https://wiki.cs.hse.ru/api.php?action=feedcontributions&feedformat=atom&user=Anna.KosovskayaWiki - Факультет компьютерных наук - Вклад [ru]2026-09-21T22:36:32ZВкладMediaWiki 1.43.9https://wiki.cs.hse.ru/index.php?title=%D0%9C%D0%B5%D1%82%D0%BE%D0%B4%D1%8B_%D0%BE%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D0%B8_%D0%B2_%D0%BC%D0%B0%D1%88%D0%B8%D0%BD%D0%BD%D0%BE%D0%BC_%D0%BE%D0%B1%D1%83%D1%87%D0%B5%D0%BD%D0%B8%D0%B8_2023/24&diff=82920Методы оптимизации в машинном обучении 2023/242024-01-16T14:27:06Z<p>Anna.Kosovskaya: </p>
<hr />
<div>Материалы курса и вся информация доступны на сайте<br />
https://hse24.fmin.xyz</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=%D0%9C%D0%B5%D1%82%D0%BE%D0%B4%D1%8B_%D0%BE%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D0%B8_%D0%B2_%D0%BC%D0%B0%D1%88%D0%B8%D0%BD%D0%BD%D0%BE%D0%BC_%D0%BE%D0%B1%D1%83%D1%87%D0%B5%D0%BD%D0%B8%D0%B8_2023/24&diff=82919Методы оптимизации в машинном обучении 2023/242024-01-16T14:19:53Z<p>Anna.Kosovskaya: Новая страница: «Материалы курса доступны на сайте https://hse24.fmin.xyz»</p>
<hr />
<div>Материалы курса доступны на сайте<br />
https://hse24.fmin.xyz</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2020/2021&diff=48178LAaG DSBA 2020/20212020-12-04T20:56:47Z<p>Anna.Kosovskaya: /* Homework */</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 201 (M+P+) !! 202 !! 203 !! 204<br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]<br />
|- <br />
|| Schedule || || || || Thursday, 13.00, online<br />
[https://us02web.zoom.us/j/84167365375?pwd=SlhoalJDRkEveTNiZjQ5Q00vTXBxdz09 Zoom]<br />
<br />
Passcode: algebra<br />
<br />
|- <br />
|| Consultations || Wed, 18:00 -- 21:00, room S808<br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| Wednesday, 17:00, write @medvednikita beforehands || Saturday, 16:00-17:30<br />
<br />
[https://us02web.zoom.us/j/88331684853?pwd=Uk9QZWYzOGtaZFBrZGFlMThXdDkzdz09 Zoom]<br />
<br />
Passcode: algebra<br />
<br />
In case I'm offline text me via [https://t.me/galinakaleeva telegram]<br />
|-<br />
|| Assistant || Астанина Ксения <br> kkastanina@edu.hse.ru<br />
|| Васильев Борис <br> bavasilev@edu.hse.ru<br />
|| Княжевский Владимир <br> vvknyazhevskiy@edu.hse.ru<br />
|| Косовская Анна <br> a.dtc@yandex.ru, tg: @a_dtc<br />
|-<br />
|| Course <br> Assistant ||colspan="4"| Астанина Ксения <br> kkastanina@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 />
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 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, 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 />
== Lecture Notes ==<br />
<br />
''' Module 2'''<br />
* [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (30.11.2020) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br />
<br />
* [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (23.11.2020) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br />
<br />
* [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (16.11.2020) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br />
<br />
* [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (09.11.2020) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br />
<br />
* [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (26.10.2020) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (17.10.2020) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br />
<br />
* [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2020) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br />
<br />
* [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2020) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br />
<br />
* [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2019) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br />
<br />
* [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2020) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (non-singular) matrices; the trace of a matrix; main properties of matrix transposition, matrix inverse, and the trace.<br />
<br />
* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) 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 />
== Seminar Notes ==<br />
<br />
'''Module 1'''<br />
<br />
'''Group 201:'''<br />
*[ '''S 1'''] (09.09.2020)<br />
<br />
<br />
'''Group 202:'''<br />
*[https://www.dropbox.com/s/dcfylf04ls5jz9z/13.11.pdf?dl=0 '''Seminar 9 (online)'''] (13.11.2020)<br />
*[https://miro.com/app/board/o9J_leTnA8g=/ '''Seminar 10 (online)'''] (20.11.2020)<br />
*[https://miro.com/app/board/o9J_ldEr9eI=/ '''Seminar 11 (online)'''] (27.11.2020)<br />
<br />
'''Group 203:'''<br />
*[https://www.dropbox.com/s/dcfylf04ls5jz9z/13.11.pdf?dl=0 '''Seminar 9 (online)'''] (13.11.2020)<br />
*[https://miro.com/app/board/o9J_leTnA-s=/ '''Seminar 10 (online)'''] (20.11.2020)<br />
*[https://miro.com/app/board/o9J_ldLgtaQ=/ '''Seminar 11 (online)'''] (27.11.2020)<br />
<br />
'''Group 204:'''<br />
*[ '''S 1'''] (ХХ.09.2020)<br />
<br />
== Homework ==<br />
<br />
'''The obligatory homework for group 201:'''<br />
<br />
'''Module 2'''<br />
*[https://www.dropbox.com/s/7evow683qc69tt8/LAaG_HW_11_C%28201%29.pdf?dl=0 '''HW 11'''] (release: 02.12.2020; deadline: 09.12.2020)<br />
*[https://www.dropbox.com/s/f23fmckianqtr1t/LAaG_HW_10_C%28201%29.pdf?dl=0 '''HW 10'''] (release: 29.11.2020; deadline: 04.12.2020)<br />
*[https://www.dropbox.com/s/2d1z2oiq6nonuwy/LAaG_HW_9_C%28201%29.pdf?dl=0 '''HW 9'''] (release: 22.11.2020; deadline: 27.11.2020)<br />
*[https://www.dropbox.com/s/hixv9pd6ryhbhjg/LAaG_HW_8_C%28201%29.pdf?dl=0 '''HW 8'''] (release: 13.11.2020; deadline: 18.11.2020)<br />
*[https://www.dropbox.com/s/bmhjz4up4dlu18f/LAaG_HW_7_C%28201%29.pdf?dl=0 '''HW 7'''] (release: 06.11.2020; deadline: 11.11.2020)<br />
<br />
'''Module 1'''<br />
<br />
*[https://www.dropbox.com/s/e4i66jsnprzb0j1/LAaG_HW_6_C%28201%29.pdf?dl=0 '''HW 6'''] (release: 22.10.2020; deadline: 28.10.2020)<br />
*[https://www.dropbox.com/s/9u1bevtnfvypnvs/LAaG_HW_5_C%28201%29.pdf?dl=0 '''HW 5'''] (release: 08.10.2020; deadline: 15.10.2020)<br />
*[https://www.dropbox.com/s/54bqdcbvrit5ea6/LAaG_HW_4_C%28201%29.pdf?dl=0 '''HW 4'''] (release: 01.10.2020; deadline: 07.10.2020)<br />
*[https://www.dropbox.com/s/4fvmtbfpuki5tlx/LAaG_HW_3_C%28201%29.pdf?dl=0 '''HW 3'''] (release: 26.09.2020; deadline: 01.10.2020)<br />
*[https://www.dropbox.com/s/lz0953mwyxy3ybt/LAaG_HW_2_C%28201%29.pdf?dl=0 '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020)<br />
*[https://www.dropbox.com/s/m9y2wopr1lq0dtv/LAaG_HW_1_C%28201%29.pdf?dl=0 '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)<br />
<br />
<br />
'''The obligatory homework for groups 202 and 203:'''<br />
*An invite to Google Classroom for group 203: 3fyhfue (you can also use [https://classroom.google.com/c/MTU5OTQ0NzgyMTI3?cjc=3fyhfue this link])<br />
*Google Classroom to submit your work for group 202: [https://classroom.google.com/c/MjA0MzM4Nzg3NjUw?cjc=syrty2b link]<br />
*[https://www.dropbox.com/s/7lewr979nkqwyy3/LAaG_HW_8.pdf?dl=0 '''HW 8'''] (release: 21.11.2020; deadline: 29.11.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/jbznunxbx3soq90/LAaG_HW_7.pdf?dl=0 '''HW 7'''] (release: 08.11.2020; deadline: 15.11.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/b2ebqxgdc6d3dn9/LAaG_HW_6.pdf?dl=0 '''HW 6'''] (release: 01.11.2020; deadline: 09.11.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/evonkhx6mj0oz8v/LAaG_HW_5.pdf?dl=0 '''HW 5'''] (release: 14.10.2020; deadline: 22.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/1brumdjhlqmbh68/LAaG_HW_4.pdf?dl=0 '''HW 4'''] (release: 07.10.2020; deadline: 14.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/k76x5dd19v8zbzq/LAaG_HW_3.pdf?dl=0 '''HW 3'''] (release: 03.10.2020; deadline: 09.10.2020, extended to 23:59 p.m.)<br />
