Algebra DSBA 2025/2026: различия между версиями
| (не показано 16 промежуточных версий 4 участников) | |||
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! Группа !! 251 !! 252 !! 253 !! 254 !! 255 !! 256 !! 257 | ! Группа !! 251 !! 252 !! 253 !! 254 !! 255 !! 256 !! 257 | ||
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|| Lecturer ||colspan="7"| [https://www.hse.ru | || Lecturer ||colspan="7"| [https://www.hse.ru/org/persons/209508745 Дима Трушин], [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] | ||
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|| Teacher || [https://www.hse.ru/ | || 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] | ||
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|| 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] | || 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] | ||
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! !! Teacher/Assistant !! How to contact !! When | ! !! Teacher/Assistant !! How to contact !! When | ||
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| <center>1</center> || | | <center>1</center> || Ivan Beldiev || || | ||
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| <center>2</center> || Andrew Mazhuga | | <center>2</center> || Andrew Mazhuga || | ||
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| <center>3</center> || Andey Zhizhin || || | | <center>3</center> || Andey Zhizhin || || | ||
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= 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 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. | '''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. | ||
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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. | 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/i/ | '''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 = | = Test = | ||
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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] | ||
|} | |} | ||
= Links = | = Links = | ||
* Telegram [ | * Telegram [https://t.me/+FfauFK5xoc02OTVi group] of the course. | ||
* [https://github.com/DimaTrushin/Algebra-DSBA/ Lecture Notes] | * [https://github.com/DimaTrushin/Algebra-DSBA/ Lecture Notes] | ||
* [https://www.hse.ru/ba/data/courses/1071149750.html Syllabus] | * [https://www.hse.ru/ba/data/courses/1071149750.html Syllabus] | ||
Текущая версия от 18:12, 19 июня 2026
Teachers and assistants
| Группа | 251 | 252 | 253 | 254 | 255 | 256 | 257 |
|---|---|---|---|---|---|---|---|
| Lecturer | Дима Трушин, Andrew Mazhuga | ||||||
| Teacher | Дима Трушин, Ivan Beldiev | Andrew Mazhuga | Andey Zhizhin | Dmitry Gayfulin | Subin Pulari | Dmitry Gayfulin | Ananya Pal |
| Assistant | Viktoriya Sliva | Illarion Illarionov-Zervas | Maria Sudarikova | Vadim Andrianov | Zakhar Zinkin | Zlata Vronskaya | Ignat Kostyuchenko |
Consultations schedule
| Teacher/Assistant | How to contact | When | |
|---|---|---|---|
| Ivan Beldiev | |||
| Andrew Mazhuga | |||
| Andey Zhizhin | |||
| Dmitry Gayfulin | |||
| Subin Pulari | |||
| 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 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 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 0.7t 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 Problems
Seminar 2 Problems
Seminar 3 Problems
Seminar 4 Problems
Seminar 5 Problems
Seminar 6 Problems
Seminar 7 Problems
Seminar 8 Problems
Seminar 9 Problems
Test
Exam
Results
- Homework
| 251 | 252 | 253 | 254 | 255 | 256 | 257 |
|---|
- Written Test, Exam, Final Grade
| 251 | 252 | 253 | 254 | 255 | 256 | 257 |
|---|
Links
- Telegram group of the course.