2. Teaching
3. MAT 612
4. Materials

Course Notes

I’ll post notes here as they become available. Each link below is to a PDF file.

• Chapter 1: Ring Theory (Slides Version, Student Version)
  • 1.1 Definitions and Examples
  • 1.2 Ideals and Quotient Rings
  • 1.3 Maximal and Prime Ideals
  • 1.4 Rings of Fractions
  • 1.5 Principal Ideal Domains
  • 1.6 Euclidean Domains
  • 1.7 Unique Factorization Domains
  • 1.8 More on Polynomial Rings
• Chapter 2: Field Theory (Slides Version, Student Version)
  • 2.1 Field Extensions
  • 2.2 Algebraic Extensions
  • 2.3 Splitting Fields
  • 2.4 Separable and Inseparable Extensions
• Chapter 3: Galois Theory (Slides Version, Student Version)
  • 3.1 Definitions and Examples
  • 3.2 The Fundamental Theorem of Galois Theory
• Chapter 4: Module Theory (Slides Version, Student Version)
  • 4.1 Definitions and Examples
  • 4.2 Quotient Modules and Module Homomorphisms
  • 4.3 Generation of Modules, Direct Sums, and Free Modules

Exams

Below are links to each exam.

• Exam 1 (take-home) (PDF). If you are interested in using LaTeX to type up your solutions, then you can obtain the .tex file for the exam here. (Due Friday, March 4)
• Exam 2 (take-home) (PDF). If you are interested in using LaTeX to type up your solutions, then you can obtain the .tex file for the exam here. (Due Friday, April 22)
• Exam 3 (take-home) (PDF). If you are interested in using LaTeX to type up your solutions, then you can obtain the .tex file for the exam here. (Due by 5pm on Thursday, May 12)

Free Abstract Algebra Textbooks

Here is a list of free abstract algebra texts that you may use as an additional resource. If you find one of these more helpful than another, please let me know. Also, if you know of other resources, please let me know.

• An Inquiry-Based Approach to Abstract Algebra is a set of IBL course materials that I wrote for an abstract algebra course that emphasizes visualization and incorporates technology.
• Abstract Algebra: Theory and Applications by Tom Judson (Stephen F. Austin University).
• Elementary Abstract Algebra: Examples and Applications by Justin Hill (Temple College) and Chris Thron (Texas A\&M University-Central Texas) with contributions from others. The text is designed for students who are planning to become secondary-school teachers. The authors particularly emphasize material that has relevance to high school math, as well as practical applications. Much of the content is derived from the Judson book mentioned above.
• Essential Group Theory by Michael Batty (University of Durham).
• Group Theory: Birdtracks, Lie’s, and Exceptional Groups by Predrag Cvitanović (Georgia Tech).