https://wiki.cs.hse.ru/api.php?action=feedcontributions&feedformat=atom&user=DbashminovaaWiki - Факультет компьютерных наук - Вклад [ru]2026-09-21T17:40:01ZВкладMediaWiki 1.43.9https://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2025/2026&diff=92961LAaG DSBA 2025/20262025-10-09T15:46:58Z<p>Dbashminovaa: hw5 254 255</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 251 (M+P+) !! 252 (P+) !! 253 !! 254 !! 255 !! 256 !! 257<br />
|-<br />
|| Lecturer ||colspan="7"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || colspan="2" | [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || Сергей Смирнов ([https://t.me/ssmirnov1977 tg]) || colspan="2" | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||colspan="2" | Сергей Смирнов ([https://t.me/ssmirnov1977 tg])<br />
|- <br />
|| Consultations ||colspan="2" | Mon, 18:00 -- 21:00, via Zoom <br><span style="color:#DC143C">One must notify me beforehand</span> || ??? ||colspan="2" |by agreement <br><span style="color:#DC143C">One must notify me beforehand via telegram</span> ||colspan="2" | ??? <br />
|-<br />
|| Assistant || Анастасия Полищук ([https://t.me/anm9ith tg]) <br> Никита Чариков ([https://t.me/ncharikov tg])<br />
|| Аиша Абтини ([https://t.me/abtini_aisha tg]) <br> Микаил Халмурзиев ([https://t.me/kh1mrzv tg])<br />
|| Егор Кондрашов ([https://t.me/ekondrashov tg]) <br> Пётр Греков ([https://t.me/dandelionwiner tg])<br />
|| Полина Гребенникова ([https://t.me/gggggggagagaa tg]) <br> Арина Мирошниченко (???)<br />
|| Анастасия Бронникова ([https://t.me/an4stic tg]) <br> Саадетдинов Руслан ([https://t.me/cristeronaldosui tg])<br />
|| Вержбицкий Макар ([https://t.me/makaroshh tg]) <br> Рязанов Данила ([https://ixlle tg])<br />
|| Слива Виктория ([https://svvika06 tg]) <br> Колесников Михаил ([https://michalcolesnikov tg])<br />
|- <!--<br />
|| Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru <br />
|- --><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 />
<div class="mw-collapsible"><br />
<br />
During the academic year, the student will be formally graded on the following:<br />
*two in-class oral tests (O<sub>1</sub> and O<sub>2</sub>);<br />
*two in-class written tests (W<sub>1</sub> and W<sub>2</sub>);<br />
*several quizzes (Q<sub>1</sub> and Q<sub>2</sub>, where Q<sub>i</sub> is the average grade of all the quizzes in the i-th semester);<br />
*several homework assignments (H<sub>1</sub> and H<sub>2</sub>, where H<sub>i</sub> is the average grade of all the homework assignments in the i-th semester);<br />
*two written exams (E<sub>1</sub> and E<sub>2</sub>).<br />
<br />
All grades (namely, O<sub>1</sub>, O<sub>2</sub>, W<sub>1</sub>, W<sub>2</sub>, Q<sub>1</sub>, Q<sub>2</sub>, H<sub>1</sub>, H<sub>2</sub>, E<sub>1</sub>, and E<sub>2</sub>) are real numbers from 0 to 10.<br />
<br />
'''<span style="color:#228B22">The cumulative course grade for the first semester</span>''', C<sub>1</sub>, is obtained '''without rounding''' by the following formula:<br />
<br />
'''C<sub>1</sub> = 5/16*O<sub>1</sub> + 4/16*W<sub>1</sub> + 4/16*Q<sub>1</sub> + 3/16*H<sub>1</sub>.'''<br />
<br />
'''<span style="color:#0000CD">The intermediate course grade for the first semester</span>''', I<sub>1</sub>, is obtained by the following formula:<br />
<br />
'''I<sub>1</sub> = Round<sub>1</sub>(3/10*E<sub>1</sub> + 7/10*C<sub>1</sub>),'''<br />
<br />
where the function Round<sub>1</sub>(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 />
'''<span style="color:#228B22">The cumulative course grade for the second semester</span>''', C<sub>2</sub>, is obtained '''without rounding''' by the following formula:<br />
<br />
'''C<sub>2</sub> = 5/16*O<sub>2</sub> + 4/16*W<sub>2</sub> + 4/16*Q<sub>2</sub> + 3/16*H<sub>2</sub>.'''<br />
<br />
'''<span style="color:#0000CD">The intermediate course grade for the second semester</span>''', I<sub>2</sub>, is obtained by the following formula:<br />
<br />
'''I<sub>2</sub> = Round<sub>2</sub>(3/10*E<sub>2</sub> + 7/10*C<sub>2</sub>),'''<br />
<br />
where the function Round<sub>2</sub>(x) is defined as Round<sub>1</sub>(x) but with "during the first semester" replaced by "during the second semester".<br />
<br />
'''<span style="color:#DC143C">The final grade for the course</span>''', F, is obtained by the following formula:<br />
<br />
'''F = Round(1/4*I<sub>1</sub> + 3/4*I<sub>2</sub>),'''<br />
<br />
where the function Round(x) is defined as Round<sub>1</sub>(x) but with "during the first semester" replaced by "during the academic year".<br />
<br />
The final grade for the course is included in a diploma supplement.<br />
<br />
</div><br />
<br />
== Lecture Notes ==<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (08.10.2025) 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'''] (01.10.2025) 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'''] (24.09.2025) 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'''] (17.09.2025) 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'''] (10.09.2025) 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'''] (03.09.2025) 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 />
{| class="wikitable"<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
!| 251 || 252 || 253 || 254 || 255 || 256 || 257<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/lfqw13fp36hau7mdv0gwi/LAaG_HW_1_g251.pdf?rlkey=7hect7s0e5lltb3p8ym7y7hf1&st=30n3f3i6&dl=0 HW_1] (17.09.25)<br> [https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&dl=0 Seminar_1 Notes] || [https://www.dropbox.com/scl/fi/ax1dhz6bldg14ry9swl81/LAaG_HW_1_g252.pdf?rlkey=fdy7l33qeorbivnmc3c8qoroc&st=mbk6tg89&dl=0 HW_1] (17.09.25)<br> [https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&dl=0 Seminar_1 Notes] || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25) || [https://www.dropbox.com/scl/fi/1cafkadmvo66rwxw44js4/HW1_laag.pdf?rlkey=44iwfa6wbs8ie4fgzt9hhqcm1&st=6p276ytr&dl=0 HW_1] || [https://www.dropbox.com/scl/fi/1cafkadmvo66rwxw44js4/HW1_laag.pdf?rlkey=44iwfa6wbs8ie4fgzt9hhqcm1&st=6p276ytr&dl=0 HW_1] || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25) || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/5nwkuuiukg7d152napc22/LAaG_HW_2_g251.pdf?rlkey=us5ap81ka30931pvtoadtdpph&st=wwvc8h9u&dl=0 HW_2] (24.09.25)<br> [https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&st=drivxf0a&dl=0 Seminar_2 Notes] || [https://www.dropbox.com/scl/fi/crga61a14v5w7hpqm500u/LAaG_HW_2_g252.pdf?rlkey=xwm4xjwj27x9sj2rrpzgw7n0j&st=e0f6r0vk&dl=0 HW_2] (24.09.25)<br> [https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&st=drivxf0a&dl=0 Seminar_2 Notes] || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25) || [https://www.dropbox.com/scl/fi/2vcf0649ewh28t7dbuv6q/HW2_laag.pdf?rlkey=1ydv7r357z6owm3qieqj0ur8d&st=tgsjy27t&dl=0 HW_2] || [https://www.dropbox.com/scl/fi/2vcf0649ewh28t7dbuv6q/HW2_laag.pdf?rlkey=1ydv7r357z6owm3qieqj0ur8d&st=tgsjy27t&dl=0 HW_2] || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25) || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/jr1pev59sbb5jfzaq1k40/LAaG_HW_3_g251.pdf?rlkey=vxi8fsfx2xvjgcuogz5c4qve5&st=6754k8ju&dl=0 HW_3] (01.10.25)<br> [https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&dl=0 Seminar_3 Notes] || [https://www.dropbox.com/scl/fi/hez67oos2s7vqrof8t0ln/LAaG_HW_3_g252.pdf?rlkey=yx0zprzl9hbuovzxoq7vbscbd&st=v61z88ns&dl=0 HW_3] (01.10.25)<br> [https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&dl=0 Seminar_3 Notes] || [https://www.dropbox.com/scl/fi/90un5qxzubsivfav1llyo/LAaG_HW_3.pdf?rlkey=xp5oi0o4dgfvmjuzbmys1j6el&st=awpa8wud&dl=0 HW_3] (01.10.25) || [https://www.dropbox.com/scl/fi/ohvl1o0nbcfqgipqektm2/HW3.pdf?rlkey=dj6igb48jpzpeznff15iamyof&st=p2czj6dl&dl=0 HW_3] || [https://www.dropbox.com/scl/fi/ohvl1o0nbcfqgipqektm2/HW3.pdf?rlkey=dj6igb48jpzpeznff15iamyof&st=p2czj6dl&dl=0 HW_3] || [https://www.dropbox.com/scl/fi/90un5qxzubsivfav1llyo/LAaG_HW_3.pdf?rlkey=xp5oi0o4dgfvmjuzbmys1j6el&st=awpa8wud&dl=0 HW_3] (01.10.25) || [https://www.dropbox.com/scl/fi/90un5qxzubsivfav1llyo/LAaG_HW_3.pdf?rlkey=xp5oi0o4dgfvmjuzbmys1j6el&st=awpa8wud&dl=0 HW_3] (01.10.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/c6fdf136f56u2w8itufqe/LAaG_HW_4_g251.pdf?rlkey=icdjen64kwsgy7btx10pvfyyi&st=z2d4f7ke&dl=0 HW_4] (08.10.25)<br> [https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&dl=0 Seminar_4 Notes] || [https://www.dropbox.com/scl/fi/tnadmlgzuyfk5vmx8ikyo/LAaG_HW_4_g252.pdf?rlkey=rm5j6jsorido8s7c41piq6h95&st=hzvhj8gf&dl=0 HW_4] (08.10.25)<br> [https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&dl=0 Seminar_4 Notes] || [https://www.dropbox.com/scl/fi/s713bzvm76t3hdqnvax3e/LAaG_HW_4.pdf?rlkey=5j735zhbqxskrvsg1u842d599&st=sn5c1z40&dl=0 HW_4] (08.10.25) || [https://www.dropbox.com/scl/fi/82orkmnydnte3bwisdr94/HW4.pdf?rlkey=pwvtw0h05uyoatn7lqmxepeox&st=gfrtasqr&dl=0 HW_4] || [https://www.dropbox.com/scl/fi/82orkmnydnte3bwisdr94/HW4.pdf?rlkey=pwvtw0h05uyoatn7lqmxepeox&st=gfrtasqr&dl=0 HW_4] || [https://www.dropbox.com/scl/fi/s713bzvm76t3hdqnvax3e/LAaG_HW_4.pdf?rlkey=5j735zhbqxskrvsg1u842d599&st=sn5c1z40&dl=0 HW_4] (08.10.25) || [https://www.dropbox.com/scl/fi/s713bzvm76t3hdqnvax3e/LAaG_HW_4.pdf?rlkey=5j735zhbqxskrvsg1u842d599&st=sn5c1z40&dl=0 HW_4] (08.10.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/6qpetp6qs2nl1jrdb91yx/LAaG_HW_5_g251.pdf?rlkey=8bnwp76w79moahnz0pp1j4c4d&st=4zn7lvk4&dl=0 HW_5] (15.10.25)<br> [https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&st=nh8ms6mw&dl=0 Seminar_5 Notes] || [https://www.dropbox.com/scl/fi/rr3s5xmmfokipxhaus9cd/LAaG_HW_5_g252.pdf?rlkey=bb0kjxjcymv1yprf36zyz4rmb&st=129ajklo&dl=0 HW_5] (15.10.25)<br> [https://www.dropbox.com/scl/fi/q7nube6y6o9pa2pz45nua/LAaG_Seminar_5.pdf?rlkey=umbgn4dey3r8zu2zd0c30z3ip&st=nh8ms6mw&dl=0 Seminar_5 Notes] || [https://www.dropbox.com/scl/fi/xuphak0bv1etofsqsrmce/LAaG_HW_5.pdf?rlkey=lgxelnendareoj22h6dx87ctc&st=73hoz7g2&dl=0 HW_5] (15.10.25) || [https://www.dropbox.com/scl/fi/g8fprniwe4sta1bpvkpvm/HW5_laag.pdf?rlkey=5s2j7p7y2h85o6mm48c96lish&st=4ve9xk4c&dl=0 HW_5] || [https://www.dropbox.com/scl/fi/g8fprniwe4sta1bpvkpvm/HW5_laag.pdf?rlkey=5s2j7p7y2h85o6mm48c96lish&st=4ve9xk4c&dl=0 HW_5] || [https://www.dropbox.com/scl/fi/xuphak0bv1etofsqsrmce/LAaG_HW_5.pdf?rlkey=lgxelnendareoj22h6dx87ctc&st=73hoz7g2&dl=0 HW_5] (15.10.25) || [https://www.dropbox.com/scl/fi/xuphak0bv1etofsqsrmce/LAaG_HW_5.pdf?rlkey=lgxelnendareoj22h6dx87ctc&st=73hoz7g2&dl=0 HW_5] (15.10.25)<br />
