Math 122: Modules and Group Representation Theory

This class will MWF at 10:30 AM in 380X.

• Instructor: Daniel Bump (bump at math dot stanford dot edu)
• Office hours (Bump): MWF 12-1 PM. (Other times by appointment)
• Course Assistant: Cole Daniel Franklin
• Office hours (Franklin): Tu-Th 10:30-noon starting April 2.

Canvas and Gradescope

• Canvas link.
• Gradescope for this class.

Exams

Midterm Date: May 6 at 7-9 PM in 380W.

Final Exam Date: June 05, 3:30-6:30 PM.

Syllabus

ExploreCourses syllabus: Modules over a principal ideal domain. Tensor products over fields. Group representations and group rings. Maschke's theorem and character theory. Character tables, construction of representations.

In Dummit and Foote, we will cover Sections 10.1-4 and Chapters 12,18,19. We will also review semidirect products from Section 5.5. I will emphasize induced representations more than Dummit and Foote do.

Homeworks

Homeworks will usually be due on Tuesdays on Gradescope.

Tuesday April 7, 2026	Homework1 10.1 # 7,8a,18,19; 10.3 # 9,10,11	Latex file	Solutions
Tuesday April 14, 2026	Homework2 10.2 # 10; 10.4 # 2,6,11; Linear Algebra Problems 5,6,7	Latex file	Solutions
Tuesday April 20, 2026	Homework3 18.1 # 3,11,15,16,20; 18.2 # 3	Latex file	Solutions
Tuesday April 27, 2026	Homework4 18.3 # 1,2a,4,5,11,20	Latex file
Tuesday May 5, 2026	Homework5 18.3 # 6,7; 19.1 # 2,3,7,8,9	Latex file

Links

• Tensor Products. This is an alternative to Section 10.4 of Dummit and Foote.
• Group representation theory (notes from a previous course).
• Terence Tao's post on Frobenius groups. Frobenius' theorem has never been proved without using group representation theory. We'll prove it in Math 122.