*[https://www.dropbox.com/s/h2whl2uds7tcwp8/LAaG_HW_2.pdf?dl=0 '''HW 2'''] (release: 18.09.2020; deadline: 25.09.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/2z5gdd4hgyknqpz/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)<br />
<br />
'''The obligatory homework for group 204:'''<br />
<br />
Send your works to Google classroom (HW 9+)! Access code: gskby43.<br />
*[https://yadi.sk/i/DxTSxgatPrLSWA '''HW 9'''] (release: 27.11.2020; deadline: 05.12.2020, 9:00 a. m., you can pass with a fine of 20% until 9.00 on December 6)<br />
*[https://yadi.sk/i/BhS7fNUJ5p7aYA '''HW 8'''] (release: 20.11.2020; deadline: 28.11.2020, 9:00 a. m.; [https://forms.gle/bvDTPLghpZwwTacx7 '''send here'''])<br />
*[https://yadi.sk/i/BBhmaHPb2V6CLQ '''HW 7'''] (release: 14.11.2020; deadline: 21.11.2020, 9:00 a. m.; [https://forms.gle/qiEpPoMpqYFCZ25S9 '''send here'''])<br />
*[https://yadi.sk/i/fXDIqGN49peJtA '''HW 6'''] (release: 1.11.2020; deadline: 9.11.2020, 9:00 a. m.; [https://forms.gle/hPmu8jHfopXNGYJ6A '''send here'''])<br />
*[https://yadi.sk/i/8d2ValKaq6uaZg '''HW 5'''] (release: 8.10.2020; deadline: 15.10.2020, 9:00 a. m.; [https://forms.gle/jN6eimdhkdZGMVL38 '''send here'''])<br />
*[https://yadi.sk/i/hzNK0ANZL_LPBw '''HW 4'''] (release: 2.10.2020; deadline: 9.10.2020, 9:00 a. m.; [https://forms.gle/wNxeDUZwXGfRggQR6 '''send here'''])<br />
*[https://yadi.sk/i/93RguRqucteczQ '''HW 3'''] (release: 27.09.2020; deadline: 05.10.2020, 9:00 a. m.; [https://forms.gle/5kr9ns6ntvXBZiUr9 '''send here'''])<br />
*[https://yadi.sk/i/zNOaULSelp5egw '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020, 9:00 a. m.; [https://forms.gle/P5PWSAtannwiVTHn9 '''send here'''])<br />
*[https://yadi.sk/i/AX-zxO6kW18GlQ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; [https://clck.ru/Qkq26 '''send here''']) Any computational tools are not allowed.<br />
<br />
== Results ==<br />
[https://docs.google.com/spreadsheets/d/1qF7mi0aHJCewqH08hXzGGHn2IXzQ-HOOrCRJ_LSX7vE/edit#gid=732068137 Results Sheet]<br />
<br />
3.10.2020. Quiz results (group 204) are published. You will be able to see your paper and ask questions during Monday Q&A or on Wednesday after the seminar.</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2020/2021&diff=48043LAaG DSBA 2020/20212020-12-02T13:11:48Z<p>Anna.Kosovskaya: /* Homework */</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 201 (M+P+) !! 202 !! 203 !! 204<br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]<br />
|- <br />
|| Schedule || || || || Thursday, 13.00, online<br />
[https://us02web.zoom.us/j/84167365375?pwd=SlhoalJDRkEveTNiZjQ5Q00vTXBxdz09 Zoom]<br />
<br />
Passcode: algebra<br />
<br />
|- <br />
|| Consultations || Wed, 18:00 -- 21:00, room S808<br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| Wednesday, 17:00, write @medvednikita beforehands || Saturday, 16:00-17:30<br />
<br />
[https://us02web.zoom.us/j/88331684853?pwd=Uk9QZWYzOGtaZFBrZGFlMThXdDkzdz09 Zoom]<br />
<br />
Passcode: algebra<br />
<br />
In case I'm offline text me via [https://t.me/galinakaleeva telegram]<br />
|-<br />
|| Assistant || Астанина Ксения <br> kkastanina@edu.hse.ru<br />
|| Васильев Борис <br> bavasilev@edu.hse.ru<br />
|| Княжевский Владимир <br> vvknyazhevskiy@edu.hse.ru<br />
|| Косовская Анна <br> a.dtc@yandex.ru, tg: @a_dtc<br />
|-<br />
|| Course <br> Assistant ||colspan="4"| Астанина Ксения <br> kkastanina@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 />
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 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, 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 />
== Lecture Notes ==<br />
<br />
''' Module 2'''<br />
* [https://www.dropbox.com/s/lqtmy2vaatj11em/LAaG_Lecture_11.pdf?dl=0 '''Lecture 11'''] (30.11.2020) Polynomials; the degree of a polynomial; division with remainder; a root of a polynomial; factor theorem; the multiplicity of a root; algebraically closed fields; fundamental theorem of algebra; interpolation polynomials in the Lagrange form.<br />
<br />
* [https://www.dropbox.com/s/o4xtwn4a5hth67j/LAaG_Lecture_10.pdf?dl=0 '''Lecture 10'''] (23.11.2020) Complex numbers (part II); main properties of the conjugate and the absolute value of a complex number; polar (= trigonometric) form of a complex number; de Moivre's Formula; the set of n-th roots of a complex number, its description.<br />
<br />
* [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (16.11.2020) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br />
<br />
* [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (09.11.2020) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br />
<br />
* [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (26.10.2020) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (17.10.2020) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br />
<br />
* [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2020) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br />
<br />
* [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2020) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br />
<br />
* [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2019) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br />
<br />
* [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2020) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (non-singular) matrices; the trace of a matrix; main properties of matrix transposition, matrix inverse, and the trace.<br />
<br />
* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) 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 />
== Seminar Notes ==<br />
<br />
'''Module 1'''<br />
<br />
'''Group 201:'''<br />
*[ '''S 1'''] (09.09.2020)<br />
<br />
<br />
'''Group 202:'''<br />
*[https://www.dropbox.com/s/dcfylf04ls5jz9z/13.11.pdf?dl=0 '''Seminar 9 (online)'''] (13.11.2020)<br />
*[https://miro.com/app/board/o9J_leTnA8g=/ '''Seminar 10 (online)'''] (20.11.2020)<br />
*[https://miro.com/app/board/o9J_ldEr9eI=/ '''Seminar 11 (online)'''] (27.11.2020)<br />
<br />
'''Group 203:'''<br />
*[https://www.dropbox.com/s/dcfylf04ls5jz9z/13.11.pdf?dl=0 '''Seminar 9 (online)'''] (13.11.2020)<br />
*[https://miro.com/app/board/o9J_leTnA-s=/ '''Seminar 10 (online)'''] (20.11.2020)<br />
*[https://miro.com/app/board/o9J_ldLgtaQ=/ '''Seminar 11 (online)'''] (27.11.2020)<br />
<br />
'''Group 204:'''<br />
*[ '''S 1'''] (ХХ.09.2020)<br />
<br />
== Homework ==<br />
<br />
'''The obligatory homework for group 201:'''<br />
<br />
'''Module 2'''<br />
*[https://www.dropbox.com/s/f23fmckianqtr1t/LAaG_HW_10_C%28201%29.pdf?dl=0 '''HW 10'''] (release: 29.11.2020; deadline: 04.12.2020)<br />
*[https://www.dropbox.com/s/2d1z2oiq6nonuwy/LAaG_HW_9_C%28201%29.pdf?dl=0 '''HW 9'''] (release: 22.11.2020; deadline: 27.11.2020)<br />
*[https://www.dropbox.com/s/hixv9pd6ryhbhjg/LAaG_HW_8_C%28201%29.pdf?dl=0 '''HW 8'''] (release: 13.11.2020; deadline: 18.11.2020)<br />
*[https://www.dropbox.com/s/bmhjz4up4dlu18f/LAaG_HW_7_C%28201%29.pdf?dl=0 '''HW 7'''] (release: 06.11.2020; deadline: 11.11.2020)<br />
<br />
'''Module 1'''<br />
<br />
*[https://www.dropbox.com/s/e4i66jsnprzb0j1/LAaG_HW_6_C%28201%29.pdf?dl=0 '''HW 6'''] (release: 22.10.2020; deadline: 28.10.2020)<br />
*[https://www.dropbox.com/s/9u1bevtnfvypnvs/LAaG_HW_5_C%28201%29.pdf?dl=0 '''HW 5'''] (release: 08.10.2020; deadline: 15.10.2020)<br />
*[https://www.dropbox.com/s/54bqdcbvrit5ea6/LAaG_HW_4_C%28201%29.pdf?dl=0 '''HW 4'''] (release: 01.10.2020; deadline: 07.10.2020)<br />
*[https://www.dropbox.com/s/4fvmtbfpuki5tlx/LAaG_HW_3_C%28201%29.pdf?dl=0 '''HW 3'''] (release: 26.09.2020; deadline: 01.10.2020)<br />
*[https://www.dropbox.com/s/lz0953mwyxy3ybt/LAaG_HW_2_C%28201%29.pdf?dl=0 '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020)<br />
*[https://www.dropbox.com/s/m9y2wopr1lq0dtv/LAaG_HW_1_C%28201%29.pdf?dl=0 '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)<br />
<br />
<br />
'''The obligatory homework for groups 202 and 203:'''<br />