|- <!--<br />
!| [ HW_6] (??.??.25)<br> [ Seminar_5 Notes] || [ HW_6] (??.??.25)<br> [ Seminar_5 Notes] || [ HW_6] (??.??.25) || [ HW_6] || [ HW_6] || [ HW_6] (??.??.25) || [ HW_5] (??.??.25)<br />
|- --><br />
|}<br />
<br />
== Exams ==<br />
<br />
== Results ==<br />
<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! [https://docs.google.com/spreadsheets/d/160E4MbpPyngJIc16KRggVDotSIuk-PL9LRB7oPWJd0s/edit?gid=460063859#gid=460063859 251]!![https://docs.google.com/spreadsheets/d/1Ujh4lagHaXKUYRnDCuYk--MHIIhpjn6dO7taiAAw3Q0/edit?gid=460063859#gid=460063859 252]!![https://docs.google.com/spreadsheets/d/1w52uViuY2_98QnYr9SbkMz6drP1swvY3PQDCeEPY5Ss/edit?gid=460063859#gid=460063859 253]!![https://docs.google.com/spreadsheets/d/1Bm_EeZmDGoGZokvUyC-2vcvCZUTOQKNkSTMz66zsv9E/edit?gid=460063859#gid=460063859 254]!![https://docs.google.com/spreadsheets/d/1GA89gvCY6tfhJB2Ji1BkkRSZ9P_4-zynOritOp4nY58/edit?gid=460063859#gid=460063859 255]!![https://docs.google.com/spreadsheets/d/1tcZ2S8IL51In8lteh36lQ5jLkx2Oj9F5za3CNtu2rOs/edit?gid=460063859#gid=460063859 256]!![https://docs.google.com/spreadsheets/d/1888W-OQoYermlUWeJ16Vn0jsIuVImrk5mx-6MwnXhJs/edit?gid=460063859#gid=460063859 257]<br />
|}<br />
<br />
== Navigation ==<br />
<div style="border:1px; border-style:solid; border-color:#a2a9b1; padding:3px"><br />
<table style="border-spacing:0; background:transparent; color:inherit; width:100%"><br />
<tr><br />
<th scope="colgroup" style="background-color:#cfe3ff" colspan="2"><div id="DSBA22" style="font-size:114%; margin:0 5em">DSBA 2022/2023</div></th><br />
</tr><br />
<tr ><br />
<th scope="row" style="border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff">First year</th><br />
<td style="text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px"><br />
<div style="padding:0em 0.25em"><br />
<ul><li style="display:inline-block; padding:2px">[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &bull; </li><li style="display:inline-block; padding:2px">[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &bull; </li><li style="display:inline-block; padding:2px">[[Calculus_DSBA_2022/2023|Calculus]] &bull; </li><li style="display:inline-block; padding:2px">[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &bull; </li><li style="display:inline-block; padding:2px">[[DSBA_Algebra_2022_2023|Algebra]] </li></ul><br />
</div></td><br />
</tr><br />
</table><br />
</div></div>Dbashminovaahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2025/2026&diff=92822LAaG DSBA 2025/20262025-10-03T21:04:55Z<p>Dbashminovaa: добавление ДЗ</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 251 (M+P+) !! 252 (P+) !! 253 !! 254 !! 255 !! 256 !! 257<br />
|-<br />
|| Lecturer ||colspan="7"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || colspan="2" | [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || Сергей Смирнов ([https://t.me/ssmirnov1977 tg]) || colspan="2" | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||colspan="2" | Сергей Смирнов ([https://t.me/ssmirnov1977 tg])<br />
|- <br />
|| Consultations ||colspan="2" | Mon, 18:00 -- 21:00, via Zoom <br><span style="color:#DC143C">One must notify me beforehand</span> || ??? ||colspan="2" |by agreement <br><span style="color:#DC143C">One must notify me beforehand via telegram</span> ||colspan="2" | ??? <br />
|-<br />
|| Assistant || Анастасия Полищук ([https://t.me/anm9ith tg]) <br> Никита Чариков ([https://t.me/ncharikov tg])<br />
|| Аиша Абтини ([https://t.me/abtini_aisha tg]) <br> Микаил Халмурзиев ([https://t.me/kh1mrzv tg])<br />
|| Егор Кондрашов ([https://t.me/ekondrashov tg]) <br> Пётр Греков ([https://t.me/dandelionwiner tg])<br />
|| Полина Гребенникова ([https://t.me/gggggggagagaa tg]) <br> Арина Мирошниченко (???)<br />
|| Анастасия Бронникова ([https://t.me/an4stic tg]) <br> Саадетдинов Руслан ([https://t.me/cristeronaldosui tg])<br />
|| Вержбицкий Макар ([https://t.me/makaroshh tg]) <br> Рязанов Данила ([https://ixlle tg])<br />
|| Слива Виктория ([https://svvika06 tg]) <br> Колесников Михаил ([https://michalcolesnikov tg])<br />
|- <!--<br />
|| Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru <br />
|- --><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 />
<div class="mw-collapsible"><br />
<br />
During the academic year, the student will be formally graded on the following:<br />
*two in-class oral tests (O<sub>1</sub> and O<sub>2</sub>);<br />
*two in-class written tests (W<sub>1</sub> and W<sub>2</sub>);<br />
*several quizzes (Q<sub>1</sub> and Q<sub>2</sub>, where Q<sub>i</sub> is the average grade of all the quizzes in the i-th semester);<br />
*several homework assignments (H<sub>1</sub> and H<sub>2</sub>, where H<sub>i</sub> is the average grade of all the homework assignments in the i-th semester);<br />
*two written exams (E<sub>1</sub> and E<sub>2</sub>).<br />
<br />
All grades (namely, O<sub>1</sub>, O<sub>2</sub>, W<sub>1</sub>, W<sub>2</sub>, Q<sub>1</sub>, Q<sub>2</sub>, H<sub>1</sub>, H<sub>2</sub>, E<sub>1</sub>, and E<sub>2</sub>) are real numbers from 0 to 10.<br />
<br />
'''<span style="color:#228B22">The cumulative course grade for the first semester</span>''', C<sub>1</sub>, is obtained '''without rounding''' by the following formula:<br />
<br />
'''C<sub>1</sub> = 5/16*O<sub>1</sub> + 4/16*W<sub>1</sub> + 4/16*Q<sub>1</sub> + 3/16*H<sub>1</sub>.'''<br />
<br />
'''<span style="color:#0000CD">The intermediate course grade for the first semester</span>''', I<sub>1</sub>, is obtained by the following formula:<br />
<br />
'''I<sub>1</sub> = Round<sub>1</sub>(3/10*E<sub>1</sub> + 7/10*C<sub>1</sub>),'''<br />
<br />
where the function Round<sub>1</sub>(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 />
'''<span style="color:#228B22">The cumulative course grade for the second semester</span>''', C<sub>2</sub>, is obtained '''without rounding''' by the following formula:<br />
<br />
'''C<sub>2</sub> = 5/16*O<sub>2</sub> + 4/16*W<sub>2</sub> + 4/16*Q<sub>2</sub> + 3/16*H<sub>2</sub>.'''<br />
<br />
'''<span style="color:#0000CD">The intermediate course grade for the second semester</span>''', I<sub>2</sub>, is obtained by the following formula:<br />
<br />
'''I<sub>2</sub> = Round<sub>2</sub>(3/10*E<sub>2</sub> + 7/10*C<sub>2</sub>),'''<br />
<br />
where the function Round<sub>2</sub>(x) is defined as Round<sub>1</sub>(x) but with "during the first semester" replaced by "during the second semester".<br />
<br />
'''<span style="color:#DC143C">The final grade for the course</span>''', F, is obtained by the following formula:<br />
<br />
'''F = Round(1/4*I<sub>1</sub> + 3/4*I<sub>2</sub>),'''<br />
<br />
where the function Round(x) is defined as Round<sub>1</sub>(x) but with "during the first semester" replaced by "during the academic year".<br />
<br />
The final grade for the course is included in a diploma supplement.<br />
<br />
</div><br />
<br />
== Lecture Notes ==<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (01.10.2025) 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'''] (24.09.2025) 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'''] (17.09.2025) 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'''] (10.09.2025) 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'''] (03.09.2025) 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 />
{| class="wikitable"<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
!| 251 || 252 || 253 || 254 || 255 || 256 || 257<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/lfqw13fp36hau7mdv0gwi/LAaG_HW_1_g251.pdf?rlkey=7hect7s0e5lltb3p8ym7y7hf1&st=30n3f3i6&dl=0 HW_1] (17.09.25)<br> [https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&dl=0 Seminar_1 Notes] || [https://www.dropbox.com/scl/fi/ax1dhz6bldg14ry9swl81/LAaG_HW_1_g252.pdf?rlkey=fdy7l33qeorbivnmc3c8qoroc&st=mbk6tg89&dl=0 HW_1] (17.09.25)<br> [https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&dl=0 Seminar_1 Notes] || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25) || [https://www.dropbox.com/scl/fi/1cafkadmvo66rwxw44js4/HW1_laag.pdf?rlkey=44iwfa6wbs8ie4fgzt9hhqcm1&st=6p276ytr&dl=0 HW_1] || [https://www.dropbox.com/scl/fi/1cafkadmvo66rwxw44js4/HW1_laag.pdf?rlkey=44iwfa6wbs8ie4fgzt9hhqcm1&st=6p276ytr&dl=0 HW_1] || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25) || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/5nwkuuiukg7d152napc22/LAaG_HW_2_g251.pdf?rlkey=us5ap81ka30931pvtoadtdpph&st=wwvc8h9u&dl=0 HW_2] (24.09.25)<br> [https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&st=drivxf0a&dl=0 Seminar_2 Notes] || [https://www.dropbox.com/scl/fi/crga61a14v5w7hpqm500u/LAaG_HW_2_g252.pdf?rlkey=xwm4xjwj27x9sj2rrpzgw7n0j&st=e0f6r0vk&dl=0 HW_2] (24.09.25)<br> [https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&st=drivxf0a&dl=0 Seminar_2 Notes] || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25) || [https://www.dropbox.com/scl/fi/2vcf0649ewh28t7dbuv6q/HW2_laag.pdf?rlkey=1ydv7r357z6owm3qieqj0ur8d&st=tgsjy27t&dl=0 HW_2] || [https://www.dropbox.com/scl/fi/2vcf0649ewh28t7dbuv6q/HW2_laag.pdf?rlkey=1ydv7r357z6owm3qieqj0ur8d&st=tgsjy27t&dl=0 HW_2] || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25) || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/jr1pev59sbb5jfzaq1k40/LAaG_HW_3_g251.pdf?rlkey=vxi8fsfx2xvjgcuogz5c4qve5&st=6754k8ju&dl=0 HW_3] (01.10.25)<br> [https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&dl=0 Seminar_3 Notes] || [https://www.dropbox.com/scl/fi/hez67oos2s7vqrof8t0ln/LAaG_HW_3_g252.pdf?rlkey=yx0zprzl9hbuovzxoq7vbscbd&st=v61z88ns&dl=0 HW_3] (01.10.25)<br> [https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&dl=0 Seminar_3 Notes] || [https://www.dropbox.com/scl/fi/90un5qxzubsivfav1llyo/LAaG_HW_3.pdf?rlkey=xp5oi0o4dgfvmjuzbmys1j6el&st=awpa8wud&dl=0 HW_3] (01.10.25) || [https://www.dropbox.com/scl/fi/ohvl1o0nbcfqgipqektm2/HW3.pdf?rlkey=dj6igb48jpzpeznff15iamyof&st=p2czj6dl&dl=0 HW_3] || [https://www.dropbox.com/scl/fi/ohvl1o0nbcfqgipqektm2/HW3.pdf?rlkey=dj6igb48jpzpeznff15iamyof&st=p2czj6dl&dl=0 HW_3] || [https://www.dropbox.com/scl/fi/90un5qxzubsivfav1llyo/LAaG_HW_3.pdf?rlkey=xp5oi0o4dgfvmjuzbmys1j6el&st=awpa8wud&dl=0 HW_3] (01.10.25) || [https://www.dropbox.com/scl/fi/90un5qxzubsivfav1llyo/LAaG_HW_3.pdf?rlkey=xp5oi0o4dgfvmjuzbmys1j6el&st=awpa8wud&dl=0 HW_3] (01.10.