Версия 21:37, 7 мая 2020

Schedule

• Lecture Monday 12:10–13:30

• Seminar 191 Monday 13:40–15:00

Teachers and assistants

Consultations schedule

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 = 0,3 * H + 0,2 T + 0,5 E

where 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 (06.04.2020). 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 (13.04.2020). Subgroups of the group of integers. Left and right cosets, examples. Normal subgroups. The Lagrange theorem and its 5 corollaries.

Lecture 3 (20.04.2020). 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 (27.04.2020). 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.

Problem sheets

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

Seminar 1 (06.04.2020). Problems

Seminar 2 (13.04.2020). Problems

Seminar 3 (20.04.2020). Problems

Seminar 4 (27.04.2020). Problems

Seminar 5 (07.05.2020). Problems

Results

Links

• Lecture Notes

• Seminars 191