*An invite to Google Classroom for group 203: 3fyhfue (you can also use [https://classroom.google.com/c/MTU5OTQ0NzgyMTI3?cjc=3fyhfue this link])<br />
*Google Classroom to submit your work for group 202: [https://classroom.google.com/c/MjA0MzM4Nzg3NjUw?cjc=syrty2b link]<br />
*[https://www.dropbox.com/s/7lewr979nkqwyy3/LAaG_HW_8.pdf?dl=0 '''HW 8'''] (release: 21.11.2020; deadline: 29.11.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/jbznunxbx3soq90/LAaG_HW_7.pdf?dl=0 '''HW 7'''] (release: 08.11.2020; deadline: 15.11.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/b2ebqxgdc6d3dn9/LAaG_HW_6.pdf?dl=0 '''HW 6'''] (release: 01.11.2020; deadline: 09.11.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/evonkhx6mj0oz8v/LAaG_HW_5.pdf?dl=0 '''HW 5'''] (release: 14.10.2020; deadline: 22.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/1brumdjhlqmbh68/LAaG_HW_4.pdf?dl=0 '''HW 4'''] (release: 07.10.2020; deadline: 14.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/k76x5dd19v8zbzq/LAaG_HW_3.pdf?dl=0 '''HW 3'''] (release: 03.10.2020; deadline: 09.10.2020, extended to 23:59 p.m.)<br />
*[https://www.dropbox.com/s/h2whl2uds7tcwp8/LAaG_HW_2.pdf?dl=0 '''HW 2'''] (release: 18.09.2020; deadline: 25.09.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/2z5gdd4hgyknqpz/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)<br />
<br />
'''The obligatory homework for group 204:'''<br />
<br />
Send your works to Google classroom (HW 9+)! Access code: gskby43.<br />
*[https://yadi.sk/i/DxTSxgatPrLSWA '''HW 9'''] (release: 27.11.2020; deadline: 05.12.2020, 9:00 a. m.)<br />
*[https://yadi.sk/i/BhS7fNUJ5p7aYA '''HW 8'''] (release: 20.11.2020; deadline: 28.11.2020, 9:00 a. m.; [https://forms.gle/bvDTPLghpZwwTacx7 '''send here'''])<br />
*[https://yadi.sk/i/BBhmaHPb2V6CLQ '''HW 7'''] (release: 14.11.2020; deadline: 21.11.2020, 9:00 a. m.; [https://forms.gle/qiEpPoMpqYFCZ25S9 '''send here'''])<br />
*[https://yadi.sk/i/fXDIqGN49peJtA '''HW 6'''] (release: 1.11.2020; deadline: 9.11.2020, 9:00 a. m.; [https://forms.gle/hPmu8jHfopXNGYJ6A '''send here'''])<br />
*[https://yadi.sk/i/8d2ValKaq6uaZg '''HW 5'''] (release: 8.10.2020; deadline: 15.10.2020, 9:00 a. m.; [https://forms.gle/jN6eimdhkdZGMVL38 '''send here'''])<br />
*[https://yadi.sk/i/hzNK0ANZL_LPBw '''HW 4'''] (release: 2.10.2020; deadline: 9.10.2020, 9:00 a. m.; [https://forms.gle/wNxeDUZwXGfRggQR6 '''send here'''])<br />
*[https://yadi.sk/i/93RguRqucteczQ '''HW 3'''] (release: 27.09.2020; deadline: 05.10.2020, 9:00 a. m.; [https://forms.gle/5kr9ns6ntvXBZiUr9 '''send here'''])<br />
*[https://yadi.sk/i/zNOaULSelp5egw '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020, 9:00 a. m.; [https://forms.gle/P5PWSAtannwiVTHn9 '''send here'''])<br />
*[https://yadi.sk/i/AX-zxO6kW18GlQ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; [https://clck.ru/Qkq26 '''send here''']) Any computational tools are not allowed.<br />
<br />
== Results ==<br />
[https://docs.google.com/spreadsheets/d/1qF7mi0aHJCewqH08hXzGGHn2IXzQ-HOOrCRJ_LSX7vE/edit#gid=732068137 Results Sheet]<br />
<br />
3.10.2020. Quiz results (group 204) are published. You will be able to see your paper and ask questions during Monday Q&A or on Wednesday after the seminar.</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2020/2021&diff=47570LAaG DSBA 2020/20212020-11-20T22:56:00Z<p>Anna.Kosovskaya: /* Homework */</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 201 (M+P+) !! 202 !! 203 !! 204<br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]<br />
|- <br />
|| Schedule || || || || Wednesday, 13.00, online<br />
[https://us02web.zoom.us/j/84167365375?pwd=SlhoalJDRkEveTNiZjQ5Q00vTXBxdz09 Zoom]<br />
<br />
Passcode: algebra<br />
<br />
|- <br />
|| Consultations || Wed, 18:00 -- 21:00, room S808<br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| TBD || Saturday, 16:00-17:30<br />
<br />
[https://us02web.zoom.us/j/88331684853?pwd=Uk9QZWYzOGtaZFBrZGFlMThXdDkzdz09 Zoom]<br />
<br />
Passcode: algebra<br />
<br />
In case I'm offline text me via [https://t.me/galinakaleeva telegram]<br />
|-<br />
|| Assistant || Астанина Ксения <br> kkastanina@edu.hse.ru<br />
|| Васильев Борис <br> bavasilev@edu.hse.ru<br />
|| Княжевский Владимир <br> vvknyazhevskiy@edu.hse.ru<br />
|| Косовская Анна <br> a.dtc@yandex.ru, tg: @a_dtc<br />
|-<br />
|| Course <br> Assistant ||colspan="4"| Астанина Ксения <br> kkastanina@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 />
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 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, 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 />
== Lecture Notes ==<br />
<br />
''' Module 2'''<br />
* [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (16.11.2020) The determinant of a Vandermonde matrix; fields; the field of complex munbers; Cartesian and algebraic forms of a complex number; the absolute value (=module) and the argument of a complex number, the complex conjugate.<br />
<br />
* [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (09.11.2020) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br />
<br />
* [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (26.10.2020) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (17.10.2020) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br />
<br />
* [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2020) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br />
<br />
* [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2020) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br />
<br />
* [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2019) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br />
<br />
* [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2020) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (non-singular) matrices; the trace of a matrix; main properties of matrix transposition, matrix inverse, and the trace.<br />
<br />
* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) 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 />
== Seminar Notes ==<br />
<br />
'''Module 1'''<br />
<br />
'''Group 201:'''<br />
*[ '''S 1'''] (09.09.2020)<br />
<br />
<br />
'''Groups 202 and 203:'''<br />
*[https://www.dropbox.com/s/dcfylf04ls5jz9z/13.11.pdf?dl=0 '''Seminar 9 (online)'''] (13.11.2020)<br />
<br />
<br />
'''Group 204:'''<br />
*[ '''S 1'''] (ХХ.09.2020)<br />
<br />
== Homework ==<br />
<br />
'''The obligatory homework for group 201:'''<br />
<br />
'''Module 2'''<br />
*[https://www.dropbox.com/s/hixv9pd6ryhbhjg/LAaG_HW_8_C%28201%29.pdf?dl=0 '''HW 8'''] (release: 13.11.2020; deadline: 18.11.2020)<br />
*[https://www.dropbox.com/s/bmhjz4up4dlu18f/LAaG_HW_7_C%28201%29.pdf?dl=0 '''HW 7'''] (release: 06.11.2020; deadline: 11.11.2020)<br />
<br />
'''Module 1'''<br />
<br />
*[https://www.dropbox.com/s/e4i66jsnprzb0j1/LAaG_HW_6_C%28201%29.pdf?dl=0 '''HW 6'''] (release: 22.10.2020; deadline: 28.10.2020)<br />
*[https://www.dropbox.com/s/9u1bevtnfvypnvs/LAaG_HW_5_C%28201%29.pdf?dl=0 '''HW 5'''] (release: 08.10.2020; deadline: 15.10.2020)<br />
*[https://www.dropbox.com/s/54bqdcbvrit5ea6/LAaG_HW_4_C%28201%29.pdf?dl=0 '''HW 4'''] (release: 01.10.2020; deadline: 07.10.2020)<br />
*[https://www.dropbox.com/s/4fvmtbfpuki5tlx/LAaG_HW_3_C%28201%29.pdf?dl=0 '''HW 3'''] (release: 26.09.2020; deadline: 01.10.2020)<br />
*[https://www.dropbox.com/s/lz0953mwyxy3ybt/LAaG_HW_2_C%28201%29.pdf?dl=0 '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020)<br />
*[https://www.dropbox.com/s/m9y2wopr1lq0dtv/LAaG_HW_1_C%28201%29.pdf?dl=0 '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)<br />
<br />
<br />
'''The obligatory homework for groups 202 and 203:'''<br />
*An invite to Google Classroom for group 203: 3fyhfue (you can also use [https://classroom.google.com/c/MTU5OTQ0NzgyMTI3?cjc=3fyhfue this link])<br />