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/c6fdf136f56u2w8itufqe/LAaG_HW_4_g251.pdf?rlkey=icdjen64kwsgy7btx10pvfyyi&st=z2d4f7ke&dl=0 HW_4] (08.10.25)<br> [https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&dl=0 Seminar_4 Notes] || [https://www.dropbox.com/scl/fi/tnadmlgzuyfk5vmx8ikyo/LAaG_HW_4_g252.pdf?rlkey=rm5j6jsorido8s7c41piq6h95&st=hzvhj8gf&dl=0 HW_4] (08.10.25)<br> [https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&dl=0 Seminar_4 Notes] || [https://www.dropbox.com/scl/fi/s713bzvm76t3hdqnvax3e/LAaG_HW_4.pdf?rlkey=5j735zhbqxskrvsg1u842d599&st=sn5c1z40&dl=0 HW_4] (08.10.25) || [https://www.dropbox.com/scl/fi/82orkmnydnte3bwisdr94/HW4.pdf?rlkey=pwvtw0h05uyoatn7lqmxepeox&st=gfrtasqr&dl=0 HW_4] || [https://www.dropbox.com/scl/fi/82orkmnydnte3bwisdr94/HW4.pdf?rlkey=pwvtw0h05uyoatn7lqmxepeox&st=gfrtasqr&dl=0 HW_4] || [https://www.dropbox.com/scl/fi/s713bzvm76t3hdqnvax3e/LAaG_HW_4.pdf?rlkey=5j735zhbqxskrvsg1u842d599&st=sn5c1z40&dl=0 HW_4] (08.10.25) || [https://www.dropbox.com/scl/fi/s713bzvm76t3hdqnvax3e/LAaG_HW_4.pdf?rlkey=5j735zhbqxskrvsg1u842d599&st=sn5c1z40&dl=0 HW_4] (08.10.25)<br />
|}<br />
<br />
== Exams ==<br />
<br />
== Results ==<br />
<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! [https://docs.google.com/spreadsheets/d/160E4MbpPyngJIc16KRggVDotSIuk-PL9LRB7oPWJd0s/edit?gid=460063859#gid=460063859 251]!![https://docs.google.com/spreadsheets/d/1Ujh4lagHaXKUYRnDCuYk--MHIIhpjn6dO7taiAAw3Q0/edit?gid=460063859#gid=460063859 252]!![https://docs.google.com/spreadsheets/d/1w52uViuY2_98QnYr9SbkMz6drP1swvY3PQDCeEPY5Ss/edit?gid=460063859#gid=460063859 253]!![https://docs.google.com/spreadsheets/d/1Bm_EeZmDGoGZokvUyC-2vcvCZUTOQKNkSTMz66zsv9E/edit?gid=460063859#gid=460063859 254]!![https://docs.google.com/spreadsheets/d/1GA89gvCY6tfhJB2Ji1BkkRSZ9P_4-zynOritOp4nY58/edit?gid=460063859#gid=460063859 255]!![https://docs.google.com/spreadsheets/d/1tcZ2S8IL51In8lteh36lQ5jLkx2Oj9F5za3CNtu2rOs/edit?gid=460063859#gid=460063859 256]!![https://docs.google.com/spreadsheets/d/1888W-OQoYermlUWeJ16Vn0jsIuVImrk5mx-6MwnXhJs/edit?gid=460063859#gid=460063859 257]<br />
|}<br />
<br />
== Navigation ==<br />
<div style="border:1px; border-style:solid; border-color:#a2a9b1; padding:3px"><br />
<table style="border-spacing:0; background:transparent; color:inherit; width:100%"><br />
<tr><br />
<th scope="colgroup" style="background-color:#cfe3ff" colspan="2"><div id="DSBA22" style="font-size:114%; margin:0 5em">DSBA 2022/2023</div></th><br />
</tr><br />
<tr ><br />
<th scope="row" style="border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff">First year</th><br />
<td style="text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px"><br />
<div style="padding:0em 0.25em"><br />
<ul><li style="display:inline-block; padding:2px">[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &bull; </li><li style="display:inline-block; padding:2px">[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &bull; </li><li style="display:inline-block; padding:2px">[[Calculus_DSBA_2022/2023|Calculus]] &bull; </li><li style="display:inline-block; padding:2px">[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &bull; </li><li style="display:inline-block; padding:2px">[[DSBA_Algebra_2022_2023|Algebra]] </li></ul><br />
</div></td><br />
</tr><br />
</table><br />
</div></div>Dbashminovaahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2025/2026&diff=92821LAaG DSBA 2025/20262025-10-03T20:59:38Z<p>Dbashminovaa: строчка консультаций</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 251 (M+P+) !! 252 (P+) !! 253 !! 254 !! 255 !! 256 !! 257<br />
|-<br />
|| Lecturer ||colspan="7"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || colspan="2" | [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || Сергей Смирнов ([https://t.me/ssmirnov1977 tg]) || colspan="2" | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||colspan="2" | Сергей Смирнов ([https://t.me/ssmirnov1977 tg])<br />
|- <br />
|| Consultations ||colspan="2" | Mon, 18:00 -- 21:00, via Zoom <br><span style="color:#DC143C">One must notify me beforehand</span> || ??? ||colspan="2" |by agreement <br><span style="color:#DC143C">One must notify me beforehand via telegram</span> ||colspan="2" | ??? <br />
|-<br />
|| Assistant || Анастасия Полищук ([https://t.me/anm9ith tg]) <br> Никита Чариков ([https://t.me/ncharikov tg])<br />
|| Аиша Абтини ([https://t.me/abtini_aisha tg]) <br> Микаил Халмурзиев ([https://t.me/kh1mrzv tg])<br />
|| Егор Кондрашов ([https://t.me/ekondrashov tg]) <br> Пётр Греков ([https://t.me/dandelionwiner tg])<br />
|| Полина Гребенникова ([https://t.me/gggggggagagaa tg]) <br> Арина Мирошниченко (???)<br />
|| Анастасия Бронникова ([https://t.me/an4stic tg]) <br> Саадетдинов Руслан ([https://t.me/cristeronaldosui tg])<br />
|| Вержбицкий Макар ([https://t.me/makaroshh tg]) <br> Рязанов Данила ([https://ixlle tg])<br />
|| Слива Виктория ([https://svvika06 tg]) <br> Колесников Михаил ([https://michalcolesnikov tg])<br />
|- <!--<br />
|| Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru <br />
|- --><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 />
<div class="mw-collapsible"><br />
<br />
During the academic year, the student will be formally graded on the following:<br />
*two in-class oral tests (O<sub>1</sub> and O<sub>2</sub>);<br />
*two in-class written tests (W<sub>1</sub> and W<sub>2</sub>);<br />
*several quizzes (Q<sub>1</sub> and Q<sub>2</sub>, where Q<sub>i</sub> is the average grade of all the quizzes in the i-th semester);<br />
*several homework assignments (H<sub>1</sub> and H<sub>2</sub>, where H<sub>i</sub> is the average grade of all the homework assignments in the i-th semester);<br />
*two written exams (E<sub>1</sub> and E<sub>2</sub>).<br />
<br />
All grades (namely, O<sub>1</sub>, O<sub>2</sub>, W<sub>1</sub>, W<sub>2</sub>, Q<sub>1</sub>, Q<sub>2</sub>, H<sub>1</sub>, H<sub>2</sub>, E<sub>1</sub>, and E<sub>2</sub>) are real numbers from 0 to 10.<br />
<br />
'''<span style="color:#228B22">The cumulative course grade for the first semester</span>''', C<sub>1</sub>, is obtained '''without rounding''' by the following formula:<br />
<br />
'''C<sub>1</sub> = 5/16*O<sub>1</sub> + 4/16*W<sub>1</sub> + 4/16*Q<sub>1</sub> + 3/16*H<sub>1</sub>.'''<br />
<br />
'''<span style="color:#0000CD">The intermediate course grade for the first semester</span>''', I<sub>1</sub>, is obtained by the following formula:<br />
<br />
'''I<sub>1</sub> = Round<sub>1</sub>(3/10*E<sub>1</sub> + 7/10*C<sub>1</sub>),'''<br />
<br />
where the function Round<sub>1</sub>(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 />
'''<span style="color:#228B22">The cumulative course grade for the second semester</span>''', C<sub>2</sub>, is obtained '''without rounding''' by the following formula:<br />
<br />
'''C<sub>2</sub> = 5/16*O<sub>2</sub> + 4/16*W<sub>2</sub> + 4/16*Q<sub>2</sub> + 3/16*H<sub>2</sub>.'''<br />
<br />
'''<span style="color:#0000CD">The intermediate course grade for the second semester</span>''', I<sub>2</sub>, is obtained by the following formula:<br />
<br />
'''I<sub>2</sub> = Round<sub>2</sub>(3/10*E<sub>2</sub> + 7/10*C<sub>2</sub>),'''<br />
<br />
where the function Round<sub>2</sub>(x) is defined as Round<sub>1</sub>(x) but with "during the first semester" replaced by "during the second semester".<br />
<br />
'''<span style="color:#DC143C">The final grade for the course</span>''', F, is obtained by the following formula:<br />
<br />
'''F = Round(1/4*I<sub>1</sub> + 3/4*I<sub>2</sub>),'''<br />
<br />
where the function Round(x) is defined as Round<sub>1</sub>(x) but with "during the first semester" replaced by "during the academic year".<br />
<br />
The final grade for the course is included in a diploma supplement.<br />
<br />
</div><br />
<br />
== Lecture Notes ==<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (01.10.2025) 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'''] (24.09.2025) 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'''] (17.09.2025) 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'''] (10.09.2025) 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'''] (03.09.2025) 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 />
{| class="wikitable"<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
