LAaG DSBA 2020/2021
Teachers and Assistants
|Teacher||Andrey Mazhuga||Nikita Medved||Galina Kaleeva|
|Schedule|| Wednesday, 13.00, D501
Zoom (for distance learners)
|Consultations|| Wed, ??:?? -- ??:??, room S808
One must notify me beforehand
|TBD|| Monday, 14:40-17:00, S913
To join via Zoom text me
|Assistant|| Астанина Ксения
| Васильев Борис
| Княжевский Владимир
| Косовская Анна |
| Астанина Ксения |
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.
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 0.6, 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.
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 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.
- 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.
- [ S 1] (09.09.2020)
Groups 202 and 203:
- [ S 1] (XX.09.2020)
- [ S 1] (ХХ.09.2020)
The obligatory homework for group 201:
The obligatory homework for groups 202 and 203:
- An invite to Google Classroom for group 203: 3fyhfue (you can also use this link)
- Google Form to submit your work for group 202: link
- HW 2 (release: 18.09.2020; deadline: 25.09.2020, 9:00 a.m.)
- HW 1 (release: 11.09.2020; deadline: 18.09.2020, 9:00 a.m.)
The obligatory homework for group 204:
- HW 1 (release: 09.09.2020; deadline: 16.09.2020, 9:00 a. m.; send here: https://clck.ru/Qkq26) Any computational tools are not allowed.
- HW 2 (release: 17.09.2020; deadline: 23.09.2020, 9:00 a. m.)