Algebra 2 in 2018

Informations

The course takes place from August 21 till November 29, every Tuesday and Thursday at 15:30--17:00 in room 349. There are occasional additional classes, which are announced below.

The course will have weekly exercise lists, which will be corrected and returned in the exercise class. The exercise classes take place on Mondays in rooms 333 and 349, 10:30--12:00. The monitors are Eduardo Santos Silva and Bely Rodriguez Gonzales.

Exams

The course has two exams. The grades for the course will be calculated from the grades of hand in exercises and the grades of the exams. The exams are open book exams, i.e. you can take your notes and books and use them during the exam. Electronical gadgets (computer, tablet, cell phone, et cetera) are not allowed.

The first exam takes place on Thursday, October 4, from 15:30-18:30 in room 349. The second exam takes place on Tuesday, November 27.

Changes in schedule

Friday, 31.8., 15:30--17:00, room 347: additional class

Friday, 14.9., 15:30--17:00, room 347: additional class

Wednesday, 19.9., 13:30--15:00, room 349: additional class

Thursday, 4.10., 15:30--18:30, room 349: first exam

Wednesday, 17.10., 13:30--15:00, room 349: additional class

Wednesday, 31.10., 13:30--15:00, room 349: additional class

Thursday, 1.11.: no class

Tuesday, 6.11.: no class

Wednesday, 7.11., 13:30--15:00, room 347: additional class

Thursday, 8.11., 15:30--17:00, room 228: change of room

Thursday, 15.11.: holiday

Tuesday, 20.11.: holiday

Thursday, 22.11., 15:30--18:30, room 349: second exam

Exercise lists

List 1

List 2

List 3

List 4

List 5

List 6

List 7

List 8

List 9

List 10

List 11

List 12

References

The course consists of two parts. The first part covers Galois theory, the second part the representation theory of finite groups. There are numerous books and lecture notes for both topics available, and I encourage students to have a look for themselves, which material is best for them to learn. Here are merely a few suggestions, including my own notes on the part about Galois theory.

Galois theory

Lecture notes accompanying this course (link).

Serge Lang. Algebra. Revised third edition. Graduate Texts in Mathematics, 211. Springer-Verlag, New York, 2002.

Andrew Baker. An introduction to Galois theory. Lecture notes (link).

James Milne. Fields and Galois theory. Lecture notes (link).

Miles Reid. Galois theory. Lecture notes (link).

Representations of finite groups

Jean-Pierre Serre. Linear representations of finite groups. Graduate Texts in Mathematics, Vol. 42. Springer-Verlag, New York-Heidelberg, 1977.

Etingof, Golberg, Hensel, Liu, Schwendner, Vaintrob, and Yudovina. Introduction to representation theory. Student Mathematical Library, 59. American Mathematical Society, Providence, 2011.

Andrew Baker. Representations of finite groups. Lecture notes (link).

S. Martin. Representation theory. Lecture notes (link).

Constantin Teleman. Representation theory. Lecture notes (link).

Some useful links

Character tables for groups with at most 10 conjugacy classes (link).

Methods to determine character tables: by Bump (link); on the Groups Properties Wiki (link).