ABSTRACT

By integrating the use of GAP and Mathematica, Abstract Algebra: An Interactive Approach presents a hands-on approach to learning about groups, rings, and fields. Each chapter includes both GAP and Mathematica commands, corresponding Mathematica notebooks, traditional exercises, and several interactive computer problems that utilize GAP and Mathema

chapter 1|26 pages

Understanding the Group Concept

chapter 2|26 pages

The Structure within a Group

chapter 3|26 pages

Patterns within the Cosets of Groups

chapter 4|28 pages

Mappings between Groups

chapter 5|28 pages

Permutation Groups

chapter 6|40 pages

Building Larger Groups from Smaller Groups

chapter 7|34 pages

The Search for Normal Subgroups

chapter 8|36 pages

Solvable and Insoluble Groups

chapter 9|28 pages

Introduction to Rings

chapter 10|36 pages

The Structure within Rings

chapter 11|42 pages

Integral Domains and Fields

chapter 12|40 pages

Unique Factorization

chapter 13|38 pages

Finite Division Rings

chapter 14|30 pages

The Theory of Fields

chapter 15|38 pages

Galois Theory