!| 251 || 252 || 253 || 254 || 255 || 256 || 257<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/lfqw13fp36hau7mdv0gwi/LAaG_HW_1_g251.pdf?rlkey=7hect7s0e5lltb3p8ym7y7hf1&st=30n3f3i6&dl=0 HW_1] (17.09.25)<br> [https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&dl=0 Seminar_1 Notes] || [https://www.dropbox.com/scl/fi/ax1dhz6bldg14ry9swl81/LAaG_HW_1_g252.pdf?rlkey=fdy7l33qeorbivnmc3c8qoroc&st=mbk6tg89&dl=0 HW_1] (17.09.25)<br> [https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&dl=0 Seminar_1 Notes] || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25) || [https://www.dropbox.com/scl/fi/1cafkadmvo66rwxw44js4/HW1_laag.pdf?rlkey=44iwfa6wbs8ie4fgzt9hhqcm1&st=6p276ytr&dl=0] || [https://www.dropbox.com/scl/fi/1cafkadmvo66rwxw44js4/HW1_laag.pdf?rlkey=44iwfa6wbs8ie4fgzt9hhqcm1&st=6p276ytr&dl=0] || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25) || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/5nwkuuiukg7d152napc22/LAaG_HW_2_g251.pdf?rlkey=us5ap81ka30931pvtoadtdpph&st=wwvc8h9u&dl=0 HW_2] (24.09.25)<br> [https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&st=drivxf0a&dl=0 Seminar_2 Notes] || [https://www.dropbox.com/scl/fi/crga61a14v5w7hpqm500u/LAaG_HW_2_g252.pdf?rlkey=xwm4xjwj27x9sj2rrpzgw7n0j&st=e0f6r0vk&dl=0 HW_2] (24.09.25)<br> [https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&st=drivxf0a&dl=0 Seminar_2 Notes] || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25) || [https://www.dropbox.com/scl/fi/2vcf0649ewh28t7dbuv6q/HW2_laag.pdf?rlkey=1ydv7r357z6owm3qieqj0ur8d&st=tgsjy27t&dl=0] || [https://www.dropbox.com/scl/fi/2vcf0649ewh28t7dbuv6q/HW2_laag.pdf?rlkey=1ydv7r357z6owm3qieqj0ur8d&st=tgsjy27t&dl=0] || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25) || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/jr1pev59sbb5jfzaq1k40/LAaG_HW_3_g251.pdf?rlkey=vxi8fsfx2xvjgcuogz5c4qve5&st=6754k8ju&dl=0 HW_3] (01.10.25)<br> [https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&dl=0 Seminar_3 Notes] || [https://www.dropbox.com/scl/fi/hez67oos2s7vqrof8t0ln/LAaG_HW_3_g252.pdf?rlkey=yx0zprzl9hbuovzxoq7vbscbd&st=v61z88ns&dl=0 HW_3] (01.10.25)<br> [https://www.dropbox.com/scl/fi/01ii8a8wyg1da5tk7jyel/LAaG_Seminar_3.pdf?rlkey=lvu0ae3e4n1aqv6yn4k7np472&dl=0 Seminar_3 Notes] || [https://www.dropbox.com/scl/fi/90un5qxzubsivfav1llyo/LAaG_HW_3.pdf?rlkey=xp5oi0o4dgfvmjuzbmys1j6el&st=awpa8wud&dl=0 HW_3] (01.10.25) || [] || [] || [https://www.dropbox.com/scl/fi/90un5qxzubsivfav1llyo/LAaG_HW_3.pdf?rlkey=xp5oi0o4dgfvmjuzbmys1j6el&st=awpa8wud&dl=0 HW_3] (01.10.25) || [https://www.dropbox.com/scl/fi/90un5qxzubsivfav1llyo/LAaG_HW_3.pdf?rlkey=xp5oi0o4dgfvmjuzbmys1j6el&st=awpa8wud&dl=0 HW_3] (01.10.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/c6fdf136f56u2w8itufqe/LAaG_HW_4_g251.pdf?rlkey=icdjen64kwsgy7btx10pvfyyi&st=z2d4f7ke&dl=0 HW_4] (08.10.25)<br> [https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&dl=0 Seminar_4 Notes] || [https://www.dropbox.com/scl/fi/tnadmlgzuyfk5vmx8ikyo/LAaG_HW_4_g252.pdf?rlkey=rm5j6jsorido8s7c41piq6h95&st=hzvhj8gf&dl=0 HW_4] (08.10.25)<br> [https://www.dropbox.com/scl/fi/bqwokbvzxygpkgjpmg6a3/LAaG_Seminar_4.pdf?rlkey=098u7702pnmdy9wpx9cmuexdk&dl=0 Seminar_4 Notes] || [https://www.dropbox.com/scl/fi/s713bzvm76t3hdqnvax3e/LAaG_HW_4.pdf?rlkey=5j735zhbqxskrvsg1u842d599&st=sn5c1z40&dl=0 HW_4] (08.10.25) || [] || [] || [https://www.dropbox.com/scl/fi/s713bzvm76t3hdqnvax3e/LAaG_HW_4.pdf?rlkey=5j735zhbqxskrvsg1u842d599&st=sn5c1z40&dl=0 HW_4] (08.10.25) || [https://www.dropbox.com/scl/fi/s713bzvm76t3hdqnvax3e/LAaG_HW_4.pdf?rlkey=5j735zhbqxskrvsg1u842d599&st=sn5c1z40&dl=0 HW_4] (08.10.25)<br />
|}<br />
<br />
== Exams ==<br />
<br />
== Results ==<br />
<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! [https://docs.google.com/spreadsheets/d/160E4MbpPyngJIc16KRggVDotSIuk-PL9LRB7oPWJd0s/edit?gid=460063859#gid=460063859 251]!![https://docs.google.com/spreadsheets/d/1Ujh4lagHaXKUYRnDCuYk--MHIIhpjn6dO7taiAAw3Q0/edit?gid=460063859#gid=460063859 252]!![https://docs.google.com/spreadsheets/d/1w52uViuY2_98QnYr9SbkMz6drP1swvY3PQDCeEPY5Ss/edit?gid=460063859#gid=460063859 253]!![https://docs.google.com/spreadsheets/d/1Bm_EeZmDGoGZokvUyC-2vcvCZUTOQKNkSTMz66zsv9E/edit?gid=460063859#gid=460063859 254]!![https://docs.google.com/spreadsheets/d/1GA89gvCY6tfhJB2Ji1BkkRSZ9P_4-zynOritOp4nY58/edit?gid=460063859#gid=460063859 255]!![https://docs.google.com/spreadsheets/d/1tcZ2S8IL51In8lteh36lQ5jLkx2Oj9F5za3CNtu2rOs/edit?gid=460063859#gid=460063859 256]!![https://docs.google.com/spreadsheets/d/1888W-OQoYermlUWeJ16Vn0jsIuVImrk5mx-6MwnXhJs/edit?gid=460063859#gid=460063859 257]<br />
|}<br />
<br />
== Navigation ==<br />
<div style="border:1px; border-style:solid; border-color:#a2a9b1; padding:3px"><br />
<table style="border-spacing:0; background:transparent; color:inherit; width:100%"><br />
<tr><br />
<th scope="colgroup" style="background-color:#cfe3ff" colspan="2"><div id="DSBA22" style="font-size:114%; margin:0 5em">DSBA 2022/2023</div></th><br />
</tr><br />
<tr ><br />
<th scope="row" style="border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff">First year</th><br />
<td style="text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px"><br />
<div style="padding:0em 0.25em"><br />
<ul><li style="display:inline-block; padding:2px">[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &bull; </li><li style="display:inline-block; padding:2px">[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &bull; </li><li style="display:inline-block; padding:2px">[[Calculus_DSBA_2022/2023|Calculus]] &bull; </li><li style="display:inline-block; padding:2px">[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &bull; </li><li style="display:inline-block; padding:2px">[[DSBA_Algebra_2022_2023|Algebra]] </li></ul><br />
</div></td><br />
</tr><br />
</table><br />
</div></div>Dbashminovaahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2025/2026&diff=92508LAaG DSBA 2025/20262025-09-22T15:29:22Z<p>Dbashminovaa: изменение файла HW1</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 251 (M+P+) !! 252 (P+) !! 253 !! 254 !! 255 !! 256 !! 257<br />
|-<br />
|| Lecturer ||colspan="7"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || colspan="2" | [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || Сергей Смирнов ([https://t.me/ssmirnov1977 tg]) || colspan="2" | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||colspan="2" | Сергей Смирнов ([https://t.me/ssmirnov1977 tg])<br />
|- <br />
|| Consultations ||colspan="2" | Mon, 18:00 -- 21:00, via Zoom <br><span style="color:#DC143C">One must notify me beforehand</span> || ??? ||colspan="2" | ??? ||colspan="2" | ??? <br />
|-<br />
|| Assistant || Анастасия Полищук ([https://t.me/anm9ith tg]) <br> Никита Чариков ([https://t.me/ncharikov tg])<br />
|| Аиша Абтини ([https://t.me/abtini_aisha tg]) <br> Микаил Халмурзиев ([https://t.me/kh1mrzv tg])<br />
|| Егор Кондрашов ([https://t.me/ekondrashov tg]) <br> Пётр Греков ([https://t.me/dandelionwiner tg])<br />
|| Полина Гребенникова ([https://t.me/gggggggagagaa tg]) <br> Арина Мирошниченко (???)<br />
|| Анастасия Бронникова ([https://t.me/an4stic tg]) <br> Саадетдинов Руслан ([https://t.me/cristeronaldosui tg])<br />
|| Вержбицкий Макар ([https://t.me/makaroshh tg]) <br> Рязанов Данила ([https://ixlle tg])<br />
|| Слива Виктория ([https://svvika06 tg]) <br> Колесников Михаил ([https://michalcolesnikov tg])<br />
|- <!--<br />
|| Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru <br />
|- --><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 />
<div class="mw-collapsible"><br />
<br />
During the academic year, the student will be formally graded on the following:<br />
*two in-class oral tests (O<sub>1</sub> and O<sub>2</sub>);<br />
*two in-class written tests (W<sub>1</sub> and W<sub>2</sub>);<br />
*several quizzes (Q<sub>1</sub> and Q<sub>2</sub>, where Q<sub>i</sub> is the average grade of all the quizzes in the i-th semester);<br />
*several homework assignments (H<sub>1</sub> and H<sub>2</sub>, where H<sub>i</sub> is the average grade of all the homework assignments in the i-th semester);<br />
*two written exams (E<sub>1</sub> and E<sub>2</sub>).<br />
<br />
All grades (namely, O<sub>1</sub>, O<sub>2</sub>, W<sub>1</sub>, W<sub>2</sub>, Q<sub>1</sub>, Q<sub>2</sub>, H<sub>1</sub>, H<sub>2</sub>, E<sub>1</sub>, and E<sub>2</sub>) are real numbers from 0 to 10.<br />
<br />
'''<span style="color:#228B22">The cumulative course grade for the first semester</span>''', C<sub>1</sub>, is obtained '''without rounding''' by the following formula:<br />
<br />
'''C<sub>1</sub> = 5/16*O<sub>1</sub> + 4/16*W<sub>1</sub> + 4/16*Q<sub>1</sub> + 3/16*H<sub>1</sub>.'''<br />
<br />
'''<span style="color:#0000CD">The intermediate course grade for the first semester</span>''', I<sub>1</sub>, is obtained by the following formula:<br />
<br />
'''I<sub>1</sub> = Round<sub>1</sub>(3/10*E<sub>1</sub> + 7/10*C<sub>1</sub>),'''<br />
<br />
where the function Round<sub>1</sub>(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 />
'''<span style="color:#228B22">The cumulative course grade for the second semester</span>''', C<sub>2</sub>, is obtained '''without rounding''' by the following formula:<br />
<br />
'''C<sub>2</sub> = 5/16*O<sub>2</sub> + 4/16*W<sub>2</sub> + 4/16*Q<sub>2</sub> + 3/16*H<sub>2</sub>.'''<br />
<br />
'''<span style="color:#0000CD">The intermediate course grade for the second semester</span>''', I<sub>2</sub>, is obtained by the following formula:<br />
<br />
'''I<sub>2</sub> = Round<sub>2</sub>(3/10*E<sub>2</sub> + 7/10*C<sub>2</sub>),'''<br />
<br />
where the function Round<sub>2</sub>(x) is defined as Round<sub>1</sub>(x) but with "during the first semester" replaced by "during the second semester".<br />
<br />
