LAaG DSBA 2022/2023

Teachers and Assistants

Group	211 (M+P+)	212	213	214
Lecturer	Andrey Mazhuga
Teacher	Andrey Mazhuga	Nikita Medved (tg)		Vladislav Balakirev
Consultations	Sat, 17:00 -- 21:00, via Zoom One must notify me beforehand			??
Assistant	Белоновский Пётр pibelonovskiy@edu.hse.ru	Астанина Ксения kkastanina@edu.hse.ru	Боженов Олег @obozhenov	Науменко Дарья @yalmess

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

During the academic year, the student will be formally graded on the following:

• two in-class oral tests (O₁ and O₂);
• two in-class written tests (W₁ and W₂);
• several quizzes (Q₁ and Q₂, where Q_i is the average grade of all the quizzes in the i-th semester);
• several homework assignments (H₁ and H₂, where H_i is the average grade of all the homework assignments in the i-th semester);
• two written exams (E₁ and E₂).

All grades (namely, O₁, O₂, W₁, W₂, Q₁, Q₂, H₁, H₂, E₁, and E₂) are real numbers from 0 to 10.

The cumulative course grade for the first semester, C₁, is obtained without rounding by the following formula:

C₁ = 5/16*O₁ + 4/16*W₁ + 4/16*Q₁ + 3/16*H₁.

The intermediate course grade for the first semester, I₁, is obtained by the following formula:

I₁ = Round₁(3/10*E₁ + 7/10*C₁),

where the function Round₁(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.

The cumulative course grade for the second semester, C₂, is obtained without rounding by the following formula:

C₂ = 5/16*O₂ + 4/16*W₂ + 4/16*Q₂ + 3/16*H₂.

The intermediate course grade for the second semester, I₂, is obtained by the following formula:

I₂ = Round₂(3/10*E₂ + 7/10*C₂),

where the function Round₂(x) is defined as Round₁(x) but with "during the first semester" replaced by "during the second semester".

The final grade for the course, F, is obtained by the following formula:

F = Round(1/4*I₁ + 3/4*I₂),

where the function Round(x) is defined as Round₁(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.

Lecture Notes

Module 1

• Lecture 6 (15.10.2022) 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.

• Lecture 5 (10.10.2022) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.

• Lecture 4 (03.10.2022) 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.

• Lecture 3 (21.09.2022) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.

• Lecture 2 (14.09.2022) 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.

• Lecture 1 (07.09.2022) 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.

Homework

The obligatory homework for group 221:

Module 1

• HW_6 (release: 17.10.2022; deadline: 31.10.2022) (seminar notes)
• HW_5 (release: 15.10.2022; deadline: 23.10.2022) (seminar notes)
• HW_4 (release: 10.10.2022; deadline: 16.10.2022)
• HW_3 (release: 03.10.2022; deadline: 09.10.2022)
• HW_2 (release: 21.09.2022; deadline: 02.10.2022)
• HW_1 (release: 13.09.2022; deadline: 20.09.2022)

The obligatory homework for groups 222 and 223:

Module 1

• HW 5 (release: 13.10.2022; deadline: 18.10.2022 9a.m.) (seminar notes)
• HW 4 (release: 03.10.2022; deadline: 10.10.2022 9a.m.) (seminar notes)
• HW 3 (release: 24.09.2022; deadline: 29.09.2022 9a.m.) (seminar notes)
• HW 2 (release: 15.09.2022; deadline: 22.09.2022 9a.m.) (seminar notes)
• HW 1 (release: 08.09.2022; deadline: 15.09.2022 9a.m.) (seminar notes)

The obligatory homework for group 224:

Module 1

• HW_5 (release: 16.10.2022; deadline: 23.10.2022) (seminar notes)
• HW_4 (release: 08.10.2022; deadline: 14.10.2022)
• HW_3 (release: 01.10.2022; deadline: 07.10.2022)
• HW_2 (release: 23.09.2022; deadline: 29.09.2022)
• HW_1 (release: 15.09.2022; deadline: 21.09.2022)

Materials

Folder with some seminar (and lectures?) recordings (managed by the Study Office)

Results

221	222-223	224