Math 202B - Applied Algebra II (Winter 2022)

Lecture times and location: pre-recorded, posted below
Instructor: Steven Sam email
Instructor office hours: Zoom, Thursdays 11:30AM-12:20PM or by appointment
TA office hours: Zoom, Fridays 1-3PM
Discord server: link (we'll use this to discuss the class)

We will cover representation theory of finite groups and symmetric functions with an emphasis on representation theory of symmetric groups and time permitting, polynomial functors.
There is no single textbook for this course, but you may find some of the following books useful:

Fulton, Harris, Representation Theory
James, The Representation Theory of the Symmetric Groups
Sagan, The Symmetric Group
Serre, Linear Representations of Finite Groups
Stanley, Enumerative Combinatorics Vol. 2

Homework

Turn in all assignments through Gradescope.

Homework 1 (due Jan. 17)
Homework 2 (due Jan. 31)
Homework 3 (due Feb. 14)
Homework 4 (due Feb. 28)
Homework 5 (due Mar. 14)

My notes for the course

Notes (last updated 3/3/22)

Schedule

We will go by weeks rather than individual lectures. I will break up videos based on logical stopping places rather than set time limits.
Each week corresponds to roughly 5-7 pages of the course notes (how much I cover in an in-person lecture).
Unfortunately there may be small mistakes in the videos. I list them in the video description if that happens.
I list some sections from the reference books above that are related to the lecture.

Week 1 (Jan 3)
- Notes: Sections 1.1-1.4
- Serre: 1.1-1.5, 2.1-2.2
- Videos: Lecture 1, Lecture 2, Lecture 3
- Notes from lectures: Lecture 1, Lecture 2, Lecture 3
Week 2 (Jan 10)
- Notes: Sections 1.5-1.8
- Serre: 2.3-2.5, 3.1-3.3, 5.1, 5.3, 5.8, 6.1, 7.1-7.2
- Videos: Lecture 4, Lecture 5, Lecture 6
- Notes from lectures: Lecture 4, Lecture 5, Lecture 6
Week 3 (Jan 17)
- Notes: Sections 1.9, 2.1-2.3
- Serre: 6.4-6.5, James: Sections 3-4
- Videos: Lecture 7, Lecture 8, Lecture 9
- Notes from lectures: Lecture 7, Lecture 8, Lecture 9
Week 4 (Jan 24)
- Notes: Sections 2.4-2.5, 3.1-3.3
- James: Sections 7-8, Stanley: 7.1-7.4
- Videos: Lecture 10, Lecture 11, Lecture 12
- Notes from lectures: Lecture 10, Lecture 11, Lecture 12
Week 5 (Jan 31)
- Notes: Sections 3.4-3.7
- Stanley: 7.5-7.7, 7.9
- Videos: Lecture 13, Lecture 14, Lecture 15
- Notes from lectures: Lecture 13, Lecture 14, Lecture 15
Week 6 (Feb 7)
- Notes: Sections 3.8, 4.1-4.2
- Stanley: 7.10-7.11, 7.18
- Videos: Lecture 16, Lecture 17, Lecture 18
- Notes from lectures: Lecture 16, Lecture 17, Lecture 18
Week 7 (Feb 14)
- Notes: Sections 4.3-4.7
- Stanley: 7.11-7.12, 7.14-7.16
- Videos: Lecture 19, Lecture 20, Lecture 21
- Notes from lectures: Lecture 19, Lecture 20, Lecture 21
Week 8 (Feb 21)
- Notes: Sections 5.1-5.3
- Stanley: 7.17, Fulton-Harris: 4.1, A.1
- Videos: Lecture 22, Lecture 23, Lecture 24
- Notes from lectures: Lecture 22, Lecture 23, Lecture 24
Week 9 (Feb 28)
- Notes: Sections 5.4, 6.1-6.2
- Stanley: 7.A1.3, Fulton-Harris: Appendix B, 6.1
- Videos: Lecture 25, Lecture 26, Lecture 27
- Notes from lectures: Lecture 25, Lecture 26, Lecture 27
Week 10 (Mar 7)
- Notes: Sections 6.3-6.4
- Fulton-Harris: 15.5
- Videos: Lecture 28, Lecture 29
- Notes from lectures: Lecture 28, Lecture 29