'''<span style="color:#DC143C">The final grade for the course</span>''', F, is obtained by the following formula:<br />
<br />
'''F = Round(1/4*I<sub>1</sub> + 3/4*I<sub>2</sub>),'''<br />
<br />
where the function Round(x) is defined as Round<sub>1</sub>(x) but with "during the first semester" replaced by "during the academic year".<br />
<br />
The final grade for the course is included in a diploma supplement.<br />
<br />
</div><br />
<br />
== Lecture Notes ==<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (17.09.2025) 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'''] (10.09.2025) 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'''] (03.09.2025) 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 />
{| class="wikitable"<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
!| 251 || 252 || 253 || 254 || 255 || 256 || 257<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/lfqw13fp36hau7mdv0gwi/LAaG_HW_1_g251.pdf?rlkey=7hect7s0e5lltb3p8ym7y7hf1&st=30n3f3i6&dl=0 HW_1] (17.09.25)<br> [https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&dl=0 Seminar_1 Notes] || [https://www.dropbox.com/scl/fi/ax1dhz6bldg14ry9swl81/LAaG_HW_1_g252.pdf?rlkey=fdy7l33qeorbivnmc3c8qoroc&st=mbk6tg89&dl=0 HW_1] (17.09.25)<br> [https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&dl=0 Seminar_1 Notes] || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25) || [https://www.dropbox.com/scl/fi/1cafkadmvo66rwxw44js4/HW1_laag.pdf?rlkey=44iwfa6wbs8ie4fgzt9hhqcm1&st=6p276ytr&dl=0] || [https://www.dropbox.com/scl/fi/1cafkadmvo66rwxw44js4/HW1_laag.pdf?rlkey=44iwfa6wbs8ie4fgzt9hhqcm1&st=6p276ytr&dl=0] || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25) || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/5nwkuuiukg7d152napc22/LAaG_HW_2_g251.pdf?rlkey=us5ap81ka30931pvtoadtdpph&st=wwvc8h9u&dl=0 HW_2] (24.09.25)<br> [https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&st=drivxf0a&dl=0 Seminar_2 Notes] || [https://www.dropbox.com/scl/fi/crga61a14v5w7hpqm500u/LAaG_HW_2_g252.pdf?rlkey=xwm4xjwj27x9sj2rrpzgw7n0j&st=e0f6r0vk&dl=0 HW_2] (24.09.25)<br> [https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&st=drivxf0a&dl=0 Seminar_2 Notes] || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25) || [https://www.dropbox.com/scl/fi/2vcf0649ewh28t7dbuv6q/HW2_laag.pdf?rlkey=1ydv7r357z6owm3qieqj0ur8d&st=tgsjy27t&dl=0] || [https://www.dropbox.com/scl/fi/2vcf0649ewh28t7dbuv6q/HW2_laag.pdf?rlkey=1ydv7r357z6owm3qieqj0ur8d&st=tgsjy27t&dl=0] || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25) || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25)<br />
|}<br />
<br />
== Exams ==<br />
<br />
== Results ==<br />
<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! [https://docs.google.com/spreadsheets/d/160E4MbpPyngJIc16KRggVDotSIuk-PL9LRB7oPWJd0s/edit?gid=460063859#gid=460063859 251]!![https://docs.google.com/spreadsheets/d/1Ujh4lagHaXKUYRnDCuYk--MHIIhpjn6dO7taiAAw3Q0/edit?gid=460063859#gid=460063859 252]!![https://docs.google.com/spreadsheets/d/1w52uViuY2_98QnYr9SbkMz6drP1swvY3PQDCeEPY5Ss/edit?gid=460063859#gid=460063859 253]!![https://docs.google.com/spreadsheets/d/1Bm_EeZmDGoGZokvUyC-2vcvCZUTOQKNkSTMz66zsv9E/edit?gid=460063859#gid=460063859 254]!![https://docs.google.com/spreadsheets/d/1GA89gvCY6tfhJB2Ji1BkkRSZ9P_4-zynOritOp4nY58/edit?gid=460063859#gid=460063859 255]!![https://docs.google.com/spreadsheets/d/1tcZ2S8IL51In8lteh36lQ5jLkx2Oj9F5za3CNtu2rOs/edit?gid=460063859#gid=460063859 256]!![https://docs.google.com/spreadsheets/d/1888W-OQoYermlUWeJ16Vn0jsIuVImrk5mx-6MwnXhJs/edit?gid=460063859#gid=460063859 257]<br />
|}<br />
<br />
== Navigation ==<br />
<div style="border:1px; border-style:solid; border-color:#a2a9b1; padding:3px"><br />
<table style="border-spacing:0; background:transparent; color:inherit; width:100%"><br />
<tr><br />
<th scope="colgroup" style="background-color:#cfe3ff" colspan="2"><div id="DSBA22" style="font-size:114%; margin:0 5em">DSBA 2022/2023</div></th><br />
</tr><br />
<tr ><br />
<th scope="row" style="border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff">First year</th><br />
<td style="text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px"><br />
<div style="padding:0em 0.25em"><br />
<ul><li style="display:inline-block; padding:2px">[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &bull; </li><li style="display:inline-block; padding:2px">[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &bull; </li><li style="display:inline-block; padding:2px">[[Calculus_DSBA_2022/2023|Calculus]] &bull; </li><li style="display:inline-block; padding:2px">[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &bull; </li><li style="display:inline-block; padding:2px">[[DSBA_Algebra_2022_2023|Algebra]] </li></ul><br />
</div></td><br />
</tr><br />
</table><br />
</div></div>Dbashminovaahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2025/2026&diff=92471LAaG DSBA 2025/20262025-09-20T20:07:07Z<p>Dbashminovaa: ссылка на дз для 254 и 255</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 251 (M+P+) !! 252 (P+) !! 253 !! 254 !! 255 !! 256 !! 257<br />
|-<br />
|| Lecturer ||colspan="7"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || colspan="2" | [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || Сергей Смирнов ([https://t.me/ssmirnov1977 tg]) || colspan="2" | [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/EndorFlame tg]) ||colspan="2" | Сергей Смирнов ([https://t.me/ssmirnov1977 tg])<br />
|- <br />
|| Consultations ||colspan="2" | Mon, 18:00 -- 21:00, via Zoom <br><span style="color:#DC143C">One must notify me beforehand</span> || ??? ||colspan="2" | ??? ||colspan="2" | ??? <br />
|-<br />
|| Assistant || Анастасия Полищук ([https://t.me/anm9ith tg]) <br> Никита Чариков ([https://t.me/ncharikov tg])<br />
|| Аиша Абтини ([https://t.me/abtini_aisha tg]) <br> Микаил Халмурзиев ([https://t.me/kh1mrzv tg])<br />
|| Егор Кондрашов ([https://t.me/ekondrashov tg]) <br> Пётр Греков ([https://t.me/dandelionwiner tg])<br />
|| Полина Гребенникова ([https://t.me/gggggggagagaa tg]) <br> Арина Мирошниченко (???)<br />
|| Анастасия Бронникова ([https://t.me/an4stic tg]) <br> Саадетдинов Руслан ([https://t.me/cristeronaldosui tg])<br />
|| Вержбицкий Макар ([https://t.me/makaroshh tg]) <br> Рязанов Данила ([https://ixlle tg])<br />
|| Слива Виктория ([https://svvika06 tg]) <br> Колесников Михаил ([https://michalcolesnikov tg])<br />
|- <!--<br />
|| Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru <br />
|- --><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 />
<div class="mw-collapsible"><br />
<br />
During the academic year, the student will be formally graded on the following:<br />
*two in-class oral tests (O<sub>1</sub> and O<sub>2</sub>);<br />
*two in-class written tests (W<sub>1</sub> and W<sub>2</sub>);<br />
*several quizzes (Q<sub>1</sub> and Q<sub>2</sub>, where Q<sub>i</sub> is the average grade of all the quizzes in the i-th semester);<br />
*several homework assignments (H<sub>1</sub> and H<sub>2</sub>, where H<sub>i</sub> is the average grade of all the homework assignments in the i-th semester);<br />
*two written exams (E<sub>1</sub> and E<sub>2</sub>).<br />
<br />
All grades (namely, O<sub>1</sub>, O<sub>2</sub>, W<sub>1</sub>, W<sub>2</sub>, Q<sub>1</sub>, Q<sub>2</sub>, H<sub>1</sub>, H<sub>2</sub>, E<sub>1</sub>, and E<sub>2</sub>) are real numbers from 0 to 10.<br />
<br />
'''<span style="color:#228B22">The cumulative course grade for the first semester</span>''', C<sub>1</sub>, is obtained '''without rounding''' by the following formula:<br />
<br />
'''C<sub>1</sub> = 5/16*O<sub>1</sub> + 4/16*W<sub>1</sub> + 4/16*Q<sub>1</sub> + 3/16*H<sub>1</sub>.'''<br />
<br />
'''<span style="color:#0000CD">The intermediate course grade for the first semester</span>''', I<sub>1</sub>, is obtained by the following formula:<br />
<br />
'''I<sub>1</sub> = Round<sub>1</sub>(3/10*E<sub>1</sub> + 7/10*C<sub>1</sub>),'''<br />
<br />
where the function Round<sub>1</sub>(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 />
'''<span style="color:#228B22">The cumulative course grade for the second semester</span>''', C<sub>2</sub>, is obtained '''without rounding''' by the following formula:<br />
<br />
'''C<sub>2</sub> = 5/16*O<sub>2</sub> + 4/16*W<sub>2</sub> + 4/16*Q<sub>2</sub> + 3/16*H<sub>2</sub>.'''<br />
<br />
'''<span style="color:#0000CD">The intermediate course grade for the second semester</span>''', I<sub>2</sub>, is obtained by the following formula:<br />
<br />
'''I<sub>2</sub> = Round<sub>2</sub>(3/10*E<sub>2</sub> + 7/10*C<sub>2</sub>),'''<br />
<br />
where the function Round<sub>2</sub>(x) is defined as Round<sub>1</sub>(x) but with "during the first semester" replaced by "during the second semester".<br />
<br />
'''<span style="color:#DC143C">The final grade for the course</span>''', F, is obtained by the following formula:<br />
<br />
'''F = Round(1/4*I<sub>1</sub> + 3/4*I<sub>2</sub>),'''<br />
<br />
where the function Round(x) is defined as Round<sub>1</sub>(x) but with "during the first semester" replaced by "during the academic year".<br />
<br />
The final grade for the course is included in a diploma supplement.<br />
<br />
</div><br />
<br />
== Lecture Notes ==<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (17.09.2025) 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'''] (10.09.2025) 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'''] (03.09.2025) 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 />
{| class="wikitable"<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
