Tentative Schedule for Abstract Algebra I
Math 171, Spring 2013, Harvey Mudd College
Prof. Orrison
Part I
- Groups and Subgroups
- Dihedral Groups and Symmetric Groups
- Homomorphisms
- Quotient Groups
- Cosets and Lagrange's Theorem
- Isomorphism Theorems
- Review and Practice
- In-Class Exam: Thursday, February 14
Part II
- Group Actions
- Centralizers, Normalizers, Stabilizers, and Kernels
- Cyclic Groups and Alternating Groups
- Groups Acting on Themselves
- Sylow's Theorems
- Sylow's Theorems
- Review and Practice
- In-Class Exam: Thursday, March 14
Part III
- Rings and Subrings
- Rings and Subrings
- Polynomial Rings, Matrix Rings, and Group Rings
- Ring Homomorphisms and Quotient Rings
- Properties of Ideals
- Properties of Ideals
- Review and Practice
- In-Class Exam: Thursday, April 18
Part IV
- Euclidean Domains
- Principal Ideal Domains
- Unique Factorization Domains
- What's in Math 172 and Math 174?
- Final Exam: Friday, May 17, 2:00 PM -- 5:00 PM