WikiAdmin: Auto-sync from wiki.cs.hse.ru rev 96890 at 2026-06-19T18:12:42Z

2026-06-19T18:19:07Z

Auto-sync from wiki.cs.hse.ru rev 96890 at 2026-06-19T18:12:42Z

← Предыдущая версия		Версия от 21:19, 19 июня 2026
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	* Test		* Written Test, Exam, Final Grade

	{\| class="wikitable" style="text-align:center"		{\| class="wikitable" style="text-align:center"
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	! [ 251] !! [ 252] !! [ 253] !! [ 254] !! [ 255] !! [ 256] !! [ ~~257]~~		! [https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=0#gid=0 251] !! [https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=414893016#gid=414893016 252] !! [https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=238120772#gid=238120772 253] !! [https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=2026788883#gid=2026788883 254] !! [https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=15906055#gid=15906055 255] !! [https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=140868039#gid=140868039 256] !! [https://docs.google.com/spreadsheets/d/1VdyBS-2at8ULg_Zu9JTWDDh1drQgTDm2oMQEC2hcMsQ/edit?gid=1523429419#gid=1523429419 257]
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	* Summary Statement

	~~{\| class~~=~~"wikitable" style~~=~~"text-align:center"~~
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	~~! [ 251] !! [ 252] !! [ 253] !! [ 254] !! [ 255] !! [ 256] !! [~~ 257]
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WikiAdmin: Auto-sync from wiki.cs.hse.ru rev 96782 at 2026-06-06T15:54:02Z

2026-06-06T15:59:28Z

Auto-sync from wiki.cs.hse.ru rev 96782 at 2026-06-06T15:54:02Z

← Предыдущая версия		Версия от 18:59, 6 июня 2026
Строка 44:		Строка 44:

	= Lecture abstracts =		= Lecture abstracts =
			'''Lecture 10''' (15.06.2026). The Diamond Lemma. A proof of the Buchberger criterion.

			'''Lecture 9''' (06.06.2026). 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.

	'''Lecture 8''' (01.06.2026). 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 8''' (01.06.2026). 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.

imported>Mazhuga.A.M.: /* Teachers and assistants */

2026-05-31T13:30:21Z

Teachers and assistants

Новая страница

= Teachers and assistants =

{| class="wikitable" style="text-align:center"
|-
! Группа !! 251 !! 252 !! 253 !! 254 !! 255 !! 256 !! 257
|-
|| Lecturer ||colspan="7"| [https://www.hse.ru/org/persons/209508745 Дима Трушин], [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga]
|-
|| Teacher || [https://www.hse.ru/org/persons/209508745 Дима Трушин], [https://www.hse.ru/org/persons/225516943/ Ivan Beldiev] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/org/persons/305077523/ Andey Zhizhin] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1083814039/ Subin Pulari] || [https://www.hse.ru/org/persons/697229842 Dmitry Gayfulin] || [https://www.hse.ru/en/org/persons/1087367159/ Ananya Pal]
|-
|| Assistant || [https://t.me/svvika06 Viktoriya Sliva] || [https://t.me/zilervarls Illarion Illarionov-Zervas] || [https://t.me/marshmel_m Maria Sudarikova] || [https://t.me/yachatoyer Vadim Andrianov] || [https://t.me/Avgustine_iw Zakhar Zinkin] || [https://t.me/zlata_vr Zlata Vronskaya] || [https://t.me/Ignkos Ignat Kostyuchenko]
|}

= Consultations schedule =

{| class="wikitable"
|-
! !! Teacher/Assistant !! How to contact !! When
|-
| <center>1</center> || Ivan Beldiev || ||
|-
| <center>2</center> || Andrew Mazhuga ||
|-
| <center>3</center> || Andey Zhizhin || ||
|-
| <center>4</center> || Dmitry Gayfulin || ||
|-
| <center>5</center> || Subin Pulari || ||
|-
| <center>6</center> || Ananya Pal || ||
|}

= 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 8''' (01.06.2026). 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 7''' (25.05.2026). 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 6''' (18.05.2026). 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 5''' (11.05.2026). 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 4''' (27.04.2026). Cryptography. Exponentiation by squaring (fast raising to a power algorithm). The discrete logarithm problem. Diffie-Hellman key exchange.

