This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.
Access also available here: http://abstract.ups.edu/contact.html
Table of Contents
Preliminaries
The Integers
Groups
Cyclic Groups
Permutation Groups
Cosets and Lagrange's Theorem
Introduction to Cryptography
Algebraic Coding Theory
Isomorphisms
Normal Subgroups and Factor Groups
Homomorphisms
Matrix Groups and Symmetry
The Structure of Groups
Group Actions
The Sylow Theorems
Rings
Polynomials
Integral Domains
Lattices and Boolean Algebras
Vector Spaces
Fields
Finite Fields
Galois Theory
- Subject:
- Algebra
- Material Type:
- Textbook
- Provider:
- University of Puget Sound
- Author:
- Thomas Judson
- Date Added:
- 01/01/2016