!| 251 || 252 || 253 || 254 || 255 || 256 || 257<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/lfqw13fp36hau7mdv0gwi/LAaG_HW_1_g251.pdf?rlkey=7hect7s0e5lltb3p8ym7y7hf1&st=30n3f3i6&dl=0 HW_1] (17.09.25)<br> [https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&dl=0 Seminar_1 Notes] || [https://www.dropbox.com/scl/fi/ax1dhz6bldg14ry9swl81/LAaG_HW_1_g252.pdf?rlkey=fdy7l33qeorbivnmc3c8qoroc&st=mbk6tg89&dl=0 HW_1] (17.09.25)<br> [https://www.dropbox.com/scl/fi/rbiwkvrp0wv5pwg5tw5bx/LAaG_Seminar_1.pdf?rlkey=mpmvtgqre17cvep0u7q4ipw58&dl=0 Seminar_1 Notes] || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25) || [https://www.dropbox.com/scl/fi/vpkca6ixpiowk1cl21mp8/HW1.pdf?rlkey=dkxigvt2dlfr7bhulnuivksqy&st=mw5gze3b&dl=0] || [https://www.dropbox.com/scl/fi/vpkca6ixpiowk1cl21mp8/HW1.pdf?rlkey=dkxigvt2dlfr7bhulnuivksqy&st=mw5gze3b&dl=0] || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25) || [https://www.dropbox.com/scl/fi/0hokvhnx6ktzxb2s5b8v6/LAaG_HW_1.pdf?rlkey=rlrvn55cr94icy8lpgnnow1ap&st=5zvwemmy&dl=0 HW_1] (17.09.25)<br />
|-<br />
!| [https://www.dropbox.com/scl/fi/5nwkuuiukg7d152napc22/LAaG_HW_2_g251.pdf?rlkey=us5ap81ka30931pvtoadtdpph&st=wwvc8h9u&dl=0 HW_2] (24.09.25)<br> [https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&st=drivxf0a&dl=0 Seminar_2 Notes] || [https://www.dropbox.com/scl/fi/crga61a14v5w7hpqm500u/LAaG_HW_2_g252.pdf?rlkey=xwm4xjwj27x9sj2rrpzgw7n0j&st=e0f6r0vk&dl=0 HW_2] (24.09.25)<br> [https://www.dropbox.com/scl/fi/0pjnumqwkvq1hm3l9bv9n/LAaG_Sem_2.pdf?rlkey=009giak7xgqr3i33o8udtoc8a&st=drivxf0a&dl=0 Seminar_2 Notes] || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25) || [https://www.dropbox.com/scl/fi/2vcf0649ewh28t7dbuv6q/HW2_laag.pdf?rlkey=1ydv7r357z6owm3qieqj0ur8d&st=tgsjy27t&dl=0] || [https://www.dropbox.com/scl/fi/2vcf0649ewh28t7dbuv6q/HW2_laag.pdf?rlkey=1ydv7r357z6owm3qieqj0ur8d&st=tgsjy27t&dl=0] || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25) || [https://www.dropbox.com/scl/fi/89z4ln21dylk4q3pxlbcb/LAaG_HW_2.pdf?rlkey=ap8x58ub99kdu3k2w9j2ukvr8&st=d5wj73f2&dl=0 HW_2] (24.09.25)<br />
|}<br />
<br />
== Exams ==<br />
<br />
== Results ==<br />
<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! [https://docs.google.com/spreadsheets/d/160E4MbpPyngJIc16KRggVDotSIuk-PL9LRB7oPWJd0s/edit?gid=460063859#gid=460063859 251]!![https://docs.google.com/spreadsheets/d/1Ujh4lagHaXKUYRnDCuYk--MHIIhpjn6dO7taiAAw3Q0/edit?gid=460063859#gid=460063859 252]!![https://docs.google.com/spreadsheets/d/1w52uViuY2_98QnYr9SbkMz6drP1swvY3PQDCeEPY5Ss/edit?gid=460063859#gid=460063859 253]!![https://docs.google.com/spreadsheets/d/1Bm_EeZmDGoGZokvUyC-2vcvCZUTOQKNkSTMz66zsv9E/edit?gid=460063859#gid=460063859 254]!![https://docs.google.com/spreadsheets/d/1GA89gvCY6tfhJB2Ji1BkkRSZ9P_4-zynOritOp4nY58/edit?gid=460063859#gid=460063859 255]!![https://docs.google.com/spreadsheets/d/1tcZ2S8IL51In8lteh36lQ5jLkx2Oj9F5za3CNtu2rOs/edit?gid=460063859#gid=460063859 256]!![https://docs.google.com/spreadsheets/d/1888W-OQoYermlUWeJ16Vn0jsIuVImrk5mx-6MwnXhJs/edit?gid=460063859#gid=460063859 257]<br />
|}<br />
<br />
== Navigation ==<br />
<div style="border:1px; border-style:solid; border-color:#a2a9b1; padding:3px"><br />
<table style="border-spacing:0; background:transparent; color:inherit; width:100%"><br />
<tr><br />
<th scope="colgroup" style="background-color:#cfe3ff" colspan="2"><div id="DSBA22" style="font-size:114%; margin:0 5em">DSBA 2022/2023</div></th><br />
</tr><br />
<tr ><br />
<th scope="row" style="border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff">First year</th><br />
<td style="text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px"><br />
<div style="padding:0em 0.25em"><br />
<ul><li style="display:inline-block; padding:2px">[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &bull; </li><li style="display:inline-block; padding:2px">[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &bull; </li><li style="display:inline-block; padding:2px">[[Calculus_DSBA_2022/2023|Calculus]] &bull; </li><li style="display:inline-block; padding:2px">[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &bull; </li><li style="display:inline-block; padding:2px">[[DSBA_Algebra_2022_2023|Algebra]] </li></ul><br />
</div></td><br />
</tr><br />
</table><br />
</div></div>Dbashminovaahttps://wiki.cs.hse.ru/index.php?title=Differential_Equations_2023/24&diff=84040Differential Equations 2023/242024-03-05T14:50:21Z<p>Dbashminovaa: ссылка на таблицу с результатами</p>
<hr />
<div>== [https://www.hse.ru/en/ba/data/courses/301393255.html Syllabus] ==<br />
<br />
“Differential Equations” is a spring semester course for second-year students studying at the Faculty of Computer Sciences. It is designed to suit the requirements of the Faculty of Computer Sciences curriculum as well as UoL where DE is a part of the mathematical curriculum. Besides the course on differential equations is included as a topic in “Mathematical methods for economists” external exam. <br />
<br />
This course is an important part of the bachelor stage in the education of the future applied mathematicians and computer scientists. It has to give students skills for the implementation of mathematical knowledge and expertise. Its prerequisite is the knowledge of the single variable calculus. <br />
<br />
In the spring semester, the course is split into two unequal parts: it is taught from January through the end of April and after the students finish with their UoL exams in May it will resume and will continue till mid-June. <br />
<br />
The assessment of the students will be done by setting mock exam by the end of the 3rd module, then later by the University of London (UoL) examinations in May and final exam will be set in late June. But the final grade will depend solely on mock, final exams performance and home assignments grades.<br />
<br />
As a general policy, personal computing devices such as laptops, calculators etc. are ''' not supposed to be used in the course'''. They are ''' absolutely prohibited in all exams'''. Students are expected to do all necessary arithmetic computations by hand.<br />
<br />
== Lecturers and Teachers==<br />
<br />
== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 221 (M+P+) !! 222 !! 223 !! 224 <br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/757685153 Александр Тараканов]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/757685153 Александр Тараканов] ([tg]) || [https://www.hse.ru/org/persons/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([https://t.me/dariabashminova tg])<br />
|- <br />
|| Assistants || Кульпанович Данила <br> drkulpanovich@edu.hse.ru<br />
|| Кульпанович Данила <br> drkulpanovich@edu.hse.ru<br />
|| Сипаров Иван <br> ivsiparov@edu.hse.ru<br />
||Сипаров Иван <br> ivsiparov@edu.hse.ru<br />
|- <!--<br />
|| Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru <br />
|- --><br />
|}<br />
<br />
== Lectures ==<br />
<br />
== Seminars ==<br />
<br />
<br />
== Midterm test ==<br />
<br />
== Final exam ==<br />
<br />
== UoL Materials ==<br />
<br />
== Assignments ==<br />
221: https://classroom.google.com/c/NjYzODMzMjQzNzkz?cjc=iolrmoh<br />
<br />
222: https://classroom.google.com/c/NjYzODMzNDExOTgw?cjc=3fsel77<br />
<br />
223: https://classroom.google.com/c/NjYzODMzMjQzODU1?cjc=ymftble<br />
<br />
224: https://classroom.google.com/c/NjYzODMzMjQzODY2?cjc=b6nlxhg<br />
<br />
=== Home assignments 2023 ===<br />
<br />
[https://www.dropbox.com/scl/fi/pw8r1t15ps6nvw3xfeo3n/homework_2.pdf?rlkey=1fad0bpo596iduvn34ofjmdxp&dl=0 Home assignment 2], due on "March 11th"<br />
<br />
[https://www.dropbox.com/scl/fi/aujksrvygtym1tic3b9js/homework_1.pdf?rlkey=u5f2rnicw1yd6fcypgvb065ak&dl=0 Home assignment 1], due on "February 26th"<br />
<br />
== Overall Results ==<br />
<br />
https://docs.google.com/spreadsheets/d/1V8B8msPMgAs8HcPthklAkMMsKdRVCHz5V2eaXbKOWw8/edit?usp=sharing<br />
<br />
== Grading System ==<br />
<br />
The home assignments constitute 30% of the final grade. The final exam is 40% of the final grade. The rest of the grade is formed by Midterm test which is due in the end of the 3rd module.<br />
<br />
''' The final grade on the course''' will be determined according to the formula:<br />
<br />
'''Grade''' = 0.4 * Final Exam + 0.3 * Midterm test + 0.3 * Home assignments<br />
<br />
All grades are given initially out of 100. The final grades are also transferred to 10- and 5-points grades in accordance with the table (to be posted).<br />
3. The scale of corresponding grades<br />
3.1. Total grades for a given course are converted from the 100-point scale to the 5-point<br />
and 10-point scale.<br />
3.2. The following basic scale has been established to convert grades from the 100-point scale to the 10-point scale<br />
100-point scale 10-point scale<br />
<br />
0-19,99 -> 1<br />
<br />
20-29,99 -> 2<br />
<br />
30-39,99 -> 3<br />
<br />
40-46,99 -> 4<br />
<br />
47-53,99 -> 5<br />
<br />
54-61,99 -> 6<br />
<br />
62-69,99 -> 7<br />
<br />
70-77,99 -> 8<br />
<br />
78-85,9 -> 9<br />
<br />
86-100 -> 10<br />
<br />
== Reading ==<br />
'''Obligatory:'''<br/><br />
- Mathematics for economists, Simon C. P., Blume L., 1994 <br/><br />
'''Optional:'''<br/><br />
- A.F. Fillipov. Collection of problems on differential equations. Moscow, “Nauka”, 1973 and later editions.<br/><br />
- V.K. Romanko, Course on Differential Equations and Calculus of Variations. Moscow and Saint-Petersburg, “Fizmatlit”, 2001 and later editions.<br/><br />
== Internet Resources ==<br />
[http://www.londonexternal.ac.uk/current_students/programme_resources/lse/index.shtml University of London Exam papers and Examiners reports for the last three years].<br/></div>Dbashminovaahttps://wiki.cs.hse.ru/index.php?title=Differential_Equations_2023/24&diff=83729Differential Equations 2023/242024-02-18T08:54:10Z<p>Dbashminovaa: Classrooms</p>
