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

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6

Homework 7

Homework 8

Homework 9

Homework 10

Homework 11

Homework 12

Homework 13

Homework 14

Homework 15

Homework 16

Homework 17

Exams for Math 851/852

Math 851 Midterm

Math 851 Final Exam

Math 852 Midterm

Math 852 Midterm Solutions