*Google Classroom to submit your work for group 202: [https://classroom.google.com/c/MjA0MzM4Nzg3NjUw?cjc=syrty2b link]<br />
*[https://www.dropbox.com/s/jbznunxbx3soq90/LAaG_HW_7.pdf?dl=0 '''HW 7'''] (release: 08.11.2020; deadline: 15.11.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/b2ebqxgdc6d3dn9/LAaG_HW_6.pdf?dl=0 '''HW 6'''] (release: 01.11.2020; deadline: 09.11.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/evonkhx6mj0oz8v/LAaG_HW_5.pdf?dl=0 '''HW 5'''] (release: 14.10.2020; deadline: 22.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/1brumdjhlqmbh68/LAaG_HW_4.pdf?dl=0 '''HW 4'''] (release: 07.10.2020; deadline: 14.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/k76x5dd19v8zbzq/LAaG_HW_3.pdf?dl=0 '''HW 3'''] (release: 03.10.2020; deadline: 09.10.2020, extended to 23:59 p.m.)<br />
*[https://www.dropbox.com/s/h2whl2uds7tcwp8/LAaG_HW_2.pdf?dl=0 '''HW 2'''] (release: 18.09.2020; deadline: 25.09.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/2z5gdd4hgyknqpz/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)<br />
<br />
'''The obligatory homework for group 204:'''<br />
*[https://yadi.sk/i/BhS7fNUJ5p7aYA '''HW 8'''] (release: 20.11.2020; deadline: 28.11.2020, 9:00 a. m.; [https://forms.gle/bvDTPLghpZwwTacx7 '''send here'''])<br />
*[https://yadi.sk/i/BBhmaHPb2V6CLQ '''HW 7'''] (release: 14.11.2020; deadline: 21.11.2020, 9:00 a. m.; [https://forms.gle/qiEpPoMpqYFCZ25S9 '''send here'''])<br />
*[https://yadi.sk/i/fXDIqGN49peJtA '''HW 6'''] (release: 1.11.2020; deadline: 9.11.2020, 9:00 a. m.; [https://forms.gle/hPmu8jHfopXNGYJ6A '''send here'''])<br />
*[https://yadi.sk/i/8d2ValKaq6uaZg '''HW 5'''] (release: 8.10.2020; deadline: 15.10.2020, 9:00 a. m.; [https://forms.gle/jN6eimdhkdZGMVL38 '''send here'''])<br />
*[https://yadi.sk/i/hzNK0ANZL_LPBw '''HW 4'''] (release: 2.10.2020; deadline: 9.10.2020, 9:00 a. m.; [https://forms.gle/wNxeDUZwXGfRggQR6 '''send here'''])<br />
*[https://yadi.sk/i/93RguRqucteczQ '''HW 3'''] (release: 27.09.2020; deadline: 05.10.2020, 9:00 a. m.; [https://forms.gle/5kr9ns6ntvXBZiUr9 '''send here'''])<br />
*[https://yadi.sk/i/zNOaULSelp5egw '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020, 9:00 a. m.; [https://forms.gle/P5PWSAtannwiVTHn9 '''send here'''])<br />
*[https://yadi.sk/i/AX-zxO6kW18GlQ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; [https://clck.ru/Qkq26 '''send here''']) Any computational tools are not allowed.<br />
<br />
== Results ==<br />
[https://docs.google.com/spreadsheets/d/1qF7mi0aHJCewqH08hXzGGHn2IXzQ-HOOrCRJ_LSX7vE/edit#gid=732068137 Results Sheet]<br />
<br />
3.10.2020. Quiz results (group 204) are published. You will be able to see your paper and ask questions during Monday Q&A or on Wednesday after the seminar.</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2020/2021&diff=47298LAaG DSBA 2020/20212020-11-15T19:06:24Z<p>Anna.Kosovskaya: /* Homework */</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 201 (M+P+) !! 202 !! 203 !! 204<br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]<br />
|- <br />
|| Schedule || || || || Wednesday, 13.00, online<br />
[https://us02web.zoom.us/j/84167365375?pwd=SlhoalJDRkEveTNiZjQ5Q00vTXBxdz09 Zoom]<br />
<br />
Passcode: algebra<br />
<br />
|- <br />
|| Consultations || Wed, ??:?? -- ??:??, room S808<br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| TBD || Saturday, 16:00-17:30<br />
<br />
[https://us04web.zoom.us/j/78196389793?pwd=N0QzR3pUWW5ueTBvZ3NsSytWTjdZZz09 Zoom]<br />
<br />
Passcode: algebra<br />
<br />
In case I'm offline text me via [https://t.me/galinakaleeva telegram]<br />
|-<br />
|| Assistant || Астанина Ксения <br> kkastanina@edu.hse.ru<br />
|| Васильев Борис <br> bavasilev@edu.hse.ru<br />
|| Княжевский Владимир <br> vvknyazhevskiy@edu.hse.ru<br />
|| Косовская Анна <br> a.dtc@yandex.ru, tg: @a_dtc<br />
|-<br />
|| Course <br> Assistant ||colspan="4"| Астанина Ксения <br> kkastanina@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 />
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 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, 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 />
== Lecture Notes ==<br />
<br />
''' Module 2'''<br />
<br />
* [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (09.11.2020) Block matrices; the determinant of a block matrix; minors and cofactors of a matrix; Laplace expansion; false expansion; the adjugate of a matrix; Cramer's rule.<br />
<br />
* [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (26.10.2020) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (17.10.2020) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br />
<br />
* [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2020) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br />
<br />
* [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2020) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br />
<br />
* [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2019) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br />
<br />
* [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2020) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (non-singular) matrices; the trace of a matrix; main properties of matrix transposition, matrix inverse, and the trace.<br />
<br />
* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) 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 />
== Seminar Notes ==<br />
<br />
'''Module 1'''<br />
<br />
'''Group 201:'''<br />
*[ '''S 1'''] (09.09.2020)<br />
<br />
<br />
'''Groups 202 and 203:'''<br />
*[https://www.dropbox.com/s/dcfylf04ls5jz9z/13.11.pdf?dl=0 '''Seminar 9 (online)'''] (13.11.2020)<br />
<br />
<br />
'''Group 204:'''<br />
*[ '''S 1'''] (ХХ.09.2020)<br />
<br />
== Homework ==<br />
<br />
'''The obligatory homework for group 201:'''<br />
<br />
'''Module 2'''<br />
*[https://www.dropbox.com/s/hixv9pd6ryhbhjg/LAaG_HW_8_C%28201%29.pdf?dl=0 '''HW 8'''] (release: 13.11.2020; deadline: 18.11.2020)<br />
*[https://www.dropbox.com/s/bmhjz4up4dlu18f/LAaG_HW_7_C%28201%29.pdf?dl=0 '''HW 7'''] (release: 06.11.2020; deadline: 11.11.2020)<br />
<br />
'''Module 1'''<br />
<br />
*[https://www.dropbox.com/s/e4i66jsnprzb0j1/LAaG_HW_6_C%28201%29.pdf?dl=0 '''HW 6'''] (release: 22.10.2020; deadline: 28.10.2020)<br />
*[https://www.dropbox.com/s/9u1bevtnfvypnvs/LAaG_HW_5_C%28201%29.pdf?dl=0 '''HW 5'''] (release: 08.10.2020; deadline: 15.10.2020)<br />
*[https://www.dropbox.com/s/54bqdcbvrit5ea6/LAaG_HW_4_C%28201%29.pdf?dl=0 '''HW 4'''] (release: 01.10.2020; deadline: 07.10.2020)<br />
*[https://www.dropbox.com/s/4fvmtbfpuki5tlx/LAaG_HW_3_C%28201%29.pdf?dl=0 '''HW 3'''] (release: 26.09.2020; deadline: 01.10.2020)<br />
*[https://www.dropbox.com/s/lz0953mwyxy3ybt/LAaG_HW_2_C%28201%29.pdf?dl=0 '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020)<br />
*[https://www.dropbox.com/s/m9y2wopr1lq0dtv/LAaG_HW_1_C%28201%29.pdf?dl=0 '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)<br />
<br />
<br />
'''The obligatory homework for groups 202 and 203:'''<br />
*An invite to Google Classroom for group 203: 3fyhfue (you can also use [https://classroom.google.com/c/MTU5OTQ0NzgyMTI3?cjc=3fyhfue this link])<br />
*Google Classroom to submit your work for group 202: [https://classroom.google.com/c/MjA0MzM4Nzg3NjUw?cjc=syrty2b link]<br />
*[https://www.dropbox.com/s/jbznunxbx3soq90/LAaG_HW_7.pdf?dl=0 '''HW 7'''] (release: 08.11.2020; deadline: 15.11.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/b2ebqxgdc6d3dn9/LAaG_HW_6.pdf?dl=0 '''HW 6'''] (release: 01.11.2020; deadline: 09.11.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/evonkhx6mj0oz8v/LAaG_HW_5.pdf?dl=0 '''HW 5'''] (release: 14.10.2020; deadline: 22.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/1brumdjhlqmbh68/LAaG_HW_4.pdf?dl=0 '''HW 4'''] (release: 07.10.2020; deadline: 14.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/k76x5dd19v8zbzq/LAaG_HW_3.pdf?dl=0 '''HW 3'''] (release: 03.10.2020; deadline: 09.10.2020, extended to 23:59 p.m.)<br />