<hr />
<div>== [https://www.hse.ru/en/ba/data/courses/301393255.html Syllabus] ==<br />
<br />
“Differential Equations” is a spring semester course for second-year students studying at the Faculty of Computer Sciences. It is designed to suit the requirements of the Faculty of Computer Sciences curriculum as well as UoL where DE is a part of the mathematical curriculum. Besides the course on differential equations is included as a topic in “Mathematical methods for economists” external exam. <br />
<br />
This course is an important part of the bachelor stage in the education of the future applied mathematicians and computer scientists. It has to give students skills for the implementation of mathematical knowledge and expertise. Its prerequisite is the knowledge of the single variable calculus. <br />
<br />
In the spring semester, the course is split into two unequal parts: it is taught from January through the end of April and after the students finish with their UoL exams in May it will resume and will continue till mid-June. <br />
<br />
The assessment of the students will be done by setting mock exam by the end of the 3rd module, then later by the University of London (UoL) examinations in May and final exam will be set in late June. But the final grade will depend solely on mock, final exams performance and home assignments grades.<br />
<br />
As a general policy, personal computing devices such as laptops, calculators etc. are ''' not supposed to be used in the course'''. They are ''' absolutely prohibited in all exams'''. Students are expected to do all necessary arithmetic computations by hand.<br />
<br />
== Lecturers and Teachers==<br />
<br />
== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 221 (M+P+) !! 222 !! 223 !! 224 <br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/757685153 Александр Тараканов]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/757685153 Александр Тараканов] ([tg]) || [https://www.hse.ru/org/persons/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([tg])<br />
|- <br />
|| Assistants || Кульпанович Данила <br> drkulpanovich@edu.hse.ru<br />
|| Кульпанович Данила <br> drkulpanovich@edu.hse.ru<br />
|| Сипаров Иван <br> ivsiparov@edu.hse.ru<br />
||Сипаров Иван <br> ivsiparov@edu.hse.ru<br />
|- <!--<br />
|| Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru <br />
|- --><br />
|}<br />
<br />
== Lectures ==<br />
<br />
== Seminars ==<br />
<br />
<br />
== Midterm test ==<br />
<br />
== Final exam ==<br />
<br />
== UoL Materials ==<br />
<br />
== Assignments ==<br />
221: https://classroom.google.com/c/NjYzODMzMjQzNzkz?cjc=iolrmoh<br />
<br />
222: https://classroom.google.com/c/NjYzODMzNDExOTgw?cjc=3fsel77<br />
<br />
223: https://classroom.google.com/c/NjYzODMzMjQzODU1?cjc=ymftble<br />
<br />
224: https://classroom.google.com/c/NjYzODMzMjQzODY2?cjc=b6nlxhg<br />
<br />
=== Home assignments 2023 ===<br />
<br />
[https://www.dropbox.com/scl/fi/q367x7mthdo4eka2mvztz/homework_1.pdf?rlkey=outh1mn028j2yzyu8krwkfnf3&dl=0 Home assignment 1], due on "February 19th"<br />
<br />
== Overall Results ==<br />
<br />
== Grading System ==<br />
<br />
The home assignments constitute 30% of the final grade. The final exam is 40% of the final grade. The rest of the grade is formed by Midterm test which is due in the end of the 3rd module.<br />
<br />
''' The final grade on the course''' will be determined according to the formula:<br />
<br />
'''Grade''' = 0.4 * Final Exam + 0.3 * Midterm test + 0.3 * Home assignments<br />
<br />
All grades are given initially out of 100. The final grades are also transferred to 10- and 5-points grades in accordance with the table (to be posted).<br />
3. The scale of corresponding grades<br />
3.1. Total grades for a given course are converted from the 100-point scale to the 5-point<br />
and 10-point scale.<br />
3.2. The following basic scale has been established to convert grades from the 100-point scale to the 10-point scale<br />
100-point scale 10-point scale<br />
<br />
0-19,99 -> 1<br />
<br />
20-29,99 -> 2<br />
<br />
30-39,99 -> 3<br />
<br />
40-46,99 -> 4<br />
<br />
47-53,99 -> 5<br />
<br />
54-61,99 -> 6<br />
<br />
62-69,99 -> 7<br />
<br />
70-77,99 -> 8<br />
<br />
78-85,9 -> 9<br />
<br />
86-100 -> 10<br />
<br />
== Reading ==<br />
'''Obligatory:'''<br/><br />
- Mathematics for economists, Simon C. P., Blume L., 1994 <br/><br />
'''Optional:'''<br/><br />
- A.F. Fillipov. Collection of problems on differential equations. Moscow, “Nauka”, 1973 and later editions.<br/><br />
- V.K. Romanko, Course on Differential Equations and Calculus of Variations. Moscow and Saint-Petersburg, “Fizmatlit”, 2001 and later editions.<br/><br />
== Internet Resources ==<br />
[http://www.londonexternal.ac.uk/current_students/programme_resources/lse/index.shtml University of London Exam papers and Examiners reports for the last three years].<br/></div>Dbashminovaahttps://wiki.cs.hse.ru/index.php?title=Differential_Equations_2023/24&diff=83704Differential Equations 2023/242024-02-15T18:45:06Z<p>Dbashminovaa: ассистентство</p>
<hr />
<div>== [https://www.hse.ru/en/ba/data/courses/301393255.html Syllabus] ==<br />
<br />
“Differential Equations” is a spring semester course for second-year students studying at the Faculty of Computer Sciences. It is designed to suit the requirements of the Faculty of Computer Sciences curriculum as well as UoL where DE is a part of the mathematical curriculum. Besides the course on differential equations is included as a topic in “Mathematical methods for economists” external exam. <br />
<br />
This course is an important part of the bachelor stage in the education of the future applied mathematicians and computer scientists. It has to give students skills for the implementation of mathematical knowledge and expertise. Its prerequisite is the knowledge of the single variable calculus. <br />
<br />
In the spring semester, the course is split into two unequal parts: it is taught from January through the end of April and after the students finish with their UoL exams in May it will resume and will continue till mid-June. <br />
<br />
The assessment of the students will be done by setting mock exam by the end of the 3rd module, then later by the University of London (UoL) examinations in May and final exam will be set in late June. But the final grade will depend solely on mock, final exams performance and home assignments grades.<br />
<br />
As a general policy, personal computing devices such as laptops, calculators etc. are ''' not supposed to be used in the course'''. They are ''' absolutely prohibited in all exams'''. Students are expected to do all necessary arithmetic computations by hand.<br />
<br />
== Lecturers and Teachers==<br />
<br />
== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 221 (M+P+) !! 222 !! 223 !! 224 <br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/757685153 Александр Тараканов]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/757685153 Александр Тараканов] ([tg]) || [https://www.hse.ru/org/persons/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([tg])<br />
|- <br />
|| Assistants || Кульпанович Данила <br> drkulpanovich@edu.hse.ru<br />
|| Кульпанович Данила <br> drkulpanovich@edu.hse.ru<br />
|| Сипаров Иван <br> ivsiparov@edu.hse.ru<br />
||Сипаров Иван <br> ivsiparov@edu.hse.ru<br />
|- <!--<br />
|| Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru <br />
|- --><br />
|}<br />
<br />
== Lectures ==<br />
<br />
== Seminars ==<br />
<br />
<br />
== Midterm test ==<br />
<br />
== Final exam ==<br />
<br />
== UoL Materials ==<br />
<br />
== Assignments ==<br />
<br />
=== Home assignments 2023 ===<br />
<br />
[https://www.dropbox.com/scl/fi/q367x7mthdo4eka2mvztz/homework_1.pdf?rlkey=outh1mn028j2yzyu8krwkfnf3&dl=0 Home assignment 1], due on "February 19th"<br />
<br />
== Overall Results ==<br />
<br />
== Grading System ==<br />
<br />
The home assignments constitute 30% of the final grade. The final exam is 40% of the final grade. The rest of the grade is formed by Midterm test which is due in the end of the 3rd module.<br />
<br />
''' The final grade on the course''' will be determined according to the formula:<br />
<br />
'''Grade''' = 0.4 * Final Exam + 0.3 * Midterm test + 0.3 * Home assignments<br />
<br />
All grades are given initially out of 100. The final grades are also transferred to 10- and 5-points grades in accordance with the table (to be posted).<br />
3. The scale of corresponding grades<br />
3.1. Total grades for a given course are converted from the 100-point scale to the 5-point<br />
and 10-point scale.<br />
3.2. The following basic scale has been established to convert grades from the 100-point scale to the 10-point scale<br />
100-point scale 10-point scale<br />
<br />
0-19,99 -> 1<br />
<br />
20-29,99 -> 2<br />
<br />
30-39,99 -> 3<br />
<br />
40-46,99 -> 4<br />
<br />
47-53,99 -> 5<br />
<br />
54-61,99 -> 6<br />
<br />
62-69,99 -> 7<br />
<br />
70-77,99 -> 8<br />
<br />
78-85,9 -> 9<br />
<br />
86-100 -> 10<br />
<br />
== Reading ==<br />
'''Obligatory:'''<br/><br />
- Mathematics for economists, Simon C. P., Blume L., 1994 <br/><br />
'''Optional:'''<br/><br />
- A.F. Fillipov. Collection of problems on differential equations. Moscow, “Nauka”, 1973 and later editions.<br/><br />
- V.K. Romanko, Course on Differential Equations and Calculus of Variations. Moscow and Saint-Petersburg, “Fizmatlit”, 2001 and later editions.<br/><br />
== Internet Resources ==<br />
