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 226: Discrete Math
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Land Acknowledgement

  Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.