*[https://www.dropbox.com/s/h2whl2uds7tcwp8/LAaG_HW_2.pdf?dl=0 '''HW 2'''] (release: 18.09.2020; deadline: 25.09.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/2z5gdd4hgyknqpz/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)<br />
<br />
'''The obligatory homework for group 204:'''<br />
*[https://yadi.sk/i/BBhmaHPb2V6CLQ '''HW 7'''] (release: 14.11.2020; deadline: 21.11.2020, 9:00 a. m.; [https://forms.gle/qiEpPoMpqYFCZ25S9 '''send here'''])<br />
*[https://yadi.sk/i/fXDIqGN49peJtA '''HW 6'''] (release: 1.11.2020; deadline: 9.11.2020, 9:00 a. m.; [https://forms.gle/hPmu8jHfopXNGYJ6A '''send here'''])<br />
*[https://yadi.sk/i/8d2ValKaq6uaZg '''HW 5'''] (release: 8.10.2020; deadline: 15.10.2020, 9:00 a. m.; [https://forms.gle/jN6eimdhkdZGMVL38 '''send here'''])<br />
*[https://yadi.sk/i/hzNK0ANZL_LPBw '''HW 4'''] (release: 2.10.2020; deadline: 9.10.2020, 9:00 a. m.; [https://forms.gle/wNxeDUZwXGfRggQR6 '''send here'''])<br />
*[https://yadi.sk/i/93RguRqucteczQ '''HW 3'''] (release: 27.09.2020; deadline: 05.10.2020, 9:00 a. m.; [https://forms.gle/5kr9ns6ntvXBZiUr9 '''send here'''])<br />
*[https://yadi.sk/i/zNOaULSelp5egw '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020, 9:00 a. m.; [https://forms.gle/P5PWSAtannwiVTHn9 '''send here'''])<br />
*[https://yadi.sk/i/AX-zxO6kW18GlQ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; [https://clck.ru/Qkq26 '''send here''']) Any computational tools are not allowed.<br />
<br />
== Results ==<br />
[https://docs.google.com/spreadsheets/d/1qF7mi0aHJCewqH08hXzGGHn2IXzQ-HOOrCRJ_LSX7vE/edit#gid=732068137 Results Sheet]<br />
<br />
3.10.2020. Quiz results (group 204) are published. You will be able to see your paper and ask questions during Monday Q&A or on Wednesday after the seminar.</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2020/2021&diff=46758LAaG DSBA 2020/20212020-11-01T15:09:51Z<p>Anna.Kosovskaya: /* Homework */</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 201 (M+P+) !! 202 !! 203 !! 204<br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]<br />
|- <br />
|| Schedule || || || || Wednesday, 13.00, D501<br />
[https://docs.google.com/spreadsheets/d/1xblWv0wuX7lkbe-0I8yyBPIhEUAq-U-HhGnuJ0It6xc/edit#gid=0 Zoom]<br />
(for distance learners)<br />
|- <br />
|| Consultations || Wed, ??:?? -- ??:??, room S808<br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| TBD || Monday, 14:40-17:00, S913<br />
<span style="color:#DC143C">Oct, 31st - zoom only</span><br />
<br />
[https://zoom.us/j/94128893993 Zoom link]<br />
|-<br />
|| Assistant || Астанина Ксения <br> kkastanina@edu.hse.ru<br />
|| Васильев Борис <br> bavasilev@edu.hse.ru<br />
|| Княжевский Владимир <br> vvknyazhevskiy@edu.hse.ru<br />
|| Косовская Анна <br> a.dtc@yandex.ru, tg: @a_dtc<br />
|-<br />
|| Course <br> Assistant ||colspan="4"| Астанина Ксения <br> kkastanina@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 />
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 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, 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 />
== Lecture Notes ==<br />
<br />
''' Module 2'''<br />
<br />
* [https://www.dropbox.com/s/prpheqo8fbe12oq/LAaG_Lecture_7.pdf?dl=0 '''Lecture 7'''] (26.10.2020) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (17.10.2020) Determinant; the Leibniz Formula; Sarrus' Rule; determinant of matrix transpose; three main properties of the determinant; the determinant of a matrix with a zero row or column.<br />
<br />
* [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (07.10.2020) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.<br />
<br />
* [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2020) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br />
<br />
* [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2019) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br />
<br />
* [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2020) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (non-singular) matrices; the trace of a matrix; main properties of matrix transposition, matrix inverse, and the trace.<br />
<br />
* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) 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 />
== Seminar Notes ==<br />
<br />
'''Module 1'''<br />
<br />
'''Group 201:'''<br />
*[ '''S 1'''] (09.09.2020)<br />
<br />
<br />
'''Groups 202 and 203:'''<br />
*[ '''S 1'''] (XX.09.2020)<br />
<br />
<br />
'''Group 204:'''<br />
*[ '''S 1'''] (ХХ.09.2020)<br />
<br />
== Homework ==<br />
<br />
'''Module 1'''<br />
<br />
'''The obligatory homework for group 201:'''<br />
*[https://www.dropbox.com/s/e4i66jsnprzb0j1/LAaG_HW_6_C%28201%29.pdf?dl=0 '''HW 6'''] (release: 22.10.2020; deadline: 28.10.2020)<br />
*[https://www.dropbox.com/s/9u1bevtnfvypnvs/LAaG_HW_5_C%28201%29.pdf?dl=0 '''HW 5'''] (release: 08.10.2020; deadline: 15.10.2020)<br />
*[https://www.dropbox.com/s/54bqdcbvrit5ea6/LAaG_HW_4_C%28201%29.pdf?dl=0 '''HW 4'''] (release: 01.10.2020; deadline: 07.10.2020)<br />
*[https://www.dropbox.com/s/4fvmtbfpuki5tlx/LAaG_HW_3_C%28201%29.pdf?dl=0 '''HW 3'''] (release: 26.09.2020; deadline: 01.10.2020)<br />
*[https://www.dropbox.com/s/lz0953mwyxy3ybt/LAaG_HW_2_C%28201%29.pdf?dl=0 '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020)<br />
*[https://www.dropbox.com/s/m9y2wopr1lq0dtv/LAaG_HW_1_C%28201%29.pdf?dl=0 '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)<br />
<br />
<br />
'''The obligatory homework for groups 202 and 203:'''<br />
*An invite to Google Classroom for group 203: 3fyhfue (you can also use [https://classroom.google.com/c/MTU5OTQ0NzgyMTI3?cjc=3fyhfue this link])<br />
*Google Form to submit your work for group 202: [https://docs.google.com/forms/d/e/1FAIpQLSfO2FLHxkvu4kui05LM29J9qGzMXxsy9P7ZOYKcdfa7flaDLg/viewform hw5 link] <br />
*[https://www.dropbox.com/s/b2ebqxgdc6d3dn9/LAaG_HW_6.pdf?dl=0 '''HW 6'''] (release: 01.11.2020; deadline: 09.11.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/evonkhx6mj0oz8v/LAaG_HW_5.pdf?dl=0 '''HW 5'''] (release: 14.10.2020; deadline: 22.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/1brumdjhlqmbh68/LAaG_HW_4.pdf?dl=0 '''HW 4'''] (release: 07.10.2020; deadline: 14.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/k76x5dd19v8zbzq/LAaG_HW_3.pdf?dl=0 '''HW 3'''] (release: 03.10.2020; deadline: 09.10.2020, extended to 23:59 p.m.)<br />
*[https://www.dropbox.com/s/h2whl2uds7tcwp8/LAaG_HW_2.pdf?dl=0 '''HW 2'''] (release: 18.09.2020; deadline: 25.09.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/2z5gdd4hgyknqpz/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)<br />
<br />
'''The obligatory homework for group 204:'''<br />
*[https://yadi.sk/i/fXDIqGN49peJtA '''HW 6'''] (release: 1.11.2020; deadline: 9.11.2020, 9:00 a. m.; [https://forms.gle/hPmu8jHfopXNGYJ6A '''send here'''])<br />
*[https://yadi.sk/i/8d2ValKaq6uaZg '''HW 5'''] (release: 8.10.2020; deadline: 15.10.2020, 9:00 a. m.; [https://forms.gle/jN6eimdhkdZGMVL38 '''send here'''])<br />
*[https://yadi.sk/i/hzNK0ANZL_LPBw '''HW 4'''] (release: 2.10.2020; deadline: 9.10.2020, 9:00 a. m.; [https://forms.gle/wNxeDUZwXGfRggQR6 '''send here'''])<br />
*[https://yadi.sk/i/93RguRqucteczQ '''HW 3'''] (release: 27.09.2020; deadline: 05.10.2020, 9:00 a. m.; [https://forms.gle/5kr9ns6ntvXBZiUr9 '''send here'''])<br />
*[https://yadi.sk/i/zNOaULSelp5egw '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020, 9:00 a. m.; [https://forms.gle/P5PWSAtannwiVTHn9 '''send here'''])<br />
*[https://yadi.sk/i/AX-zxO6kW18GlQ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; [https://clck.ru/Qkq26 '''send here''']) Any computational tools are not allowed.<br />
<br />
== Results ==<br />
[https://docs.google.com/spreadsheets/d/1qF7mi0aHJCewqH08hXzGGHn2IXzQ-HOOrCRJ_LSX7vE/edit#gid=732068137 Results Sheet]<br />
<br />
3.10.2020. Quiz results (group 204) are published. You will be able to see your paper and ask questions during Monday Q&A or on Wednesday after the seminar.</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2020/2021&diff=45643LAaG DSBA 2020/20212020-10-04T23:19:20Z<p>Anna.Kosovskaya: /* Teachers and Assistants */</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 201 (M+P+) !! 202 !! 203 !! 204<br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]<br />
|- <br />
|| Schedule || || || || Wednesday, 13.00, D501<br />
[https://docs.google.com/spreadsheets/d/1xblWv0wuX7lkbe-0I8yyBPIhEUAq-U-HhGnuJ0It6xc/edit#gid=0 Zoom]<br />
(for distance learners)<br />
|- <br />
|| Consultations || Wed, ??:?? -- ??:??, room S808<br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| TBD || Monday, 14:40-17:00, S913<br />
To join via Zoom [https://t.me/galinakaleeva text me]<br />
Meeting ID: 732 2104 0735<br />
Passcode: algebra<br />
|-<br />
|| Assistant || Астанина Ксения <br> kkastanina@edu.hse.ru<br />
|| Васильев Борис <br> bavasilev@edu.hse.ru<br />
|| Княжевский Владимир <br> vvknyazhevskiy@edu.hse.ru<br />
|| Косовская Анна <br> a.dtc@yandex.ru, tg: @a_dtc<br />
|-<br />
|| Course <br> Assistant ||colspan="4"| Астанина Ксения <br> kkastanina@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 />
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 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, 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 />
== Lecture Notes ==<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2020) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br />
<br />
* [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2019) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br />
<br />
* [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2020) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (non-singular) matrices; the trace of a matrix; main properties of matrix transposition, matrix inverse, and the trace.<br />
<br />
* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) 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 />
== Seminar Notes ==<br />
<br />
'''Module 1'''<br />
<br />
'''Group 201:'''<br />
*[ '''S 1'''] (09.09.2020)<br />
<br />
<br />
'''Groups 202 and 203:'''<br />
*[ '''S 1'''] (XX.09.2020)<br />
<br />
<br />
'''Group 204:'''<br />
*[ '''S 1'''] (ХХ.09.2020)<br />
<br />
== Homework ==<br />
<br />
'''Module 1'''<br />
<br />
'''The obligatory homework for group 201:'''<br />
*[https://www.dropbox.com/s/54bqdcbvrit5ea6/LAaG_HW_4_C%28201%29.pdf?dl=0 '''HW 4'''] (release: 01.10.2020; deadline: 07.10.2020)<br />
*[https://www.dropbox.com/s/4fvmtbfpuki5tlx/LAaG_HW_3_C%28201%29.pdf?dl=0 '''HW 3'''] (release: 26.09.2020; deadline: 01.10.2020)<br />
*[https://www.dropbox.com/s/lz0953mwyxy3ybt/LAaG_HW_2_C%28201%29.pdf?dl=0 '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020)<br />
*[https://www.dropbox.com/s/m9y2wopr1lq0dtv/LAaG_HW_1_C%28201%29.pdf?dl=0 '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)<br />
<br />
<br />
'''The obligatory homework for groups 202 and 203:'''<br />
*An invite to Google Classroom for group 203: 3fyhfue (you can also use [https://classroom.google.com/c/MTU5OTQ0NzgyMTI3?cjc=3fyhfue this link])<br />
*Google Form to submit your work for group 202: [https://docs.google.com/forms/d/e/1FAIpQLSenETsrDiVDqDJdgQwtO8r2WHWCDsVczZSCZrZzCENeMzq8Ww/viewform hw2 link]<br />
*[https://www.dropbox.com/s/k76x5dd19v8zbzq/LAaG_HW_3.pdf?dl=0 '''HW 3'''] (release: 03.10.2020; deadline: 09.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/h2whl2uds7tcwp8/LAaG_HW_2.pdf?dl=0 '''HW 2'''] (release: 18.09.2020; deadline: 25.09.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/2z5gdd4hgyknqpz/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)<br />
<br />
'''The obligatory homework for group 204:'''<br />
*['''HW 5'''] (release: 8.10.2020; deadline: 15.10.2020, 9:00 a. m.; [https://forms.gle/jN6eimdhkdZGMVL38 '''send here'''])<br />
*[https://yadi.sk/i/hzNK0ANZL_LPBw '''HW 4'''] (release: 2.10.2020; deadline: 9.10.2020, 9:00 a. m.; [https://forms.gle/wNxeDUZwXGfRggQR6 '''send here'''])<br />
*[https://yadi.sk/i/93RguRqucteczQ '''HW 3'''] (release: 27.09.2020; deadline: 05.10.2020, 9:00 a. m.; [https://forms.gle/5kr9ns6ntvXBZiUr9 '''send here'''])<br />
*[https://yadi.sk/i/zNOaULSelp5egw '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020, 9:00 a. m.; [https://forms.gle/P5PWSAtannwiVTHn9 '''send here'''])<br />
*[https://yadi.sk/i/AX-zxO6kW18GlQ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; [https://clck.ru/Qkq26 '''send here''']) Any computational tools are not allowed.<br />
<br />
== Results ==<br />
[https://docs.google.com/spreadsheets/d/1qF7mi0aHJCewqH08hXzGGHn2IXzQ-HOOrCRJ_LSX7vE/edit#gid=732068137 Results Sheet]<br />
<br />
3.10.2020. Quiz results (group 204) are published. You will be able to see your paper and ask questions during Monday Q&A or on Wednesday after the seminar.</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2020/2021&diff=45623LAaG DSBA 2020/20212020-10-04T11:46:19Z<p>Anna.Kosovskaya: /* Homework */</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 201 (M+P+) !! 202 !! 203 !! 204<br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]<br />
|- <br />
|| Schedule || || || || Wednesday, 13.00, D501<br />
[https://docs.google.com/spreadsheets/d/1xblWv0wuX7lkbe-0I8yyBPIhEUAq-U-HhGnuJ0It6xc/edit#gid=0 Zoom]<br />
(for distance learners)<br />
|- <br />
|| Consultations || Wed, ??:?? -- ??:??, room S808<br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| TBD || Monday, 14:40-17:00, S913<br />
To join via Zoom [https://t.me/galinakaleeva text me]<br />
Meeting ID: 732 2104 0735<br />
Passcode: algebra<br />
|-<br />
|| Assistant || Астанина Ксения <br> kkastanina@edu.hse.ru<br />
|| Васильев Борис <br> bavasilev@edu.hse.ru<br />
|| Княжевский Владимир <br> vvknyazhevskiy@edu.hse.ru<br />
|| Косовская Анна <br> a.dtc@yandex.ru<br />
|-<br />
|| Course <br> Assistant ||colspan="4"| Астанина Ксения <br> kkastanina@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 />
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 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, 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 />
== Lecture Notes ==<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2020) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br />
<br />
* [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2019) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br />
<br />
* [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2020) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (non-singular) matrices; the trace of a matrix; main properties of matrix transposition, matrix inverse, and the trace.<br />
<br />
* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) 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 />
== Seminar Notes ==<br />
<br />
'''Module 1'''<br />
<br />
'''Group 201:'''<br />
*[ '''S 1'''] (09.09.2020)<br />
<br />
<br />
'''Groups 202 and 203:'''<br />
*[ '''S 1'''] (XX.09.2020)<br />
<br />
<br />
'''Group 204:'''<br />
*[ '''S 1'''] (ХХ.09.2020)<br />
<br />
== Homework ==<br />
<br />
'''Module 1'''<br />
<br />
'''The obligatory homework for group 201:'''<br />
*[https://www.dropbox.com/s/54bqdcbvrit5ea6/LAaG_HW_4_C%28201%29.pdf?dl=0 '''HW 4'''] (release: 01.10.2020; deadline: 07.10.2020)<br />
*[https://www.dropbox.com/s/4fvmtbfpuki5tlx/LAaG_HW_3_C%28201%29.pdf?dl=0 '''HW 3'''] (release: 26.09.2020; deadline: 01.10.2020)<br />
*[https://www.dropbox.com/s/lz0953mwyxy3ybt/LAaG_HW_2_C%28201%29.pdf?dl=0 '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020)<br />
