Просмотр исходного текста страницы LAaG DSBA 2021/2022

== Teachers and Assistants ==
{| class="wikitable" style="text-align:center"
|-
! Group !! 211 (M+P+) !! 212 !! 213 !! 214
|-
|| Lecturer ||colspan="4"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]
|- 
|| 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]
|- 
|| Schedule ||  || ||  || Thursday, 11.10, R406
September 9, 16, 23: the class starts at 14.40. 

|- 
|| Consultations || Wed, 17:00 -- 21:00, via Zoom <br><span style="color:#DC143C">One must notify me beforehand</span> || colspan="2"| Wednesday via Zoom, 17:00,<br> (write @medvednikita beforehands)<br> or Friday 14:20 after the seminar with 213 (same room or write me in telegram) || Friday, after 16.20. S812. [https://docs.google.com/forms/d/e/1FAIpQLSdbAFvvA9dQMCRXdG5Lc3G77ldPbR8UwW8NoUcX0m4mQzPEww/viewform Sign up] for q&a until Thursday, 23.59.
|-
|| Assistant || Белоновский Пётр <br> pibelonovskiy@edu.hse.ru
|| Астанина Ксения <br> kkastanina@edu.hse.ru
|| Королев Кирилл <br> [https://t.me/kkorolev1 kkorolev1]
|| Федорова Анна <br> [https://t.me/z_piranja z_piranja]
|-
|| Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru
|- 
|}

== Course Description ==
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.

We will approach the subject from both a practical point of view (learning methods and acquiring computational skills
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).

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.

== Grading system ==  

<div class="mw-collapsible">

During the academic year, the student will be formally graded on the following:
*two in-class oral tests (O<sub>1</sub> and O<sub>2</sub>);
*two in-class written tests (W<sub>1</sub> and W<sub>2</sub>);
*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);
*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);
*two written exams (E<sub>1</sub> and E<sub>2</sub>).

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.

'''<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:

'''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>.'''

'''<span style="color:#0000CD">The intermediate course grade for the first semester</span>''', I<sub>1</sub>, is obtained by the following formula:

'''I<sub>1</sub> = Round<sub>1</sub>(3/10*E<sub>1</sub> + 7/10*C<sub>1</sub>),'''

where the function Round<sub>1</sub>(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.

'''<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:

'''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>.'''

'''<span style="color:#0000CD">The intermediate course grade for the second semester</span>''', I<sub>2</sub>, is obtained by the following formula:

'''I<sub>2</sub> = Round<sub>2</sub>(3/10*E<sub>2</sub> + 7/10*C<sub>2</sub>),'''

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".

'''<span style="color:#DC143C">The final grade for the course</span>''', F, is obtained by the following formula:

'''F = Round(1/4*I<sub>1</sub> + 3/4*I<sub>2</sub>),'''

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".

The final grade for the course is included in a diploma supplement.

</div>

== Lecture Notes ==

''' Module 1 '''
* [https://www.dropbox.com/s/ph1bk3pxksea1cw/LAaG_Lecture_6.pdf?dl=0 '''Lecture 6'''] (06.10.2021) 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.

* [https://www.dropbox.com/s/rnvhxr8m3acn8r4/LAaG_Lecture_5.pdf?dl=0 '''Lecture 5'''] (29.09.2021) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.

* [https://www.dropbox.com/s/lqwfw0ytlpn2o1j/LAaG_Lecture_4.pdf?dl=0 '''Lecture 4'''] (22.09.2021) 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.

* [https://www.dropbox.com/s/h0p48gpr8cfaywf/LAaG_Lecture_3.pdf?dl=0 '''Lecture 3'''] (15.09.2021) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.

* [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (08.09.2021) 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.

* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (04.09.2021) 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.

