Algebra DSBA 2019/2020 — различия между версиями
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'''Seminar 4''' (27.04.2020). [https://yadi.sk/i/A9JjBjJfsHL9_Q '''Problems'''] | '''Seminar 4''' (27.04.2020). [https://yadi.sk/i/A9JjBjJfsHL9_Q '''Problems'''] | ||
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+ | '''Seminar 5''' (07.05.2020). [https://yadi.sk/i/xWV0DbYfPG9qiQ '''Problems'''] | ||
= Results = | = Results = |
Версия 21:37, 7 мая 2020
Содержание
Schedule
- Lecture Monday 12:10–13:30
- Seminar 191 Monday 13:40–15:00
Teachers and assistants
Группа | 191 | 192 | 193 |
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Lecturer | Dima Trushin | ||
Teacher | Dima Trushin | Sergey Gayfullin | Galina Kaleeva |
Assistant | Arina | Yunying | Timur |
Consultations schedule
Teacher/Assistant | Monday | Tuesday | Wednesday | Thursday | Friday | |
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Dima Trushin | zoom since 16:00 | ||||
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Sergey Gayfullin | 16:30–18:00 | ||||
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Galina Kaleeva | 16:30–18:00 | ||||
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Arina | |||||
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Yunying | |||||
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Timur |
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
191 | 192 | 193 |
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