*[https://www.dropbox.com/s/m9y2wopr1lq0dtv/LAaG_HW_1_C%28201%29.pdf?dl=0 '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)<br />
<br />
<br />
'''The obligatory homework for groups 202 and 203:'''<br />
*An invite to Google Classroom for group 203: 3fyhfue (you can also use [https://classroom.google.com/c/MTU5OTQ0NzgyMTI3?cjc=3fyhfue this link])<br />
*Google Form to submit your work for group 202: [https://docs.google.com/forms/d/e/1FAIpQLSenETsrDiVDqDJdgQwtO8r2WHWCDsVczZSCZrZzCENeMzq8Ww/viewform hw2 link]<br />
*[https://www.dropbox.com/s/k76x5dd19v8zbzq/LAaG_HW_3.pdf?dl=0 '''HW 3'''] (release: 03.10.2020; deadline: 09.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/h2whl2uds7tcwp8/LAaG_HW_2.pdf?dl=0 '''HW 2'''] (release: 18.09.2020; deadline: 25.09.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/2z5gdd4hgyknqpz/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)<br />
<br />
'''The obligatory homework for group 204:'''<br />
*['''HW 5'''] (release: 8.10.2020; deadline: 15.10.2020, 9:00 a. m.; [https://forms.gle/jN6eimdhkdZGMVL38 '''send here'''])<br />
*[https://yadi.sk/i/hzNK0ANZL_LPBw '''HW 4'''] (release: 2.10.2020; deadline: 9.10.2020, 9:00 a. m.; [https://forms.gle/wNxeDUZwXGfRggQR6 '''send here'''])<br />
*[https://yadi.sk/i/93RguRqucteczQ '''HW 3'''] (release: 27.09.2020; deadline: 05.10.2020, 9:00 a. m.; [https://forms.gle/5kr9ns6ntvXBZiUr9 '''send here'''])<br />
*[https://yadi.sk/i/zNOaULSelp5egw '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020, 9:00 a. m.; [https://forms.gle/P5PWSAtannwiVTHn9 '''send here'''])<br />
*[https://yadi.sk/i/AX-zxO6kW18GlQ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; [https://clck.ru/Qkq26 '''send here''']) Any computational tools are not allowed.<br />
<br />
== Results ==<br />
[https://docs.google.com/spreadsheets/d/1qF7mi0aHJCewqH08hXzGGHn2IXzQ-HOOrCRJ_LSX7vE/edit#gid=732068137 Results Sheet]<br />
<br />
3.10.2020. Quiz results (group 204) are published. You will be able to see your paper and ask questions during Monday Q&A or on Wednesday after the seminar.</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2020/2021&diff=45622LAaG DSBA 2020/20212020-10-04T11:43:37Z<p>Anna.Kosovskaya: /* Homework */</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 201 (M+P+) !! 202 !! 203 !! 204<br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]<br />
|- <br />
|| Schedule || || || || Wednesday, 13.00, D501<br />
[https://docs.google.com/spreadsheets/d/1xblWv0wuX7lkbe-0I8yyBPIhEUAq-U-HhGnuJ0It6xc/edit#gid=0 Zoom]<br />
(for distance learners)<br />
|- <br />
|| Consultations || Wed, ??:?? -- ??:??, room S808<br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| TBD || Monday, 14:40-17:00, S913<br />
To join via Zoom [https://t.me/galinakaleeva text me]<br />
Meeting ID: 732 2104 0735<br />
Passcode: algebra<br />
|-<br />
|| Assistant || Астанина Ксения <br> kkastanina@edu.hse.ru<br />
|| Васильев Борис <br> bavasilev@edu.hse.ru<br />
|| Княжевский Владимир <br> vvknyazhevskiy@edu.hse.ru<br />
|| Косовская Анна <br> a.dtc@yandex.ru<br />
|-<br />
|| Course <br> Assistant ||colspan="4"| Астанина Ксения <br> kkastanina@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 />
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 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, 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 />
== Lecture Notes ==<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (30.09.2020) Systems of linear equations (SoLE); homogeneous, inhomogeneous, consistent, and inconsistent SoLE; the matrix form of a SoLE; leading and free variables; the augmented matrix of a SoLE; a general algorithm for solving SoLE.<br />
<br />
* [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (23.09.2019) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.<br />
<br />
* [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2020) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (non-singular) matrices; the trace of a matrix; main properties of matrix transposition, matrix inverse, and the trace.<br />
<br />
* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) 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 />
== Seminar Notes ==<br />
<br />
'''Module 1'''<br />
<br />
'''Group 201:'''<br />
*[ '''S 1'''] (09.09.2020)<br />
<br />
<br />
'''Groups 202 and 203:'''<br />
*[ '''S 1'''] (XX.09.2020)<br />
<br />
<br />
'''Group 204:'''<br />
*[ '''S 1'''] (ХХ.09.2020)<br />
<br />
== Homework ==<br />
<br />
'''Module 1'''<br />
<br />
'''The obligatory homework for group 201:'''<br />
*[https://www.dropbox.com/s/54bqdcbvrit5ea6/LAaG_HW_4_C%28201%29.pdf?dl=0 '''HW 4'''] (release: 01.10.2020; deadline: 07.10.2020)<br />
*[https://www.dropbox.com/s/4fvmtbfpuki5tlx/LAaG_HW_3_C%28201%29.pdf?dl=0 '''HW 3'''] (release: 26.09.2020; deadline: 01.10.2020)<br />
*[https://www.dropbox.com/s/lz0953mwyxy3ybt/LAaG_HW_2_C%28201%29.pdf?dl=0 '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020)<br />
*[https://www.dropbox.com/s/m9y2wopr1lq0dtv/LAaG_HW_1_C%28201%29.pdf?dl=0 '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)<br />
<br />
<br />
'''The obligatory homework for groups 202 and 203:'''<br />
*An invite to Google Classroom for group 203: 3fyhfue (you can also use [https://classroom.google.com/c/MTU5OTQ0NzgyMTI3?cjc=3fyhfue this link])<br />
*Google Form to submit your work for group 202: [https://docs.google.com/forms/d/e/1FAIpQLSenETsrDiVDqDJdgQwtO8r2WHWCDsVczZSCZrZzCENeMzq8Ww/viewform hw2 link]<br />
*[https://www.dropbox.com/s/k76x5dd19v8zbzq/LAaG_HW_3.pdf?dl=0 '''HW 3'''] (release: 03.10.2020; deadline: 09.10.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/h2whl2uds7tcwp8/LAaG_HW_2.pdf?dl=0 '''HW 2'''] (release: 18.09.2020; deadline: 25.09.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/2z5gdd4hgyknqpz/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)<br />
<br />
'''The obligatory homework for group 204:'''<br />
*['''HW 5'''] (release: 8.10.2020; deadline: 15.10.2020, 9:00 a. m.)<br />
*[https://yadi.sk/i/hzNK0ANZL_LPBw '''HW 4'''] (release: 2.10.2020; deadline: 9.10.2020, 9:00 a. m.; [https://forms.gle/wNxeDUZwXGfRggQR6 '''send here'''])<br />
*[https://yadi.sk/i/93RguRqucteczQ '''HW 3'''] (release: 27.09.2020; deadline: 05.10.2020, 9:00 a. m.; [https://forms.gle/5kr9ns6ntvXBZiUr9 '''send here'''])<br />
*[https://yadi.sk/i/zNOaULSelp5egw '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020, 9:00 a. m.; [https://forms.gle/P5PWSAtannwiVTHn9 '''send here'''])<br />
*[https://yadi.sk/i/AX-zxO6kW18GlQ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; [https://clck.ru/Qkq26 '''send here''']) Any computational tools are not allowed.<br />
<br />
== Results ==<br />
[https://docs.google.com/spreadsheets/d/1qF7mi0aHJCewqH08hXzGGHn2IXzQ-HOOrCRJ_LSX7vE/edit#gid=732068137 Results Sheet]<br />
<br />
3.10.2020. Quiz results (group 204) are published. You will be able to see your paper and ask questions during Monday Q&A or on Wednesday after the seminar.</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2020/2021&diff=44736LAaG DSBA 2020/20212020-09-19T17:00:57Z<p>Anna.Kosovskaya: /* Homework */</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 201 (M+P+) !! 202 !! 203 !! 204<br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]<br />
|- <br />
|| Schedule || || || || Wednesday, 13.00, D501<br />
[https://docs.google.com/spreadsheets/d/1xblWv0wuX7lkbe-0I8yyBPIhEUAq-U-HhGnuJ0It6xc/edit#gid=0 Zoom]<br />
(for distance learners)<br />
|- <br />
|| Consultations || Wed, ??:?? -- ??:??, room S808<br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| TBD || Monday, 14:40-17:00, S913<br />
To join via Zoom [https://t.me/galinakaleeva text me]<br />
|-<br />
|| Assistant || Астанина Ксения <br> kkastanina@edu.hse.ru<br />
|| Васильев Борис <br> bavasilev@edu.hse.ru<br />
