Representations of Finite Groups

Professor A.J. de Jong, Columbia university, Department of Mathematics.

This semester I am teaching the undergraduate course on the representations of finite groups. Besides the beautiful standard theory we will discuss: an application to the theory of finite groups, the structure of invariant rings and complex reflection groups, and Jordan's theorem on subgroups of GL_n(C).

Lectures: Tuesday and Thursday 11:40 PM -- 12:55 PM in Room 307 in the mathematics building. It is very important to attend the lectures and participate in the discussion.

My office hours: Wednesday 9 - 10:30 AM in my office Room 523 in math. If you want to come by another time during the week or zoom with me, please email me. Also, feel free to email math questions any time.

TA: Ryan Xu (kx2186). You can email him math questions and questions about the problem sets and you can ask for zoom sessions with him.

Prerequisites: MATH UN2010 and MATH GU4041 or the equivalent. For Linear Algebra, some topics are matrices, vector spaces, direct sums, tensor products, linear transformations, eigenvalues and eigenvectors, and canonical forms. For Modern Algebra, some topics are groups, homomorphisms, normal subgroups, the isomorphism theorems, symmetric groups, group actions, the Sylow theorems, and the structure of finitely generated abelian groups.

Exams: There will be a midterm and there will be a final exam. The midterm will be Thursday, Oct 16, in class. According to the projected exam schedule, the final will be on Thursday, Dec 18. List of dates:

Grading: Grades will be computed using scores on weekly problem sets, a midterm, and a final exam. The course grade will be computed as follows:

Lectures and notes: It is very important to be present during the lectures and to take notes! The material covered in the lectures is the material for the course. From the book by Serre below, we have roughly covered:

Also, I've started a pdf file with a list of material I intend to cover: representations-of-finite-groups.pdf. I will update this file as the semester goes along.

Problem sets: It is very important to work on the problem sets to keep up with the course. The problem sets are due either in class on Thursday or by email to Ryan by midnight of the due day. No late homework accepted. Just hand in whatever part of the work you were able to complete by the deadline!

  1. First problem set due Thursday, September 11: problem-set-1.pdf. If a lot of people have trouble with this set, then we'll adjust the level of abstraction and/or difficulty in future sets. Please let me and Ryan know if you are having trouble and which parts you have trouble with!
  2. Second problem set due Thursday, September 18: problem-set-2.pdf.
  3. Third problem set due Thursday, September 25: problem-set-3.pdf.
  4. Fourth problem set due Thursday, October 2: problem-set-4.pdf.
  5. Fifth problem set due Thursday, October 9: problem-set-5.pdf.
  6. Sixth problem set due Thursday, October 16: problem-set-6.pdf.

Material: Online and offline texts to use: