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.


Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
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  MAT 441: Topology
  MAT 526: Combinatorics

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