|| Княжевский Владимир <br> vvknyazhevskiy@edu.hse.ru<br />
|| Косовская Анна <br> a.dtc@yandex.ru<br />
|-<br />
|| Course <br> Assistant ||colspan="4"| Астанина Ксения <br> kkastanina@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 />
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 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, 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 />
== Lecture Notes ==<br />
<br />
''' Module 1 '''<br />
* [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (16.09.2020) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (non-singular) matrices; the trace of a matrix; main properties of matrix transposition, matrix inverse, and the trace.<br />
<br />
* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) 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 />
== Seminar Notes ==<br />
<br />
'''Module 1'''<br />
<br />
'''Group 201:'''<br />
*[ '''S 1'''] (09.09.2020)<br />
<br />
<br />
'''Groups 202 and 203:'''<br />
*[ '''S 1'''] (XX.09.2020)<br />
<br />
<br />
'''Group 204:'''<br />
*[ '''S 1'''] (ХХ.09.2020)<br />
<br />
== Homework ==<br />
<br />
'''Module 1'''<br />
<br />
'''The obligatory homework for group 201:'''<br />
*[https://www.dropbox.com/s/lz0953mwyxy3ybt/LAaG_HW_2_C%28201%29.pdf?dl=0 '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020)<br />
*[https://www.dropbox.com/s/m9y2wopr1lq0dtv/LAaG_HW_1_C%28201%29.pdf?dl=0 '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)<br />
<br />
<br />
'''The obligatory homework for groups 202 and 203:'''<br />
*An invite to Google Classroom for group 203: 3fyhfue (you can also use [https://classroom.google.com/c/MTU5OTQ0NzgyMTI3?cjc=3fyhfue this link])<br />
*Google Form to submit your work for group 202: [https://docs.google.com/forms/d/e/1FAIpQLSemwTtWNBpdUKpSRnz2v3tnnX-Drd678JN1y69biULRLzF3gQ/viewform link]<br />
*[https://www.dropbox.com/s/h2whl2uds7tcwp8/LAaG_HW_2.pdf?dl=0 '''HW 2'''] (release: 18.09.2020; deadline: 25.09.2020, 9:00 a.m.)<br />
*[https://www.dropbox.com/s/2z5gdd4hgyknqpz/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)<br />
<br />
<br />
'''The obligatory homework for group 204:'''<br />
*[https://yadi.sk/i/AX-zxO6kW18GlQ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; [https://clck.ru/Qkq26 '''send here''']) Any computational tools are not allowed.<br />
*[https://yadi.sk/i/zNOaULSelp5egw '''HW 2'''] (release: 17.09.2020; deadline: 23.09.2020, 9:00 a. m.; [https://forms.gle/P5PWSAtannwiVTHn9 '''send here'''])<br />
<br />
== Results ==</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2020/2021&diff=43871LAaG DSBA 2020/20212020-09-09T09:45:38Z<p>Anna.Kosovskaya: /* Homework */</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 201 (M+P+) !! 202 !! 203 !! 204<br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]<br />
|- <br />
|| Schedule || || || || Wednesday, 13.00, G406<br />
[https://docs.google.com/spreadsheets/d/1xblWv0wuX7lkbe-0I8yyBPIhEUAq-U-HhGnuJ0It6xc/edit#gid=0 Zoom]<br />
(for distance learners)<br />
|- <br />
|| Consultations || Wed, ??:?? -- ??:??, room S808<br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| TBD || TBD<br />
|-<br />
|| Assistant || Астанина Ксения <br> kkastanina@edu.hse.ru<br />
|| Васильев Борис <br> bavasilev@edu.hse.ru<br />
|| Княжевский Владимир <br> vvknyazhevskiy@edu.hse.ru<br />
|| Косовская Анна <br> a.dtc@yandex.ru<br />
|-<br />
|| Course <br> Assistant ||colspan="4"| Астанина Ксения <br> kkastanina@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 />
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 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, 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 />
== Lecture Notes ==<br />
<br />
''' Module 1 '''<br />
<br />
* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) 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 />
== Seminar Notes ==<br />
<br />
'''Module 1'''<br />
<br />
'''Group 201:'''<br />
*[ '''S 1'''] (09.09.2020)<br />
<br />
<br />
'''Groups 202 and 203:'''<br />
*[ '''S 1'''] (XX.09.2020)<br />
<br />
<br />
'''Group 204:'''<br />
*[ '''S 1'''] (ХХ.09.2020)<br />
<br />
== Homework ==<br />
<br />
'''Module 1'''<br />
<br />
'''The obligatory homework for group 201:'''<br />
*[ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)<br />
<br />
<br />
'''The obligatory homework for groups 202 and 203:'''<br />
*[ '''HW 1'''] (release: ХХ.09.2020; deadline: ХХ.09.2020)<br />
<br />
<br />
'''The obligatory homework for group 204:'''<br />
*[ '''HW 1'''] (release: ХХ.09.2020; deadline: ХХ.09.2020; send here: https://clck.ru/Qkq26)<br />
<br />
== Results ==<br />
<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit?usp=sharing 201] !! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1476291658 202] !! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1726530362 203] !!<br />
[https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1726530362 204] <br />
|}</div>Anna.Kosovskayahttps://wiki.cs.hse.ru/index.php?title=LAaG_DSBA_2020/2021&diff=43870LAaG DSBA 2020/20212020-09-09T09:44:26Z<p>Anna.Kosovskaya: /* Homework */</p>
<hr />
<div>== Teachers and Assistants ==<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! Group !! 201 (M+P+) !! 202 !! 203 !! 204<br />
|-<br />
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br />
|- <br />
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || colspan="2"| [https://www.hse.ru/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/staff/kaleeva Galina Kaleeva]<br />
|- <br />
|| Schedule || || || || Wednesday, 13.00, G406<br />
[https://docs.google.com/spreadsheets/d/1xblWv0wuX7lkbe-0I8yyBPIhEUAq-U-HhGnuJ0It6xc/edit#gid=0 Zoom]<br />
(for distance learners)<br />
|- <br />
|| Consultations || Wed, ??:?? -- ??:??, room S808<br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| TBD || TBD<br />
|-<br />
|| Assistant || Астанина Ксения <br> kkastanina@edu.hse.ru<br />
|| Васильев Борис <br> bavasilev@edu.hse.ru<br />
|| Княжевский Владимир <br> vvknyazhevskiy@edu.hse.ru<br />
|| Косовская Анна <br> a.dtc@yandex.ru<br />
|-<br />
|| Course <br> Assistant ||colspan="4"| Астанина Ксения <br> kkastanina@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 />
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 0.6, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.6] and the student's seminar attendance during the first semester is not below 60%, 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 />
== Lecture Notes ==<br />
<br />
''' Module 1 '''<br />
<br />
* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (09.09.2020) 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 />
== Seminar Notes ==<br />
<br />
'''Module 1'''<br />
<br />
'''Group 201:'''<br />
*[ '''S 1'''] (09.09.2020)<br />
<br />
<br />
'''Groups 202 and 203:'''<br />
*[ '''S 1'''] (XX.09.2020)<br />
<br />
<br />
'''Group 204:'''<br />
*[ '''S 1'''] (ХХ.09.2020)<br />
<br />
== Homework ==<br />
<br />
'''Module 1'''<br />
<br />
'''The obligatory homework for group 201:'''<br />
*[ '''HW 1'''] (release: 09.09.2020; deadline: 16.09.2020)<br />
<br />
<br />
'''The obligatory homework for groups 202 and 203:'''<br />
*[ '''HW 1'''] (release: ХХ.09.2020; deadline: ХХ.09.2020)<br />
<br />
<br />
'''The obligatory homework for group 204:'''<br />
*[ '''HW 1'''] (release: ХХ.09.2020; deadline: ХХ.09.2020; send here: clck.ru/Qkq26)<br />
<br />
== Results ==<br />
<br />
{| class="wikitable" style="text-align:center"<br />
|-<br />
! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit?usp=sharing 201] !! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1476291658 202] !! [https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1726530362 203] !!<br />
[https://docs.google.com/spreadsheets/d/1rozrjdjNTabB2ygSTjBsYChSrQrDJCS5ni-hicaFdmU/edit#gid=1726530362 204] <br />
|}</div>Anna.Kosovskaya