== Seminar Notes ==

'''Module 1'''

'''Group 201:'''
*[ '''S 1'''] (XX.09.2021)

'''Group 202:'''
*[ '''S 1'''] (XX.09.2021)

'''Group 203:'''
*[ '''S 1'''] (XX.09.2021)

'''Group 214:'''
*[https://disk.yandex.ru/d/0U0EI5UGLOPU2A '''Seminars and home assignments''']

== Homework ==

'''The obligatory homework for group 211:'''

'''Module 1'''

* [https://www.dropbox.com/s/bb0ctr73zvqqko8/LAaG_HW_6_C%28211%29.pdf?dl=0  '''HW 6'''] (release: 11.10.2021; deadline: 29.10.2021)
* [https://www.dropbox.com/s/7ldgsvwgtyvdjr6/LAaG_HW_5_C%28211%29.pdf?dl=0  '''HW 5'''] (release: 07.10.2021; deadline: 15.10.2021)
* [https://www.dropbox.com/s/7njlrforga0gllb/LAaG_HW_4_C%28211%29.pdf?dl=0  '''HW 4'''] (release: 30.09.2021; deadline: 08.10.2021)
* [https://www.dropbox.com/s/hrseqbj1bqmxlcz/LAaG_HW_3_C%28211%29.pdf?dl=0  '''HW 3'''] (release: 26.09.2021; deadline: 01.10.2021)
* [https://www.dropbox.com/s/v89s2y16i56d61a/LAaG_HW_2_C%28211%29.pdf?dl=0  '''HW 2'''] (release: 16.09.2021; deadline: 24.09.2021)
* [https://www.dropbox.com/s/8qxvz6gejiekq93/LAaG_HW_1_C%28211%29.pdf?dl=0  '''HW 1'''] (release: 08.09.2021; deadline: 17.09.2021)


'''The obligatory homework for groups 212 and 213:'''

'''Module 1'''
* [https://www.dropbox.com/s/8bmckqje4gbpp9s/LAaG_HW_4.pdf?dl=0 '''HW 4'''] (release: 02.10.2021; deadline: '''09'''.10.2021, 9 a. m.)
* [https://www.dropbox.com/s/u8ddhexx43ygrf4/LAaG_HW_3.pdf?dl=0 '''HW 3'''] (release: 24.09.2021; deadline: 01.10.2021, 9 a. m.)
* [https://www.dropbox.com/s/mg3345wtsf5khgr/LAaG_HW_2.pdf?dl=0 '''HW 2'''] (release: 17.09.2021; deadline: 24.09.2021, 9 a. m.)
* [https://www.dropbox.com/s/uk1jiaiz50qgfk4/LAaG_HW_1.pdf?dl=0 '''HW 1'''] (release: 10.09.2021; deadline: 17.09.2021)

'''The obligatory homework for group 214:'''

Send your works to Google classroom: [https://classroom.google.com/c/Mzg5NzgwNjE0MjUw?cjc=o6k7hsj link] (access code: o6k7hsj)

'''Module 1'''

*[https://disk.yandex.ru/i/Kkf7SipPXHpQEg '''HW 5'''] (release: 7.10.2021; deadline: 15.10.2021, 9 a. m.)
*[https://disk.yandex.ru/i/SMygo30NT1XcSA '''HW 4'''] (release: 1.10.2021; deadline: 09.10.2021, 9 a. m.)
*[https://disk.yandex.ru/i/2sL_IH0NQbkKOA '''HW 3'''] (release: 23.09.2021; deadline: 01.10.2021, 9 a. m.)
*[https://disk.yandex.ru/i/7FfCszkZZ5I-Bw '''HW 2'''] (release: 16.09.2021; deadline: 24.09.2021, 9 a. m.)
*[https://disk.yandex.ru/i/A1iKb2HinDVM_A '''HW 1'''] (release: 09.09.2021; deadline: 17.09.2021, 9 a. m.)

== Results ==
[https://docs.google.com/spreadsheets/d/1qF7mi0aHJCewqH08hXzGGHn2IXzQ-HOOrCRJ_LSX7vE/edit#gid=732068137 Results Sheet]