&gt;, Q&lt;sub&gt;1&lt;/sub&gt;, Q&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;1&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;, E&lt;sub&gt;1&lt;/sub&gt;, and E&lt;sub&gt;2&lt;/sub&gt;) are real numbers from 0 to 10.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the first semester&lt;/span&gt;''', C&lt;sub&gt;1&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;1&lt;/sub&gt; = 5/16*O&lt;sub&gt;1&lt;/sub&gt; + 4/16*W&lt;sub&gt;1&lt;/sub&gt; + 4/16*Q&lt;sub&gt;1&lt;/sub&gt; + 3/16*H&lt;sub&gt;1&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the first semester&lt;/span&gt;''', I&lt;sub&gt;1&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;1&lt;/sub&gt; = Round&lt;sub&gt;1&lt;/sub&gt;(3/10*E&lt;sub&gt;1&lt;/sub&gt; + 7/10*C&lt;sub&gt;1&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;1&lt;/sub&gt;(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> '''&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative course grade for the second semester&lt;/span&gt;''', C&lt;sub&gt;2&lt;/sub&gt;, is obtained '''without rounding''' by the following formula:<br /> <br /> '''C&lt;sub&gt;2&lt;/sub&gt; = 5/16*O&lt;sub&gt;2&lt;/sub&gt; + 4/16*W&lt;sub&gt;2&lt;/sub&gt; + 4/16*Q&lt;sub&gt;2&lt;/sub&gt; + 3/16*H&lt;sub&gt;2&lt;/sub&gt;.'''<br /> <br /> '''&lt;span style=&quot;color:#0000CD&quot;&gt;The intermediate course grade for the second semester&lt;/span&gt;''', I&lt;sub&gt;2&lt;/sub&gt;, is obtained by the following formula:<br /> <br /> '''I&lt;sub&gt;2&lt;/sub&gt; = Round&lt;sub&gt;2&lt;/sub&gt;(3/10*E&lt;sub&gt;2&lt;/sub&gt; + 7/10*C&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round&lt;sub&gt;2&lt;/sub&gt;(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the second semester&quot;.<br /> <br /> '''&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;''', F, is obtained by the following formula:<br /> <br /> '''F = Round(1/4*I&lt;sub&gt;1&lt;/sub&gt; + 3/4*I&lt;sub&gt;2&lt;/sub&gt;),'''<br /> <br /> where the function Round(x) is defined as Round&lt;sub&gt;1&lt;/sub&gt;(x) but with &quot;during the first semester&quot; replaced by &quot;during the academic year&quot;.<br /> <br /> The final grade for the course is included in a diploma supplement.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> <br /> ''' Module 1 '''<br /> * [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br /> <br /> * [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (14.10.2024) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br /> <br /> * [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br /> <br /> * [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2024) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br /> <br /> * [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br /> <br /> * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2024) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace.<br /> <br /> * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2024) Matrices, main definitions; special matrices (square matrices, triangular matrices, identity matrices, zero matrices); matrix scalar multiplication; matrix addition; matrix multiplication; main properties of these operations.<br /> <br /> == Homework ==<br /> <br /> === Нomework for group 241: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&amp;st=x3os308k&amp;dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&amp;st=6hxk6zvn&amp;dl=0 '''HW 6'''] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3vsw4814iipum6cvakssf/LAaG_HW_5_C-241.pdf?rlkey=96o9d2x8pwyoziytd8mg2az39&amp;st=313w4smc&amp;dl=0 '''HW 5'''] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/vu9pzmxewdma5ljm1d3u8/LAaG_HW_4_C-241.pdf?rlkey=xsytj06u0koojczrpsdcnw6bu&amp;st=sihki1ml&amp;dl=0 '''HW 4'''] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/jl5fsngt54s9rvvhox4m3/LAaG_HW_3_C-241.pdf?rlkey=vr1964sd4guhawef3km4dron3&amp;st=2fjdzgbt&amp;dl=0 '''HW 3'''] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/3ubslydi94mxpz8v0amby/LAaG_HW_2_C-241.pdf?rlkey=9pmzfe1yv8pb48fs47z0x4dz5&amp;st=e7c8vvr5&amp;dl=0 '''HW 2'''] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/40q9bw0k1t5plebeou81c/LAaG_HW_1_C-241.pdf?rlkey=g6ke6q3lj12gzngl58eq886ya&amp;st=p27k7d68&amp;dl=0 '''HW 1'''] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === Homework for group 242: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/e6xg5ccu8f5915feqspy5/242_3-Homework-7.pdf?rlkey=lc0dm6si0f9m5a70jdwyxmq67&amp;st=ey66zpum&amp;dl=0 '''HW 