imported>Mednik: /* Exam */

2019-06-16T15:48:40Z

Exam

Новая страница

= Teachers and assistants =

{| class="wikitable" style="text-align:center"
|-
! Группа !! 181 !! 182 !! 183
|-
|| Lecturer ||colspan="3"| [http://www.hse.ru/staff/arjanstev Ivan Arzhantsev]
|-
|| Teacher || [http://www.hse.ru/staff/arjanstev Ivan Arzhantsev] || [http://www.hse.ru/org/persons/112929840 Roman Avdeev] || [https://www.hse.ru/org/persons/209813351 Nikita Medved]
mednik at mccme.ru
|-
|| Assistant || [https://t.me/Danlark Danila Kutenin] kutdanila at yandex.ru || [https://t.me/max_the_human Maksim Siplivyj] maxsev1999@yandex.ru || [https://t.me/isadrtdinov Ildus Sadrtdinov]
irsadrtdinov@edu.hse.ru
|}

= Consultations schedule =

{| class="wikitable"
|-
! !! Teacher/Assistant !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday
|-
| <center>1</center> || Ivan Arzhantsev || || 17:00–18:30, room 603 || || ||
|-
| <center>2</center> || Roman Avdeev || 15:40–17:40, room 623 || || || 15:40–16:30, 18:10–19:00, room 623 ||
|-
| <center>3</center> || Nikita Medved || 16:40–18:00, room 623 || || || || 18:10 (if you write me beforehand)
|-
| <center>4</center> || Danila Kutenin || || || 12:00-13:00, room (each time telegram announcement) || ||
|-
| <center>5</center> || Maksim Siplivyj || 16:40–18:00 || || || ||
|-
| <center>6</center> || Ildus Sadrtdinov || 16:40–18:00 || || || ||
|}

= 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

where E is the final exam grade.

Grades in all formulas are rounded according to the standard rule.

= Lecture abstracts =

[https://www.dropbox.com/s/ax7c0kae15r84rh/Algebra_Lecture_eng_01-1.pdf?dl=0 '''Lecture 1'''] (2.04.2019). Semigroups and groups: definitions and examples. Permutation groups and matrix groups. Subgroups. The order of an element and cyclic subgroups.

[https://www.dropbox.com/s/xjix49iifop4a28/Algebra_Lecture_eng_02-1.pdf?dl=0 '''Lecture 2'''] (9.04.2019). Lagrange's theorem and its corollaries. Normal subgroups. Homomorphisms and isomorphisms. A classification of cyclic groups. Factor groups and the Homomorphism theorem.

[https://www.dropbox.com/s/g5fvh96yw02tlmp/Algebra_Lecture_eng_03.pdf?dl=0 '''Lecture 3'''] (16.04.2019). The homomorphism theorem. The center and direct products of groups. Theorem on factorization of direct products and factorization of finite cyclic groups.

[https://www.dropbox.com/s/n620xut0se9jq7w/Algebra_Lecture_eng_04-1.pdf?dl=0 '''Lecture 4'''] (23.04.2019). Free abelian groups and their subgroups. Stacked bases. An algorithm for transforming an integer matrix to a diagonal form. Classification of finite abelian groups. The exponent of a finite abelian group.

[https://www.dropbox.com/s/aitc537s8d3iu9q/Algebra_Lecture_eng_05.pdf?dl=0 '''Lecture 5'''] (30.04.2019). Actions of a group on a set. Orbits and stabilizers. Transitive actions and free actions. Three actions of a group on itself. Conjugacy classes. Cayley's Theorem.

[https://www.dropbox.com/s/c6al6pjqlwc2khf/Algebra_Lecture_eng_06.pdf?dl=0 '''Lecture 6'''] (14.05.2019). Rings and fields. Zero divisors, invertible elements, nilpotents and idempotents. Ideals. Principal ideals. Factor rings and the Homomorphism Theorem.

[https://www.dropbox.com/s/123m2tv2xcg49kp/Algebra_Lecture_eng_07.pdf?dl=0 '''Lecture 7'''] (21.05.2019). Polynomials in several variables. Symmetric polynomials. The lexicographic order. Elementary symmetric polynomials. The main theorem on symmetric polynomials. Vieta's formulas. The discriminant.

