The new edition of Abstract Algebra: An Interactive Approach presents a hands-on and traditional approach to learning groups, rings, and fields. It then goes further to offer optional technology use to create opportunities for interactive learning and computer use.

This new edition offers a more traditional approach offering additional topics to the primary syllabus placed after primary topics are covered. This creates a more natural flow to the order of the subjects presented. This edition is transformed by historical notes and better explanations of why topics are covered.

This innovative textbook shows how students can better grasp difficult algebraic concepts through the use of computer programs. It encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area.

Each chapter includes, corresponding Sage notebooks, traditional exercises, and several interactive computer problems that utilize Sage and Mathematica® to explore groups, rings, fields and additional topics.

This text does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many topics not found in most standard introductory texts. The author explores semi-direct products, polycyclic groups, Rubik’s Cube®-like puzzles, and Wedderburn’s theorem. The author also incorporates problem sequences that allow students to delve into interesting topics, including Fermat’s two square theorem.

chapter Chapter 0|36 pages


chapter Chapter 1|23 pages

Understanding the Group Concept

chapter Chapter 2|28 pages

The Structure within a Group

chapter Chapter 3|30 pages

Patterns within the Cosets of Groups

chapter Chapter 4|29 pages

Mappings between Groups

chapter Chapter 5|32 pages

Permutation Groups

chapter Chapter 6|43 pages

Building Larger Groups from Smaller Groups

chapter Chapter 7|38 pages

The Search for Normal Subgroups

chapter Chapter 8|37 pages

Solvable and Insoluble Groups

chapter Chapter 9|26 pages

Introduction to Rings

chapter Chapter 10|34 pages

The Structure within Rings

chapter Chapter 11|45 pages

Integral Domains and Fields

chapter Chapter 12|43 pages

Unique Factorization

chapter Chapter 13|41 pages

Finite Division Rings

chapter Chapter 14|29 pages

The Theory of Fields

chapter Chapter 15|41 pages

Galois Theory