[http://www.londonexternal.ac.uk/current_students/programme_resources/lse/index.shtml University of London Exam papers and Examiners reports for the last three years].<br/></div>Dbashminovaahttps://wiki.cs.hse.ru/index.php?title=Differential_Equations_2023/24&diff=83703Differential Equations 2023/242024-02-15T18:42:33Z<p>Dbashminovaa: ассистенство</p>
<hr />
<div>== [https://www.hse.ru/en/ba/data/courses/301393255.html Syllabus] ==<br />
<br />
“Differential Equations” is a spring semester course for second-year students studying at the Faculty of Computer Sciences. It is designed to suit the requirements of the Faculty of Computer Sciences curriculum as well as UoL where DE is a part of the mathematical curriculum. Besides the course on differential equations is included as a topic in “Mathematical methods for economists” external exam. <br />
<br />
This course is an important part of the bachelor stage in the education of the future applied mathematicians and computer scientists. It has to give students skills for the implementation of mathematical knowledge and expertise. Its prerequisite is the knowledge of the single variable calculus. <br />
<br />
In the spring semester, the course is split into two unequal parts: it is taught from January through the end of April and after the students finish with their UoL exams in May it will resume and will continue till mid-June. <br />
<br />
The assessment of the students will be done by setting mock exam by the end of the 3rd module, then later by the University of London (UoL) examinations in May and final exam will be set in late June. But the final grade will depend solely on mock, final exams performance and home assignments grades.<br />
<br />
As a general policy, personal computing devices such as laptops, calculators etc. are ''' not supposed to be used in the course'''. They are ''' absolutely prohibited in all exams'''. Students are expected to do all necessary arithmetic computations by hand.<br />
<br />
== Lecturers and Teachers==<br />
<br />
== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 221 (M+P+) !! 222 !! 223 !! 224 <br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/757685153 Александр Тараканов]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/757685153 Александр Тараканов] ([tg]) || [https://www.hse.ru/org/persons/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([tg])<br />
|- <br />
|| Assistants || Кульпанович Данила Русланович <br> drkulpanovich@edu.hse.ru<br />
|| Кульпанович Данила Русланович <br> drkulpanovich@edu.hse.ru<br />
|| Сипаров Иван Владимирович <br> ivsiparov@edu.hse.ru<br />
||Сипаров Иван Владимирович <br> ivsiparov@edu.hse.ru<br />
|- <!--<br />
|| Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru <br />
|- --><br />
|}<br />
<br />
== Lectures ==<br />
<br />
== Seminars ==<br />
<br />
<br />
== Midterm test ==<br />
<br />
== Final exam ==<br />
<br />
== UoL Materials ==<br />
<br />
== Assignments ==<br />
<br />
=== Home assignments 2023 ===<br />
<br />
[https://www.dropbox.com/scl/fi/q367x7mthdo4eka2mvztz/homework_1.pdf?rlkey=outh1mn028j2yzyu8krwkfnf3&dl=0 Home assignment 1], due on "February 19th"<br />
<br />
== Overall Results ==<br />
<br />
== Grading System ==<br />
<br />
The home assignments constitute 30% of the final grade. The final exam is 40% of the final grade. The rest of the grade is formed by Midterm test which is due in the end of the 3rd module.<br />
<br />
''' The final grade on the course''' will be determined according to the formula:<br />
<br />
'''Grade''' = 0.4 * Final Exam + 0.3 * Midterm test + 0.3 * Home assignments<br />
<br />
All grades are given initially out of 100. The final grades are also transferred to 10- and 5-points grades in accordance with the table (to be posted).<br />
3. The scale of corresponding grades<br />
3.1. Total grades for a given course are converted from the 100-point scale to the 5-point<br />
and 10-point scale.<br />
3.2. The following basic scale has been established to convert grades from the 100-point scale to the 10-point scale<br />
100-point scale 10-point scale<br />
<br />
0-19,99 -> 1<br />
<br />
20-29,99 -> 2<br />
<br />
30-39,99 -> 3<br />
<br />
40-46,99 -> 4<br />
<br />
47-53,99 -> 5<br />
<br />
54-61,99 -> 6<br />
<br />
62-69,99 -> 7<br />
<br />
70-77,99 -> 8<br />
<br />
78-85,9 -> 9<br />
<br />
86-100 -> 10<br />
<br />
== Reading ==<br />
'''Obligatory:'''<br/><br />
- Mathematics for economists, Simon C. P., Blume L., 1994 <br/><br />
'''Optional:'''<br/><br />
- A.F. Fillipov. Collection of problems on differential equations. Moscow, “Nauka”, 1973 and later editions.<br/><br />
- V.K. Romanko, Course on Differential Equations and Calculus of Variations. Moscow and Saint-Petersburg, “Fizmatlit”, 2001 and later editions.<br/><br />
== Internet Resources ==<br />
[http://www.londonexternal.ac.uk/current_students/programme_resources/lse/index.shtml University of London Exam papers and Examiners reports for the last three years].<br/></div>Dbashminovaahttps://wiki.cs.hse.ru/index.php?title=Differential_Equations_2023/24&diff=83702Differential Equations 2023/242024-02-15T18:40:35Z<p>Dbashminovaa: добавлен ассистент</p>
<hr />
<div>== [https://www.hse.ru/en/ba/data/courses/301393255.html Syllabus] ==<br />
<br />
“Differential Equations” is a spring semester course for second-year students studying at the Faculty of Computer Sciences. It is designed to suit the requirements of the Faculty of Computer Sciences curriculum as well as UoL where DE is a part of the mathematical curriculum. Besides the course on differential equations is included as a topic in “Mathematical methods for economists” external exam. <br />
<br />
This course is an important part of the bachelor stage in the education of the future applied mathematicians and computer scientists. It has to give students skills for the implementation of mathematical knowledge and expertise. Its prerequisite is the knowledge of the single variable calculus. <br />
<br />
In the spring semester, the course is split into two unequal parts: it is taught from January through the end of April and after the students finish with their UoL exams in May it will resume and will continue till mid-June. <br />
<br />
The assessment of the students will be done by setting mock exam by the end of the 3rd module, then later by the University of London (UoL) examinations in May and final exam will be set in late June. But the final grade will depend solely on mock, final exams performance and home assignments grades.<br />
<br />
As a general policy, personal computing devices such as laptops, calculators etc. are ''' not supposed to be used in the course'''. They are ''' absolutely prohibited in all exams'''. Students are expected to do all necessary arithmetic computations by hand.<br />
<br />
== Lecturers and Teachers==<br />
<br />
== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 221 (M+P+) !! 222 !! 223 !! 224 <br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/757685153 Александр Тараканов]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/757685153 Александр Тараканов] ([tg]) || [https://www.hse.ru/org/persons/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/305059337 Дарья Башминова] ([tg])<br />
|- <br />
|| Assistants || Кульпанович Данила Русланович drkulpanovich@edu.hse.ru <br> drkulpanovich@edu.hse.ru<br />
|| <br> ([ tg])<br />
|| <br> ([ tg])<br />
|| <br> ([ tg])<br />
|- <!--<br />
|| Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru <br />
|- --><br />
|}<br />
<br />
== Lectures ==<br />
<br />
== Seminars ==<br />
<br />
<br />
== Midterm test ==<br />
<br />
== Final exam ==<br />
<br />
== UoL Materials ==<br />
<br />
== Assignments ==<br />
<br />
=== Home assignments 2023 ===<br />
<br />
[https://www.dropbox.com/scl/fi/q367x7mthdo4eka2mvztz/homework_1.pdf?rlkey=outh1mn028j2yzyu8krwkfnf3&dl=0 Home assignment 1], due on "February 19th"<br />
<br />
== Overall Results ==<br />
<br />
== Grading System ==<br />
<br />
The home assignments constitute 30% of the final grade. The final exam is 40% of the final grade. The rest of the grade is formed by Midterm test which is due in the end of the 3rd module.<br />
<br />
''' The final grade on the course''' will be determined according to the formula:<br />
<br />
'''Grade''' = 0.4 * Final Exam + 0.3 * Midterm test + 0.3 * Home assignments<br />
<br />
All grades are given initially out of 100. The final grades are also transferred to 10- and 5-points grades in accordance with the table (to be posted).<br />
3. The scale of corresponding grades<br />
3.1. Total grades for a given course are converted from the 100-point scale to the 5-point<br />
and 10-point scale.<br />
3.2. The following basic scale has been established to convert grades from the 100-point scale to the 10-point scale<br />
100-point scale 10-point scale<br />
<br />
0-19,99 -> 1<br />
<br />
20-29,99 -> 2<br />
<br />
30-39,99 -> 3<br />
<br />
40-46,99 -> 4<br />
<br />
47-53,99 -> 5<br />
<br />
54-61,99 -> 6<br />
<br />
62-69,99 -> 7<br />
<br />
70-77,99 -> 8<br />
<br />
78-85,9 -> 9<br />
<br />
86-100 -> 10<br />
<br />
== Reading ==<br />
'''Obligatory:'''<br/><br />
- Mathematics for economists, Simon C. P., Blume L., 1994 <br/><br />
'''Optional:'''<br/><br />
- A.F. Fillipov. Collection of problems on differential equations. Moscow, “Nauka”, 1973 and later editions.<br/><br />
- V.K. Romanko, Course on Differential Equations and Calculus of Variations. Moscow and Saint-Petersburg, “Fizmatlit”, 2001 and later editions.<br/><br />
== Internet Resources ==<br />
[http://www.londonexternal.ac.uk/current_students/programme_resources/lse/index.shtml University of London Exam papers and Examiners reports for the last three years].<br/></div>Dbashminovaa