Algebra DSBA 2020/2021 — различия между версиями

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(Lecture abstracts)
(Problem sheets)
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'''Seminar 4''' (29.04.2021). [https://disk.yandex.ru/i/ObhKt0v6Kj-d4A Problems]
 
'''Seminar 4''' (29.04.2021). [https://disk.yandex.ru/i/ObhKt0v6Kj-d4A Problems]
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'''Seminar 5''' (13.05.2021). [https://disk.yandex.ru/i/2cHws9wRUMkNoA Problems]
  
 
= Exam =
 
= Exam =

Версия 13:09, 14 мая 2021

Schedule

Teachers and assistants

Группа 201 202 203 204
Lecturer Dima Trushin Telegram
Teacher Dima Trushin Andrew Mazhuga Nikita Medved Galina Kaleeva
Assistant Masha Marchenko Daniil Kopytov Ваня Пешехонов Dasha Ivanova

Consultations schedule

Teacher/Assistant Monday Tuesday Wednesday Thursday Friday
1
Dima Trushin zoom since 17:00
2
Andrew Mazhuga
3
Nikita Medved write me in telegram https://t.me/medvednikita

and we will schedule a meeting

4
Galina Kaleeva 16.20-17.40.

Offline: S 913

Online: Zoom

Passcode: algebra

In case I'm offline text me via telegram

5
Masha Marchenko
6
Daniil Kopytov
7
Vanya Peshekhonov zoom c 18:20
8
Dasha Ivanova

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 (08.04.2021). 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 (15.04.2021). Subgroups of the group of integers. Left and right cosets, examples. Normal subgroups. The Lagrange theorem.

Lecture 3 (22.04.2021). Five corollaries of the Lagrange theorem. 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 4 (29.04.2021). Second 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.

Lecture 5 (13.05.2021). Rings, commutative rings, fields, subrings. Invertible elements, zero divisors, nilpotent and idempotent elements. Ideals. Description of ideals in Z and Z_n. Homomorphisms and isomorphisms of rings. The Chinese remainder theorem for rings. The kernel and the image of a homomorphism, their properties.

Problem sheets

The solutions should be sent to your teaching assistant before the beginning of the next seminar.

Seminar 1 (08.04.2021). Problems

Seminar 2 (15.04.2021). Problems

Seminar 3 (22.04.2021). Problems

Seminar 4 (29.04.2021). Problems

Seminar 5 (13.05.2021). Problems

Exam

Results

  • Homework
201 202 203 204

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