'''Lecture 3''' (20.04.2026). 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 2''' (13.04.2026). 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 1''' (06.04.2026). 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.

= 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 1''' [https://disk.yandex.ru/d/ikcTBq5kJDP1iw Problems]

'''Seminar 2''' [https://disk.yandex.ru/d/0da7rDLB2b2O_w Problems]

'''Seminar 3''' [https://disk.yandex.ru/i/lsR5vMFIwP9F_Q Problems]

'''Seminar 4''' [https://disk.yandex.ru/i/cFA__aXT662WEA Problems]

'''Seminar 5''' [https://disk.yandex.ru/i/lzYLUAMfHDBI2Q Problems]

'''Seminar 6''' [https://disk.yandex.ru/i/nUvIl-eGV6-clg Problems]

'''Seminar 7''' [https://disk.yandex.ru/i/jZFQDVf9apa-1Q Problems]

'''Seminar 8''' [https://disk.yandex.ru/i/qPfdD9lx4L4k1A Problems]

'''Seminar 9''' [https://disk.yandex.ru/i/BBa2BeQBppa8hw Problems]

= Test =

= Exam =

= Results =

* Homework

{| class="wikitable" style="text-align:center"
|-
! [https://docs.google.com/spreadsheets/d/1hK7_YGpjOuCuR1EUNRoX8MA2bvW4RBsvSOxWI_EZ0Dc/edit?gid=640844189#gid=640844189 251] !! [https://docs.google.com/spreadsheets/d/1hK7_YGpjOuCuR1EUNRoX8MA2bvW4RBsvSOxWI_EZ0Dc/edit?gid=1741402532#gid=1741402532 252] !! [https://docs.google.com/spreadsheets/d/1hK7_YGpjOuCuR1EUNRoX8MA2bvW4RBsvSOxWI_EZ0Dc/edit?gid=768569277#gid=768569277 253] !! [https://docs.google.com/spreadsheets/d/1hK7_YGpjOuCuR1EUNRoX8MA2bvW4RBsvSOxWI_EZ0Dc/edit?gid=1908497780#gid=1908497780 254] !! [https://docs.google.com/spreadsheets/d/1hK7_YGpjOuCuR1EUNRoX8MA2bvW4RBsvSOxWI_EZ0Dc/edit?gid=1202082300#gid=1202082300 255] !! [https://docs.google.com/spreadsheets/d/1hK7_YGpjOuCuR1EUNRoX8MA2bvW4RBsvSOxWI_EZ0Dc/edit?gid=1775720605#gid=1775720605 256] !! [https://docs.google.com/spreadsheets/d/1hK7_YGpjOuCuR1EUNRoX8MA2bvW4RBsvSOxWI_EZ0Dc/edit?gid=1415205961#gid=1415205961 257]
|}

* Test

{| class="wikitable" style="text-align:center"
|-
! [ 251] !! [ 252] !! [ 253] !! [ 254] !! [ 255] !! [ 256] !! [ 257]
|}

* Summary Statement

{| class="wikitable" style="text-align:center"
|-
! [ 251] !! [ 252] !! [ 253] !! [ 254] !! [ 255] !! [ 256] !! [ 257]
|}

= Links =

* Telegram [https://t.me/+FfauFK5xoc02OTVi group] of the course.

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

* [https://www.hse.ru/ba/data/courses/1071149750.html Syllabus]

Algebra DSBA 2025/2026 - История изменений

WikiAdmin: Auto-sync from wiki.cs.hse.ru rev 96890 at 2026-06-19T18:12:42Z

WikiAdmin: Auto-sync from wiki.cs.hse.ru rev 96782 at 2026-06-06T15:54:02Z

imported>Mazhuga.A.M.: /* Teachers and assistants */