Просмотр исходного текста страницы DSBA Algebra 2023 2024

= Teachers and assistants =


{| class="wikitable" style="text-align:center"
|-
! Группа !! 231 !! 232 !! 233 !! 234 !! 235
|-
|| Lecturer ||colspan="5"| [https://www.hse.ru/en/org/persons/209508745 Dima Trushin] [https://t.me/DimaTrushin Telegram]
|- 
|| 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]
|-
|| 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]

|}

= Consultations schedule =

{| class="wikitable"
|-
! !! Teacher/Assistant !! How to contact !! When
|-
| <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>3</center> || Kirill Shakhmatov ||  || 
|-
| <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>6</center> || Platon Chevychelov || [https://t.me/PJIuToN telegram] || 
|-
| <center>7</center> || Roman Bokhyan || [https://t.me/warning172 telegram]  ||
|-
| <center>8</center> || Rina Zyubanova || [https://t.me/crazy_rinchik telegram] ||
|-
| <center>9</center> || Kirill Belyakov || [https://t.me/kifbell 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&nbsp;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&nbsp;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&nbsp;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&nbsp;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&nbsp;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.

'''Lecture&nbsp;6''' (23.05.2024). Polynomials in one variable. Euclidean algorithm, greatest common divisor, ideals of F[x]. Irreducible polynomials and unique factorization of polynomials in F[x]. Ring of remainders, the Chinese Remainder Theorem for polynomials.

'''Lecture&nbsp;7''' (30.05.2024). Characteristic of a field. Field extensions, an extension by a root. Finite fields: number of elements in a finite field, multiplicative group of a finite field is cyclic, classification of finite fields (without proof). How to produce finite fields. Galois random generator. Stream cipher.

'''Lecture&nbsp;8''' (06.06.2024). Polynomials in several variables. Lexicographical orders, stabilization of strictly descending chains of monomials. An elementary reduction, a reduction with respect to a set of polynomials, remainders, Groebner basis. Stabilization of reduction.

'''Lecture&nbsp;9''' (13.06.2024).  S-polynomials and the Buchberger criterion. Ideals in a polynomial ring, the Buchberger algorithm to produce a Groebner basis of an ideal. A ring of remainders. Membership problem and variable elimination.

= 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). So, it is not an issue to send your work 1 or 2 hours after the deadline.

'''Seminar&nbsp;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&nbsp;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&nbsp;3''' (18.04.2024). [https://disk.yandex.ru/i/WZS339KMDuGWYA Problems]

'''Seminar&nbsp;4''' (25.04.2024). [https://disk.yandex.ru/i/J_1izS_MxBUyTQ Problems] Deadline for 232: May, 10th, 9:30.

'''Seminar&nbsp;5''' (08.05.2024). [https://disk.yandex.ru/i/p9OEv9IyTNky6g Problems] Deadline for 233: May, 15th, 23:00; deadline for 232: May, 18th, 9:30.

'''Seminar&nbsp;6''' (25.05.2024). [https://disk.yandex.ru/d/UA-ps7EWTg4MeQ Problems] Deadline for 233 and 235: June, 1th, 23:00;

'''Seminar&nbsp;7''' (02.06.2024). [https://disk.yandex.ru/i/R8TO_891wSIcoA Problems] Deadline for 233 and 235: June, 9th, 23:00;

'''Seminar&nbsp;8''' (06.06.2024). [https://disk.yandex.ru/i/ubSKTLy0FiqXvA Problems]

= Test =

= Exam =

= Results =

* Homework

{| class="wikitable" style="text-align:center"
|-
! [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

* Summary Statement

= Links =

* Telegram [https://t.me/+0ngThuZkH4xkZmNi channel] of the course.

* [https://github.com/DimaTrushin/Algebra-DSBA/tree/2024 Lecture Notes]