Table of Contents
1 Preliminaries
2 Complex Numbers
3 Modular Arithmetic
4 Set Theory
5 Functions: Basic Concepts
6 Application: Introduction to Cryptography
7 Sigma Notation
8 Polynomials
9 Symmetries of Plane Figures
10 Permutations
11 Abstract Groups: Definitions and Basic Properties
12 Application: Further Topics in Cryptography
13 Equivalence Relations and Equivalence Classes
14 Cosets and Factor Groups
15 Application: Error-Detecting and Correcting Codes
16 Isomorphisms of Groups
17 Exploration: relating poynomials and matrices
18 Homomorphisms of Groups
19 Group Actions, with Applications
20 Appendix: Induction proofs-patterns and examples
About the Book
This book is not intended for budding mathematicians. It was created for a math program in which most of the students in upper-level math classes are planning to become secondary school teachers. For such students, conventional abstract algebra texts are practically incomprehensible, both in style and in content. Faced with this situation, we decided to create a book that our students could actually read for themselves. In this way we have been able to dedicate class time to problem-solving and personal interaction rather than rehashing the same material in lecture format.
- Subject:
- Mathematics
- Material Type:
- Textbook
- Author:
- Chris Thron
- Justin Hill
- Date Added:
- 06/29/2020
