Algebra DSBA 2018/2019

Teachers and assistants

Группа	181	182	183
Lecturer	Ivan Arzhantsev
Teacher	Ivan Arzhantsev	Roman Avdeev	Nikita Medved mednik at mccme.ru
Assistant	Danila Kutenin kutdanila@yandex.ru	Maksim Siplivyj maxsev1999@yandex.ru	Ildus Sadrtdinov irsadrtdinov@edu.hse.ru

Consultations schedule

	Teacher/Assistant	Monday	Tuesday	Wednesday	Thursday	Friday
1	Ivan Arzhantsev		17:00–18:30, room 603
2	Roman Avdeev	15:40–17:40, room 623			15:40–16:30, 18:10–19:00, room 623
3	Nikita Medved	16:40–18:00, room 623				18:10 (if you write me beforehand)
4	Danila Kutenin			12:00-13:00, room (each time telegram announcement)
5	Maksim Siplivyj	16:40–18:00
6	Ildus Sadrtdinov	16:40–18:00

Grading system

The cumulative grade is computed as follows:

C = 0,6 * H + 0,4 * T,

where H is the grade for the home assignments and T is the written test grade.

The final course grade is given by

F = 0,5 * C + 0,5 * E

where E is the final exam grade.

Grades in all formulas are rounded according to the standard rule.

Lecture abstracts

Lecture 1 (2.04.2019). Semigroups and groups: definitions and examples. Permutation groups and matrix groups. Subgroups. The order of an element and cyclic subgroups.

Lecture 2 (9.04.2019). Lagrange's theorem and its corollaries. Normal subgroups. Homomorphisms and isomorphisms. A classification of cyclic groups. Factor groups and the Homomorphism theorem.

Problem sheets

The Nth problem sheet contains the Nth homework.

Problems to lecture 1

Problems to lecture 2

Exam

The exam will be oral.

Results

181	182	183

Reading list

Required

• Э.Б.Винберг. Курс алгебры. М.: МЦНМО, 2014 (English transl.: Ernest Vinberg. A Course in Algebra. Graduate Studies in Math. 56, Amer. Math. Soc., 2003)
• Сборник задач по алгебре под редакцией А.И.Кострикина. Новое издание. М.: МЦНМО, 2015 (English transl.: Exercises in Algebra. Edited by A. Kostrikin, CRC Press, 1996)

Optional

Serge Lang. Algebra. Revised Third Edition. Graduate Texts in Math. 211, Springer, 2002