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Algebra 2 in 2020


The times of the lecture are Tuesday and Thursday at 10:30--12:00. The times of the exercise class is Friday at 14:00--15:30.

The course is accompanied by weekly exercise lists, which will be corrected and returned in the exercise class. The monitor of the course is Manoel Zanoelo Jarra.

Online access

The platform for both the lectures and the exercise classes is Zoom. The Zoom ID is the same for all meetings: 961 7747 1599. The password can be found here.

Email contact

Please send me your email contact (to "oliver at impa dot br"), so that I can share information about the course and links to the video recording with you. Please also include your full name and your university, if you have any restriction concerning English or Portuguese, and if you wish for an evaluation (and a resulting grade).

This is automatically granted for students at IMPA. Due to the limited capacity for correcting exercises and taking exams, it might be necessary to make a choice of which guest students can be granted an evaluation. To help me taking this hard decision as fair as possible, please explain in a short paragraph your motivation to ask for an evaluation!

All additional feedback (concerning the lecture, exercises, notes, ...) is very welcome, of course!


All students that have contacted me before Monday, August 24, with the wish for an evaluation will be granted an evaluation. Since this number of students exhausts our capacities, we cannot accept any additional requests for evaluations from now on.

The students from IMPA will be graded as usual: they get a full feedback to their homework solutions and letter grades (A, B, C or F) based on their grades for homework.

This is unfortunately not possible for the large number of guest students since we have only one monitor. Therefore the guest students will receive only one correction per week and a P/F-grading based on an averaged grade for the homework. The guests are encouraged to indicate if they are curious to see corrections for a specific exercise. Manoel might not be able to always follow this request for several reasons, but he will take these indications into considerations as far as possible.

In addition, every student (from IMPA and guest students) has to give at least two presentation of homework solutions in the exercise classes. These presentations will be appointed by Manoel a few days in advance.

There are different technical ways for these presentation, depending on the technical possibilities of the student. It could be written on a tablet, it could be based on photos of a handwritten solution on paper, or it could be a latex presentation, (which is probably the most work intense way).

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

List 13

List 14

Transcripts of the lectures

Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7 Lecture 8 Lecture 9 Lecture 10 Lecture 11 Lecture 12 Lecture 13 Lecture 14 Lecture 15 Lecture 16 Lecture 17 Lecture 18 Lecture 19 Lecture 20 Lecture 21 Lecture 22 Lecture 23 Lecture 24 Lecture 25 Lecture 26 Lecture 27 Lecture 28 Lecture 29 Lecture 30 Lecture 31


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).

Background on category theory

Lecture notes on Algebra 1 (link).

Bernhard Keller. Lecture notes on abelian and derived categories (link).

Mac Lane. Categories for the working mathamatician.

The Stacks project (link).

In general, Wikipedia has very good accounts on specified topics in category theory.

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).