Tentative Schedule for Representation Theory
Math 174, Harvey Mudd College
Prof. Michael Orrison
Part I
- Modules and Submodules (10.1)
- Homomorphisms and Quotients (10.2)
- Permutation Modules for Finite Groups
- Direct Sums and Free Modules (10.3)
- Tensor Products of Modules (10.4)
- Tensor Products of Modules (10.4)
- Review and Practice
- In-Class Exam: Thursday, February 14
Part II
- Representations of Finite Groups (18.1)
- Maschke's Theorem (18.1)
- Semisimple Algebras (Clausen & Baum, Chp. 2)
- Wedderburn's Theorem (Clausen & Baum, Chp. 2)
- Characters (18.3)
- Orthogonality Relations (18.3)
- Review and Practice
- In-Class Exam: Thursday, March 14
Part III
- Idempotents from Characters
- Normal Subgroups and Lifted Characters
- Induced Modules and Characters
- Induced Modules and Characters
- Algebraic Numbers
- Burnside's Theorem
- Review and Practice
- In-Class Exam: Thursday, April 18
Part IV
- Random Walks on Groups
- Random Walks on Groups
- Random Walks on Groups
- Algebraic Voting Theory
- Final Exam: Thursday, May 16, 9:00 AM -- Noon