imported>Dima Trushin: /* Results */

2020-06-14T19:12:01Z

Results

Новая страница

= Schedule =

* [https://zoom.us/j/98706972969 Lecture] Monday 12:10–13:30

* [https://zoom.us/j/92828388875 Seminar 191] Monday 13:40–15:00

= Teachers and assistants =

{| class="wikitable" style="text-align:center"
|-
! Группа !! 191 !! 192 !! 193
|-
|| Lecturer ||colspan="3"| [https://www.hse.ru/en/org/persons/209508745 Dima Trushin]
|-
|| Teacher || [https://www.hse.ru/en/org/persons/209508745 Dima Trushin] || [https://www.hse.ru/en/org/persons/63679989 Sergey Gayfullin] || [https://www.hse.ru/en/staff/kaleeva Galina Kaleeva]
|-
|| Assistant || [mailto:aogolubitskaya@edu.hse.ru Arina] || [mailto:yupey@edu.hse.ru Yunying] || [mailto:tapetrov@edu.hse.ru Timur]
|}

= Consultations schedule =

{| class="wikitable"
|-
! !! Teacher/Assistant !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday
|-
| <center>1</center> || Dima Trushin || || || [https://us04web.zoom.us/j/5515049969 zoom since 16:00] || ||
|-
| <center>2</center> || Sergey Gayfullin || || [https://us02web.zoom.us/j/89143777345 16:30–18:00] || || ||
|-
| <center>3</center> || Galina Kaleeva || [https://us04web.zoom.us/j/75909851166?pwd=MzQ2MmpQZTFiaUs5cEd0c1NxekpSdz09 16:30–18:00] пароль: algebra|| || || || [https://us04web.zoom.us/j/75909851166?pwd=MzQ2MmpQZTFiaUs5cEd0c1NxekpSdz09 16:40–18:00] (June, 5th) пароль: algebra
|-
| <center>4</center> || Arina || || || || ||
|-
| <center>5</center> || Yunying || || || || ||
|-
| <center>6</center> || 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 4''' (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.

'''Lecture 5''' (07.05.2020). 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 6''' (12.05.2020). 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 7''' (18.05.2020). 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 8''' (25.05.2020). 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.

'''Lecture 9''' (01.06.2020). Stabilization of reduction. 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 via email before the beginning of the next seminar.

'''Seminar 1''' (06.04.2020). [https://yadi.sk/i/nkiKmPG5Aie7TA '''Problems''']

'''Seminar 2''' (13.04.2020). [https://yadi.sk/i/mcXh-_s6xpcCMA '''Problems''']

'''Seminar 3''' (20.04.2020). [https://yadi.sk/i/UkSrO9JhNa14sg '''Problems''']

'''Seminar 4''' (27.04.2020). [https://yadi.sk/i/A9JjBjJfsHL9_Q '''Problems''']

'''Seminar 5''' (07.05.2020). [https://yadi.sk/i/xWV0DbYfPG9qiQ '''Problems''']

'''Seminar 6''' (12.05.2020). [https://yadi.sk/i/jdg96r9XChrFkA '''Problems''']

'''Seminar 7''' (18.05.2020). [https://yadi.sk/i/JzwF9Rd5Ycn6dA '''Problems''']

'''Seminar 8''' (25.05.2020). [https://yadi.sk/i/qWymXdWqGB9KzA '''Problems''']

'''Seminar 9''' (01.06.2020). [https://yadi.sk/i/H0QLPDojzbQVXQ '''Problems''']

= Exam =

* [https://yadi.sk/i/oY_3ADtOrqxWww The lists of definitions and statements]

* [https://yadi.sk/i/Zb7RvwpECu8-3A The list of statements to prove]

= Results =

* Homework

{| class="wikitable" style="text-align:center"
|-
! [https://docs.google.com/spreadsheets/d/1HUJ-WoTtWmpYSNq2okUr99AKX2MmVlC3pnctCMsSEEI/edit#gid=0 191] !! [https://docs.google.com/spreadsheets/d/1HUJ-WoTtWmpYSNq2okUr99AKX2MmVlC3pnctCMsSEEI/edit#gid=1992163396 192] !! [https://docs.google.com/spreadsheets/d/1HUJ-WoTtWmpYSNq2okUr99AKX2MmVlC3pnctCMsSEEI/edit#gid=83275050 193]
|}

* Summary Statement

{| class="wikitable" style="text-align:center"
|-
! [https://docs.google.com/spreadsheets/d/1ULykRTOgC79vjbaE7hXnVsmEzO2fnWcVwCPrff-IICU/edit#gid=0 191] !! [https://docs.google.com/spreadsheets/d/1ULykRTOgC79vjbaE7hXnVsmEzO2fnWcVwCPrff-IICU/edit#gid=17634846 192] !! [https://docs.google.com/spreadsheets/d/1ULykRTOgC79vjbaE7hXnVsmEzO2fnWcVwCPrff-IICU/edit#gid=1828997773 193]
|}

= Links =

* [https://yadi.sk/d/4WqzAFDXu0iwQw '''Lecture Notes''']

* [https://yadi.sk/d/UOTiZgeClaHozQ '''Seminars 191''']

Algebra DSBA 2019/2020 - История изменений

imported>Dima Trushin: /* Results */