Algebra DSBA 2025/2026

Teachers and assistants

Группа	251	252	253	254	255	256	257
Lecturer	Dima Trushin Telegram
Teacher	Dima Trushin	Andrew Mazhuga	Andey Zhizhin	Dmitry Gayfulin	Subin Pulari	Dmitry Gayfulin	Ananya Pal
Assistant	Viktoriya Sliva	Illarion Illarionov-Zervas	Maria Sudarikova	Vadim Andrianov	Zakhar Zinkin	Zlata Vronskaya	Ignat Kostyuchenko

Consultations schedule

	Teacher/Assistant	How to contact	When
1	Dima Trushin	telegram	Wednesday since 17:00 S812
2	Andrew Mazhuga
3	Andey Zhizhin
4	Dmitry Gayfulin
5	Subin Pulari
6	Ananya Pal

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 (06.04.2026). 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 (13.04.2026). 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 (20.04.2026). 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.

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 Problems

Seminar 2 Problems

Seminar 3 Problems

Seminar 4 Problems

Seminar 5 Problems

Seminar 6 Problems

Seminar 7 Problems

Seminar 8 Problems

Seminar 9 Problems

Results

• Homework

251	252	253	254	255	256	257

• Test

[ 251]	[ 252]	[ 253]	[ 254]	[ 255]	[ 256]	[ 257]

• Summary Statement

[ 251]	[ 252]	[ 253]	[ 254]	[ 255]	[ 256]	[ 257]

Links

• Telegram group of the course.

• Lecture Notes

• Syllabus