[https://www.dropbox.com/s/cf5w1kgty44o7n5/Algebra_Lecture_eng_08.pdf?dl=0 '''Lecture 8'''] (28.05.2019). Polynomials in one variable over a field. Greatest common divisor. Irreducible polynomials. Unique factorization property. Description of ideals. Properties of factor rings.

[https://www.dropbox.com/s/uwux32beiozbfjo/Algebra_Lecture_eng_09.pdf?dl=0 '''Lecture 9'''] (04.06.2019). The characteristic of a field. Extensions of fields. Finite extensions and their degrees. Algebraic and transcendental elements. The minimal polynomial of an algebraic element.

[https://www.dropbox.com/s/a3mtcsp8s25j0nq/Algebra_Lecture_eng_10.pdf?dl=0 '''Lecture 10'''] (11.06.2019). Decomposition of a polynomial into linear factors. Finite fields. Cyclicity of the multiplicative group. Irreducible polynomials over the field $\ZZ_p$. The field with four elements.

= Problem sheets =

The Nth problem sheet contains the Nth homework.

[https://www.dropbox.com/s/93uq6ihw4t5xop5/Problems_eng_01.pdf?dl=0 '''Problems to lecture 1''']

[https://www.dropbox.com/s/fex798mxupgxyby/Problems_eng_02_1.pdf?dl=0 '''Problems to lecture 2''']

[https://www.dropbox.com/s/25u9hn96pt1ezax/Problems_eng_03.pdf?dl=0 '''Problems to lecture 3''']

[https://www.dropbox.com/s/rfuupcfxgzcttr4/Problems_eng_04.pdf?dl=0 '''Problems to lecture 4''']

[https://www.dropbox.com/s/ro0sbiwgbptguji/Problems_eng_05-1.pdf?dl=0 '''Problems to lecture 5''']

[https://www.dropbox.com/s/gvox9oq4k94o0tk/Problems_eng_06.pdf?dl=0 '''Problems to lecture 6''']

[https://www.dropbox.com/s/cft332ima9759p8/Problems_eng_07.pdf?dl=0 '''Problems to lecture 7''']

[https://www.dropbox.com/s/dvuql9acixalxm7/Problems_eng_08.pdf?dl=0 '''Problems to lecture 8''']

[https://www.dropbox.com/s/fn7apzai8bk6ufq/Problems_eng_09.pdf?dl=0 '''Problems to lecture 9''']

= Written test =
The test has been on Tuesday 11.06.2019, 16:40-19:30. You could use any printed or handwritten notes, a non-programmable calculator.

[https://www.dropbox.com/s/2fpe9hxt0h6k9vl/Control_Work_Algebra-eng.pdf?dl=0 Problems from the test]

= Exam =

The exam will be oral.

[https://www.dropbox.com/s/6tbncgwiffz5yw4/Programme.doc?dl=0 List of topics]

= Results =

{| class="wikitable" style="text-align:center"
|-
! [https://docs.google.com/spreadsheets/d/1lUYGBlpX1ep2iLw84uBX-IqSfvsOmEZ-DX2x7-Hm9lA/edit#gid=2070166471 181] !! [https://docs.google.com/spreadsheets/d/1lUYGBlpX1ep2iLw84uBX-IqSfvsOmEZ-DX2x7-Hm9lA/edit#gid=564758468 182] !! [https://docs.google.com/spreadsheets/d/1lUYGBlpX1ep2iLw84uBX-IqSfvsOmEZ-DX2x7-Hm9lA/edit#gid=1698875578 183]
|}

= Reading list =
== Required ==
* Э.Б.Винберг. Курс алгебры. М.: МЦНМО, 2014 (English transl.: Ernest Vinberg. A Course in Algebra. Graduate Studies in Math. 56, Amer. Math. Soc., 2003)
* Сборник задач по алгебре под редакцией А.И.Кострикина. Новое издание. М.: МЦНМО, 2015 (English transl.: Exercises in Algebra. Edited by A. Kostrikin, CRC Press, 1996)
== Optional ==
Serge Lang. Algebra. Revised Third Edition. Graduate Texts in Math. 211, Springer, 2002

Algebra DSBA 2018/2019 - История изменений

imported>Mednik: /* Exam */