__Course Notes for Math 851/852__

** Group Theory:**

Chapter 1: Introduction to groups

Chapter 2: Quotient groups, isomorphism theorems, group actions, and Sylow's theorem

Chapter 3: Products of groups

Chapter 3.5: Supplementary notes on semi-direct products

** Ring Theory:**

Chapter 4: Introduction to rings

Chapter 5: Euclidean domains, principal ideal domains, unique factorization domains, and Gröbner bases

Chapter 5 Supplement: A quadratic field which is Euclidean but not norm-Euclidean

** Field and Galois Theory:**

Chapter 6: Field Theory

Chapter 7: Galois Theory

Chapter 7.5: Infinite Galois Theory

Chapter 8: Modules over a PID

Chapter 9: Some additional topics

__Homework for Math 851/852__

__Exams for Math 851/852__