DSBA Algebra 2023 2024

Teachers and assistants

Группа	231	232	233	234	235
Lecturer	Dima Trushin Telegram
Teacher	Kirill Shakhmatov	Galina Kaleeva	Dima Trushin	Andrew Mazhuga	Dima Trushin
Assistant	Platon Chevychelov	Alexander Ukhanov	Roman Bokhyan	Kirill Belyakov	Rina Zyubanova

Consultations schedule

	Teacher/Assistant	How to contact	When
1	Dima Trushin	telegram	Thursday since 17:00 S812
2	Andrew Mazhuga	telegram
3	Kirill Shakhmatov
4	Galina Kaleeva	telegram, check the course chat	Office hours: Tuesday, 18.00, zoom (the link is in the course chat)
5	Alexander Ukhanov	telegram
6	Platon Chevychelov	telegram
7	Roman Bokhyan	telegram
8	Rina Zyubanova	telegram
9	Kirill Belyakov	telegram

Grading system

The final grade is computed as follows

F = 0,3 * H + 0,3 T + 0,4 E

where H is the grade for the home assignments, T is the written test grade, and E is the final exam grade.

Only the final grade is rounded in the final formula according to the standard rule.

Lecture abstracts

Lecture 1 (04.04.2024). Binary operations. Associativity, neutral element, inverse element, commutativity. Definition of a group. Additive and multiplicative notations. Subgroups and cyclic subgroups. The order of an element of a group.

Lecture 2 (11.04.2024). Classification of cyclic groups. The subgroups of the group of integers. The subgroups of the group Z_n. Left and right cosets, examples. Normal subgroups. The Lagrange theorem and its corollaries.

Lecture 3 (18.04.2024). Homomorphisms and Isomorphisms of groups. Image and kernel of a homomorphism. Normal subgroups. Direct product of groups. Finite Abelian Groups. The Chinese Remainder Theorem. Structure of a finite abelian group.

Lecture 3 (25.04.2024). Multiplicative version of the Chinese Remainder Theorem. Structure of Z_{p^n}^*. Cryptography. Exponentiation by squaring (fast raising to a power algorithm). The discrete logarithm problem. Diffie-Hellman key exchange.

Problem sheets

The solutions should be sent to your teaching assistant before the beginning of the next seminar. If you send the solution after the deadline your grade will be multiplied by 0.7^t where t -- is the time passed after the deadline in days (not rounded). So, it is not an issue to send your work 1 or 2 hours after the deadline.

Seminar 1 (04.04.2024). Problems Since I am very late with publishing the homework there is a special deadline in groups 232, 233, 235. They should send their solutions till 23:00 April, 14 on Sunday.

Seminar 2 (12.04.2024). Problems Deadline for 233 is April, 21, 23:00. Deadline for 235 is April, 22, 23:00.

Seminar 3 (18.04.2024). Problems

Seminar 4 (25.04.2024). Problems Deadline for 232: May, 10th, 9:30.

Results

• Homework

231	222	223	234	235

• Test

• Summary Statement

Links

• Telegram channel of the course.

• Lecture Notes