DSBA Algebra 2023 2024 — различия между версиями
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| (не показано 17 промежуточных версии 2 участников) | |||
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|| Teacher || [https://www.hse.ru/en/org/persons/392058502 Kirill Shakhmatov] || [https://www.hse.ru/en/staff/kaleeva Galina Kaleeva] || [https://www.hse.ru/en/org/persons/209508745 Dima Trushin] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/en/org/persons/209508745 Dima Trushin] | || Teacher || [https://www.hse.ru/en/org/persons/392058502 Kirill Shakhmatov] || [https://www.hse.ru/en/staff/kaleeva Galina Kaleeva] || [https://www.hse.ru/en/org/persons/209508745 Dima Trushin] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/en/org/persons/209508745 Dima Trushin] | ||
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| − | || Assistant || [] || [] || [] || [] || [] | + | || Assistant || [https://t.me/PJIuToN Platon Chevychelov] || [https://t.me/Spnya Alexander Ukhanov] || [https://t.me/warning172 Roman Bokhyan] || [https://t.me/kifbell Kirill Belyakov] || [https://t.me/crazy_rinchik Rina Zyubanova] |
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! !! Teacher/Assistant !! How to contact !! When | ! !! Teacher/Assistant !! How to contact !! When | ||
|- | |- | ||
| − | | <center>1</center> || Dima Trushin || [https://t.me/DimaTrushin telegram] || | + | | <center>1</center> || Dima Trushin || [https://t.me/DimaTrushin telegram] || Thursday since 17:00 S812 |
|- | |- | ||
| <center>2</center> || Andrew Mazhuga || [https://www.youtube.com/watch?v=dQw4w9WgXcQ&ab_channel=RickAstley telegram] || | | <center>2</center> || Andrew Mazhuga || [https://www.youtube.com/watch?v=dQw4w9WgXcQ&ab_channel=RickAstley telegram] || | ||
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| <center>3</center> || Kirill Shakhmatov || || | | <center>3</center> || Kirill Shakhmatov || || | ||
|- | |- | ||
| − | | <center>4</center> || Galina Kaleeva || | + | | <center>4</center> || Galina Kaleeva || telegram, check the course chat || Office hours: Tuesday, 18.00, zoom (the link is in the course chat) |
|- | |- | ||
| <center>5</center> || Alexander Ukhanov || [https://t.me/Spnya telegram] || | | <center>5</center> || Alexander Ukhanov || [https://t.me/Spnya telegram] || | ||
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'''Lecture 1''' (04.04.2024). 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 1''' (04.04.2024). 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''' (11.04.2024). 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''' (18.04.2024). 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''' (25.04.2024). Multiplicative 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''' (27.04.2024). 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 = | = 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<sup>t</sup> where t -- is the time passed after the deadline in days (not rounded). | + | 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<sup>t</sup> 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''' (04.04.2024). [https://disk.yandex.ru/i/jsNTdPxeEdDxWQ Problems] Since I am very late with publishing the homework there is a special deadline in groups 232, 233, 235. They should send their solutions till 23:00 April, 14 on Sunday. | ||
| + | |||
| + | '''Seminar 2''' (12.04.2024). [https://disk.yandex.ru/i/8t4eJ5n1wxMO6A Problems] Deadline for 233 is April, 21, 23:00. Deadline for 235 is April, 22, 23:00. | ||
| + | |||
| + | '''Seminar 3''' (18.04.2024). [https://disk.yandex.ru/i/WZS339KMDuGWYA Problems] | ||
| − | '''Seminar | + | '''Seminar 4''' (25.04.2024). [https://disk.yandex.ru/i/J_1izS_MxBUyTQ Problems] Deadline for 232: May, 10th, 9:30. |
= Test = | = Test = | ||
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{| class="wikitable" style="text-align:center" | {| class="wikitable" style="text-align:center" | ||
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| − | ! [231] !! [222] !! [223] !! [234] !! [235] | + | ! [https://docs.google.com/spreadsheets/d/1oeZyZZyrdHBCqMEg6AOZyd9a9MdeaFJCYulq_rybw0Y/edit#gid=640844189 231] !! [https://docs.google.com/spreadsheets/d/1oeZyZZyrdHBCqMEg6AOZyd9a9MdeaFJCYulq_rybw0Y/edit#gid=1612040544 222] !! [https://docs.google.com/spreadsheets/d/1oeZyZZyrdHBCqMEg6AOZyd9a9MdeaFJCYulq_rybw0Y/edit#gid=1538156963 223] !! [https://docs.google.com/spreadsheets/d/1oeZyZZyrdHBCqMEg6AOZyd9a9MdeaFJCYulq_rybw0Y/edit#gid=1067620548 234] !! [https://docs.google.com/spreadsheets/d/1oeZyZZyrdHBCqMEg6AOZyd9a9MdeaFJCYulq_rybw0Y/edit#gid=572193184 235] |
|} | |} | ||
* Test | * Test | ||
| − | |||
* Summary Statement | * Summary Statement | ||
| − | |||
= Links = | = Links = | ||
| − | * Telegram [https://t.me/+0ngThuZkH4xkZmNi | + | * Telegram [https://t.me/+0ngThuZkH4xkZmNi channel] of the course. |
* [https://github.com/DimaTrushin/Algebra-DSBA/tree/2024 Lecture Notes] | * [https://github.com/DimaTrushin/Algebra-DSBA/tree/2024 Lecture Notes] | ||
Версия 19:57, 27 апреля 2024
Содержание
Teachers and assistants
| Группа | 231 | 232 | 233 | 234 | 235 |
|---|---|---|---|---|---|
| Lecturer | Dima Trushin Telegram | ||||
| Teacher | Kirill Shakhmatov | Galina Kaleeva | Dima Trushin | Andrew Mazhuga | Dima Trushin |
| Assistant | Platon Chevychelov | Alexander Ukhanov | Roman Bokhyan | Kirill Belyakov | Rina Zyubanova |
Consultations schedule
| Teacher/Assistant | How to contact | When | |
|---|---|---|---|
| |
Dima Trushin | telegram | Thursday since 17:00 S812 |
| |
Andrew Mazhuga | telegram | |
| |
Kirill Shakhmatov | ||
| |
Galina Kaleeva | telegram, check the course chat | Office hours: Tuesday, 18.00, zoom (the link is in the course chat) |
| |
Alexander Ukhanov | telegram | |
| |
Platon Chevychelov | telegram | |
| |
Roman Bokhyan | telegram | |
| |
Rina Zyubanova | telegram | |
| |
Kirill Belyakov | telegram |
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 (04.04.2024). 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 (11.04.2024). 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 (18.04.2024). 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 (25.04.2024). Multiplicative 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 (27.04.2024). 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. If you send the solution after the deadline your grade will be multiplied by 0.7t 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 (04.04.2024). Problems Since I am very late with publishing the homework there is a special deadline in groups 232, 233, 235. They should send their solutions till 23:00 April, 14 on Sunday.
Seminar 2 (12.04.2024). Problems Deadline for 233 is April, 21, 23:00. Deadline for 235 is April, 22, 23:00.
Seminar 3 (18.04.2024). Problems
Seminar 4 (25.04.2024). Problems Deadline for 232: May, 10th, 9:30.
Test
Exam
Results
- Homework
| 231 | 222 | 223 | 234 | 235 |
|---|
- Test
- Summary Statement
Links
- Telegram channel of the course.