7'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/aj2sp62y2cv2qe8of54iv/242_3-Seminar-7.pdf?rlkey=zd5k7cy2het74cuwqtlduswzd&amp;st=p60diabt&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/2ye8k5rrstxots1u51q73/242_3-Homework-6.pdf?rlkey=71pi8i0w3z1wxkf5mbn3z1qqx&amp;st=ehno8ke2&amp;dl=0 '''HW 6'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/ajoic32145lvs4lmqa5oc/242_3-Seminar-6.pdf?rlkey=615lxiqik1l1h5jtaggeoqd0d&amp;st=pfw3r1ub&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/lixsntmopxeq24mwrp0yf/242_3-Homework-5.pdf?rlkey=9zg7xjqht9d0lkcejbp5s9p23&amp;st=8otyzkgd&amp;dl=0 '''HW 5'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/a06qon224kki4j8mri2w9/242_3-Seminar-5.pdf?rlkey=s6gjlcwlsh28edt2ljm0mqvay&amp;st=pui76cfe&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/r73ao8089bz27kwq7dblh/242_3-Homework-4.pdf?rlkey=h56xvgvj0jzmarz2agtnamsmy&amp;st=w1q7q1rj&amp;dl=0 '''HW 4'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/it6euj613hlh61ojquyy4/242_3-Seminar-4.pdf?rlkey=bhgrzo4vylr8p3lcoyr55n3v1&amp;st=g8ar2rlh&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/snxrn7ikx9wn61eq1vkuq/242_3-Homework-3.pdf?rlkey=2cc43nsh5gi5yr21nq0nt390p&amp;st=u36c6lsn&amp;dl=0 '''HW 3'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jcruibo1rvv59c3q1yoy2/242_3-Seminar-3.pdf?rlkey=chdjhtgip5vcpn96fhgch3b3t&amp;st=kn5jtwyy&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/vp7ra2znrhpmob6eeoxy9/242_3-Homework-2.pdf?rlkey=bsnt1yt4sy9qpbeou066k9x3e&amp;st=6uza4ia2&amp;dl=0 '''HW 2'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/qh5ica2zsdx08tr7q5bnv/242_3-Seminar-2.pdf?rlkey=o6r87tbm8qj12mft6j5t1p594&amp;st=l5hidw3c&amp;dl=0 seminar notes])&lt;/small&gt;<br /> * [https://www.dropbox.com/scl/fi/cf6kkcffkc79k7jumsgcr/242_3-Homework-1.pdf?rlkey=gyawvagyjfnhnt6rdbemkis6l&amp;st=mi2ckigg&amp;dl=0 '''HW 1'''] &lt;small&gt;([https://www.dropbox.com/scl/fi/jwggyfl8ld5sgnvj0ltfp/242_3-Seminar-1.pdf?rlkey=aljx1mgyyjw2elm2jevrmsps2&amp;st=deacuh7e&amp;dl=0 seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 243: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 244: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 245: ===<br /> '''Module 1'''<br /> * [ '''HW 1'''] (release: ; deadline: ) &lt;small&gt;([ seminar notes])&lt;/small&gt;<br /> <br /> === Homework for group 246: ===<br /> '''Module 1'''<br /> * [https://www.dropbox.com/scl/fi/7jug32pg8p2e5of9je3oh/LAaG_HW_7_C-246.pdf?rlkey=s8nmljpw1d7gkq56awdnr7qse&amp;st=jvcer5we&amp;dl=0 '''HW 7'''] (release: 22.10.24; deadline: 01.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/wyxoocazoapsw3c4230g4/LAaG_HW_6_C-246.pdf?rlkey=4d0f2118q95n06bjcrjtmdq1m&amp;st=1l7f1spw&amp;dl=0 '''HW 6'''] (release: 15.10.24; deadline: 22.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/pfwngjg0wp4qep9ijsoa5/LAaG_HW_5_C-246.pdf?rlkey=0y75xk7jwvx7e19p3z5dqw2td&amp;st=gelq50l7&amp;dl=0 '''HW 5'''] (release: 08.10.24; deadline: 15.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&amp;st=nh8ms6mw&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/oj45t56r2bfr6b0xy6rwn/LAaG_HW_4_C-246.pdf?rlkey=xvwybfi3y6v9tfq4nyamdivrg&amp;st=tkiuw33s&amp;dl=0 '''HW 4'''] (release: 01.10.24; deadline: 08.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/9xm6qkpggak3jslntvw1s/LAaG_HW_3_C-246.pdf?rlkey=gk47xvfr98bqtk7et0dgg82x5&amp;st=8gru7p6n&amp;dl=0 '''HW 3'''] (release: 24.09.24; deadline: 01.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/86sxgstvjmsr3izfz56o9/LAaG_HW_2_C-246.pdf?rlkey=hnh1sg869jlqtvqai0w2lo2br&amp;st=kpy2gobn&amp;dl=0 '''HW 2'''] (release: 17.09.24; deadline: 24.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&amp;st=drivxf0a&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/v6rm4sxskcot5g710rgiy/LAaG_HW_1_C-246.pdf?rlkey=u0rcabrzojhb37tq28vmxc9ij&amp;st=iopohi7l&amp;dl=0 '''HW 1'''] (release: 10.09.24; deadline: 17.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1bnIdX3Hd7RNZNMzzSWXAlJF0Lp65IwMzpOICFpy5arA/edit?gid=460063859#gid=460063859 241]!![https://docs.google.com/spreadsheets/d/1blYTf8QJuLGul2ZUJn1hRsvXiG4yYEjbbJwJ5-4giDQ/edit?gid=460063859#gid=460063859 242]!![https://docs.google.com/spreadsheets/d/1lV_Wv1Ulj56xm7Sen8RBuXq2GwI8wozrAqfRQNhs-cM/edit?gid=460063859#gid=460063859 243]!![https://docs.google.com/spreadsheets/d/1R6VolFa23SqfhlHuY_UE1h4ilcE6P8Q44kv7wpKl2lo/edit?gid=460063859#gid=460063859 244]!![https://docs.google.com/spreadsheets/d/1InsFpOS4ZgJzmEee_yNlpdwtT-swusDIGa7URRWSuG0/edit?gid=460063859#gid=460063859 245]!!<br /> [https://docs.google.com/spreadsheets/d/1vhn3SCxucv6_6Er0zMCFX_Si7mJCs_CM8eVAWIa4u9c/edit?gid=460063859#gid=460063859 246]<br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> Vvbalakirev