LAaG DSBA 2024/2025 — различия между версиями
(→Нomework for group 241:) |
(→Нomework for group 241:) |
||
| Строка 93: | Строка 93: | ||
=== Нomework for group 241: === | === Нomework for group 241: === | ||
'''Module 1''' | '''Module 1''' | ||
| − | * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&st=x3os308k&dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) <small>([https://www.dropbox.com/scl/fi/ | + | * [https://www.dropbox.com/scl/fi/6kz0pem4gfqxviwdesc9d/LAaG_HW_7_C-241.pdf?rlkey=2u4pnpdywz14lov8uhitg8m8p&st=x3os308k&dl=0 '''HW 7'''] (release: 21.10.24; deadline: 01.11.24) <small>([https://www.dropbox.com/scl/fi/tsj2gszeyx8x3kwuzf4g4/LAaG_Seminar_7.pdf?rlkey=8qd6f113u1f75uykzy2oxb6ul&dl=0 Seminar_7 notes])</small> |
* [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&st=6hxk6zvn&dl=0 '''HW 6'''] (release: 14.10.23; deadline: 21.10.23) <small>([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&dl=0 Seminar_6 notes])</small> | * [https://www.dropbox.com/scl/fi/gw2k7q3ta64rxqdnhym96/LAaG_HW_6_C-241.pdf?rlkey=ibzxh25g8036bet509uqqg0xx&st=6hxk6zvn&dl=0 '''HW 6'''] (release: 14.10.23; deadline: 21.10.23) <small>([https://www.dropbox.com/scl/fi/7w44s5f2ihe8oto2c00a8/LAaG_Seminar_6.pdf?rlkey=9lvluspt27l6d2jm7dry8flum&dl=0 Seminar_6 notes])</small> | ||
Версия 20:46, 21 октября 2024
Содержание
Teachers and Assistants
| Group | 241 (M+P+) | 242 (P+) | 243 | 244 | 245 | 246 |
|---|---|---|---|---|---|---|
| Lecturer | Andrey Mazhuga | |||||
| Teacher | Andrey Mazhuga | Vladislav Balakirev (tg) | Дарья Башминова (tg) | Andrey Mazhuga | ||
| Consultations | Sat, 17:00 -- 21:00, via Zoom One must notify me beforehand |
??? | ??? | ??? | ??? | Sat, 17:00 -- 21:00, via Zoom One must notify me beforehand |
| Assistant | Купцов Максим | Зинкин Захар | Павлов Аркадий | Бохян Роман | Дороничева Полина | Науменко Дарья |
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 7 (21.10.2024) Determinant of an elementary matrix; determinant of a product of matrices; determinant test for invertibility.
- Lecture 6 (14.10.2024) 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 (07.10.2024) Permutations; two-line notation of a permutation; the sign of a permutation; even and odd permutation; transpositions.
- Lecture 4 (30.09.2024) 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 (23.09.2024) Elementary row matrix operations; elementary matrices; elementary row operations as matrix pre-multiplication; reduced row echelon form; Gaussian elimination.
- Lecture 2 (16.09.2024) 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.
- Lecture 1 (09.09.2024) 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
Нomework for group 241:
Module 1
- HW 7 (release: 21.10.24; deadline: 01.11.24) (Seminar_7 notes)
- HW 6 (release: 14.10.23; deadline: 21.10.23) (Seminar_6 notes)
- HW 5 (release: 07.10.24; deadline: 14.10.24) (Seminar_5 notes)
- HW 4 (release: 30.09.24; deadline: 07.10.24) (Seminar_4 notes)
- HW 3 (release: 23.09.24; deadline: 30.09.24) (Seminar_3 notes)
- HW 2 (release: 16.09.24; deadline: 23.09.24) (Seminar_2 notes)
- HW 1 (release: 09.09.24; deadline: 16.09.24) (Seminar_1 notes)
Homework for group 242:
Module 1
- [ HW 1] (release: ; deadline: ) ([ seminar notes])
Homework for group 243:
Module 1
- [ HW 1] (release: ; deadline: ) ([ seminar notes])
Homework for group 244:
Module 1
- [ HW 1] (release: ; deadline: ) ([ seminar notes])
Homework for group 245:
Module 1
- [ HW 1] (release: ; deadline: ) ([ seminar notes])
Homework for group 246:
Module 1
- HW 6 (release: 15.10.23; deadline: 22.10.23) (Seminar_6 notes)
- HW 5 (release: 08.10.24; deadline: 15.10.24) (Seminar_5 notes)
- HW 4 (release: 01.10.24; deadline: 08.10.24) (Seminar_4 notes)
- HW 3 (release: 24.09.24; deadline: 01.10.24) (Seminar_3 notes)
- HW 2 (release: 17.09.24; deadline: 24.09.24) (Seminar_2 notes)
- HW 1 (release: 10.09.24; deadline: 17.09.24) (Seminar_1 notes)
Exams
Results
| 241 | 242 | 243 | 244 | 245 |
|---|
DSBA 2022/2023 |
|
|---|---|
| First year | |
