# Abstract Algebra

- Author:
- Kevin Hopkins

- Topic:
- Algebra

Files that could be used in teaching Abstract Algebra. Some are also used in other classes, (like the Complex Number files), so the section numbers may not match the sections from Abstract Algebra.
As of Spring 2016, I have started using a new Abstract Algebra book. The book by Pinter doesn't include as many concrete examples for students to work with, so I hope to expand the worksheets. I will also have to alter the Chapter number as the course proceeds.

**If you find what you think is an error, please take a screen shot and email that to me (khopkins@sbuniv.edu) so I can investigate.**## Table of Contents

### Pinter's Book

- Appendix-Set Operations
- New Operations
- Z_n Under Addition-An example of operations from Chapter 2
- Z_n Under Multiplication-An example of operations-Chapter 2
- Ordered Pair, Group Example-Chapter 3
- Chapter 7-Permutations
- Chapter 7-Permutations
- Chapter 7-Permutations
- Chapter 7-Permutations
- Chapter 8-Permutations of a Finite Set
- Chapter 8-Permutations of a Finite Set
- Chapter 10 and 11-Cyclic Groups and Subgroups
- Chapter 10 & 11-Multiplication-Hopefully now working
- Identifying Rational vs Irrationals

### Gilbert's book

- Section 2.4
- Section 2.5-2.6: Solving equations modulo n.
- Section 2.6-Inverses in Z sub n
- Section 8.4-Polynomials
- Section 8.4-Addition of Complex Numbers
- Section 8.4-Multiplication of Complex Numbers
- Section 8.4-Division of Complex Numbers
- Polar Form of Complex Numbers-Section 7.2
- Complex Numbers in Rectangular Form-Section 7.2
- Complex Products using Polar Form
- Complex Powers
- Section 7.3-Roots of Complex Numbers
- Mandelbrot Set-Extension of Use of Complex Numbers.