Course Outline

Notes

Week 1: Groups and cyclic groups (DF Chapter 1 and Section 2.3)
- Day One
- Day Two
Week 2: Subgroups and quotient groups (DF Chapter 2 and 3)
- Day Three
- Day Four
Week 3: Isomorphism theorems and group actions (DF Chapter 3 and 4)
- Day Five
- Day Six
Week 4: Cauchy and Sylow Theorems; Abelian groups (DF Chapter 4 and 5)
- Day Seven
- Day Eight
Week 5: Direct and semi-direct products; applications and classification results (DF Chapter 5)
- Day Nine
- Day Ten
Week 6: Rings and ideals (DF Chapter 7)
- Day Eleven
- Day Twelve
Week 7: Ring morphisms; fraction fields; euclidean and principal idael domains (DF Chapter 7 and 8)
Week 8: Quadratic Rings (DF Chapter 7/8 continued)
- Day Fifteen
- Day Sixteen
Week 9: Unique Factorization
- Day Seventeen
- Day Eighteen
Week 10: Vector spaces and subspaces (DF Chaper 11)
- Day Nineteen
- Day Twenty
Week 11: Duality (DF Chapter 11)
- Day TwentyOne
- Day TwentyTwo
Week 12: Traces and determinants (DF Chapter 11)
- Day TwentyThree
Week 13: Bilinear forms and the spectral theorem (DF Chapter 11)
- Day TwentyFour
- Day TwentyFive
Week 14: Additional topics on linear algebra
- Day TwentySix

Problem Sets

Exams

Prelim Exam

The study guide to the algebra prelim is available here.

DF refers to Abstract Algebra, third edition by Dummit and Foote.