LAaG DSBA 2026/2027: различия между версиями
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== Lecture Notes == | == Lecture Notes == | ||
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* [https://www.dropbox.com/s/zkamg2rgrxv7vey/LAaG_Lecture_32.pdf?dl=0 '''Lecture 31'''] (20.05.2026) Orientation on a vector space; the cross product; main properties of the cross product. | * [https://www.dropbox.com/s/zkamg2rgrxv7vey/LAaG_Lecture_32.pdf?dl=0 '''Lecture 31'''] (20.05.2026) Orientation on a vector space; the cross product; main properties of the cross product. | ||
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* [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (05.11.2025) 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. | * [https://www.dropbox.com/s/qxrzppzu8oor5zq/LAaG_Lecture_9_v_2.pdf?dl=0 '''Lecture 9'''] (05.11.2025) 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. | ||
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''' Module 1 ''' | ''' Module 1 ''' | ||
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* [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (22.10.2025) 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. | * [https://www.dropbox.com/s/s849r4boozi6qu9/LAaG_Lecture_8.pdf?dl=0 '''Lecture 8'''] (22.10.2025) 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. | ||
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* [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (10.09.2025) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace. | * [https://www.dropbox.com/s/hp9hrjorgv3ez3o/LAaG_Lecture_2.pdf?dl=0 '''Lecture 2'''] (10.09.2025) Matrix transposition; symmetric and skew-symetric matrices; inverse of a matrix; invertible (=non-singular) matrices; the trace of a matrix; main properties of the matrix transposition; the trace. | ||
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* [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] ( | * [https://www.dropbox.com/s/xbzr7b3upj63rhy/LAaG_Lecture_1.pdf?dl=0 '''Lecture 1'''] (02.09.2026) 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 == | == Homework == | ||
Версия от 10:06, 1 сентября 2026
Teachers and Assistants
| Group | 261 (M+P+) | 262 (P+) | 263 | 264 | 265 | 266 | 267 |
|---|---|---|---|---|---|---|---|
| Lecturer | Андрей Мажуга | ||||||
| Teacher | Андрей Мажуга | Сергей Смирнов (tg) | Василий Гончаренко | Дарья Башминова (tg) | Сергей Смирнов (tg) | ||
| Consultations | by agreement via Zoom One must notify me beforehand |
by agreement via Zoom | by agreement | by agreement One must notify me beforehand via telegram |
by agreement via Zoom | ||
| Assistant | Мельничук Мирослава Коковин Алексей |
Иванова Анастасия Серветник София |
Радаева Ангелина Саломадина Полина |
Бальцер Злата Кадурина Елизавета |
Карпухин Симеон Острейкова Софья |
Истомина Любовь Маризин Семён |
Зяблюк Сергей Алексеенко Андрей |
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 Qi is the average grade of all the quizzes in the i-th semester);
- several homework assignments (H1 and H2, where Hi 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 1 (02.09.2026) 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
Semester 2
| 251 | 252 | 253 | 254 | 255 | 256 | 257 |
|---|---|---|---|---|---|---|
| HW_15 (21.01.26) Seminar_15 Notes |
HW_15 (21.01.26) Seminar_15 Notes |
HW_15 (21.01.26) | [ HW_15] | [ HW15] | HW_15 (21.01.26) | HW_15 (21.01.26) |
| HW_16 (28.01.26) Seminar_16 Notes |
HW_16 (28.01.26) Seminar_16 Notes |
HW_16 (28.01.26) | [ HW_16] | [ HW16] | HW_16 (28.01.26) | HW_16 (28.01.26) |
| HW_17 (04.02.26) Seminar_17 Notes |
HW_17 (04.02.26) Seminar_17 Notes |
HW_17 (04.02.26) | [ HW_17] | [ HW17] | HW_17 (04.02.26) | HW_17 (04.02.26) |
| HW_18 (11.02.26) Seminar_18 Notes |
HW_18 (11.02.26) Seminar_18 Notes |
HW_18 (11.04.26) | [ HW_18] | [ HW18] | HW_18 (11.04.26) | HW_18 (11.04.26) |
| HW_19 (18.02.26) Seminar_19 Notes |
HW_19 (18.02.26) Seminar_19 Notes |
HW_19 (18.02.26) | [ HW_19] | [ HW19] | HW_19 (18.02.26) | HW_19 (18.02.26) |
| HW_20 (25.02.26) Seminar_20 Notes |
HW_20 (25.02.26) Seminar_20 Notes |
HW_20 (25.02.26) | [ HW_20] | [ HW20] | HW_20 (25.02.26) | HW_20 (25.02.26) |
| HW_21 (06.03.26) Seminar_21 Notes |
HW_21 (06.03.26) Seminar_21 Notes |
HW_21 (04.03.26) | [ HW_21] | [ HW21] | HW_21 (04.03.26) | HW_21 (04.03.26) |
| HW_22 (13.03.26) Seminar_22 Notes |
HW_22 (13.03.26) Seminar_22 Notes |
HW_22 (11.03.26) | [ HW_22] | [ HW22] | HW_22 (11.03.26) | HW_22 (11.03.26) |
| HW_23 (20.03.26) Seminar_23 Notes |
HW_23 (20.03.26) Seminar_23 Notes |
HW_23 (18.03.26) | [ HW_23] | [ HW23] | HW_23 (18.03.26) | HW_23 (18.03.26) |
| HW_24 (27.03.26) | HW_24 (27.03.26) | HW_24 (05.04.26) | [ HW_24] | [ HW24] | HW_24 (05.04.26) | HW_24 (05.04.26) |
| HW_25 (10.04.26) Seminar_25 Notes |
HW_25 (10.04.26) Seminar_25 Notes |
HW_25 (15.04.26) | [ HW_25] | [ HW25] | HW_25 (15.04.26) | HW_25 (15.04.26) |
| HW_26 (17.04.26) Seminar_26 Notes |
HW_26 (17.04.26) Seminar_26 Notes |
HW_26 (19.04.26) | [ HW_26] | [ HW26] | HW_26 (19.04.26) | HW_26 (19.04.26) |
| HW_27 (24.04.26) [ Seminar_27 Notes] |
HW_27 (24.04.26) [ Seminar_27 Notes] |
[ HW_27] (??.??.26) | [ HW_27] | [ HW27] | [ HW_27] (??.??.26) | [ HW_27] (??.??.26) |
| HW_28 (03.05.26) Seminar_28 Notes |
HW_28 (03.05.26) Seminar_28 Notes |
HW_28 (30.04.26) | [ HW_28] | [ HW28] | HW_28 (30.04.26) | HW_28 (30.04.26) |
| HW_29 (20.05.26) Seminar_29 Notes |
HW_29 (11.05.26) Seminar_29 Notes |
HW_29 (18.05.26) | [ HW_29] | [ HW29] | HW_29 (18.05.26) | HW_29 (18.05.26) |
| HW_30 (24.05.26) | HW_30 (22.05.26) | [ HW_30] (??.??.26) | [ HW_30] | [ HW30] | [ HW_30] (??.??.26) | [ HW_30] (??.??.26) |
| HW_31 (29.05.26) | HW_31 (29.05.26) | [ HW_31] (??.??.26) | [ HW_31] | [ HW31] | [ HW_31] (??.??.26) | [ HW_31] (??.??.26) |
Semester 1
| 251 | 252 | 253 | 254 | 255 | 256 | 257 |
|---|---|---|---|---|---|---|
| HW_1 (17.09.25) Seminar_1 Notes |
HW_1 (17.09.25) Seminar_1 Notes |
HW_1 (17.09.25) | HW_1 | HW_1 | HW_1 (17.09.25) | HW_1 (17.09.25) |
| HW_2 (24.09.25) Seminar_2 Notes |
HW_2 (24.09.25) Seminar_2 Notes |
HW_2 (24.09.25) | HW_2 | HW_2 | HW_2 (24.09.25) | HW_2 (24.09.25) |
| HW_3 (01.10.25) Seminar_3 Notes |
HW_3 (01.10.25) Seminar_3 Notes |
HW_3 (01.10.25) | HW_3 | HW_3 | HW_3 (01.10.25) | HW_3 (01.10.25) |
| HW_4 (08.10.25) Seminar_4 Notes |
HW_4 (08.10.25) Seminar_4 Notes |
HW_4 (08.10.25) | HW_4 | HW_4 | HW_4 (08.10.25) | HW_4 (08.10.25) |
| HW_5 (15.10.25) Seminar_5 Notes |
HW_5 (15.10.25) Seminar_5 Notes |
HW_5 (15.10.25) | HW_5 | HW_5 | HW_5 (15.10.25) | HW_5 (15.10.25) |
| HW_6 (22.10.25) Seminar_6 Notes |
HW_6 (22.10.25) Seminar_6 Notes |
HW_6 (22.10.25) | [ HW_6] | [ HW_6] | HW_6 (22.10.25) | HW_6 (22.10.25) |
| HW_7 (01.11.25) Seminar_7 Notes |
HW_7 (01.11.25) Seminar_7 Notes |
HW_7 (02.11.25) | [ HW_7] | [ HW_7] | HW_7 (02.11.25) | HW_7 (02.11.25) |
| HW_8 (12.11.25) Seminar_8 Notes |
HW_8 (12.11.25) Seminar_8 Notes |
HW_8 (12.11.25) | [ HW_8] | [ HW_8] | HW_8 (12.11.25) | HW_8 (12.11.25) |
| HW_9 (19.11.25) |
HW_9 (19.11.25) |
HW_9 (19.11.25) | [ HW_9] | [ HW_9] | HW_9 (19.11.25) | HW_9 (19.11.25) |
| HW_10 (26.11.25) Seminar_10 Notes |
HW_10 (26.11.25) Seminar_10 Notes |
HW_10 (26.11.25) | [ HW_10] | [ HW_10] | HW_10 (26.11.25) | HW_10 (26.11.25) |
| HW_11 (15.12.25) Seminar_11 Notes |
HW_11 (15.12.25) Seminar_11 Notes |
HW_11 (03.12.25) | [ HW_11] | [ HW11] | HW_11 (03.12.25) | HW_11 (03.12.25) |
| HW_12 (15.12.25) Seminar_12 Notes |
HW_12 (15.12.25) Seminar_12 Notes |
HW_12 (10.12.25) | [ HW_12] | [ HW12] | HW_12 (10.12.25) | HW_12 (10.12.25) |
| HW_13 (14.01.26) Seminar_13 Notes Seminar_14 Notes |
HW_13 (14.01.26) Seminar_13 Notes Seminar_14 Notes |
HW_13 (14.01.26) | [ HW_13] | [ HW13] | HW_13 (14.01.26) | HW_13 (14.01.26) |
Exams
Results
| 251 | 252 | 253 | 254 | 255 | 256 | 257 |
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DSBA 2022/2023 |
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|---|---|
| First year | |