Abstract Algebra: Theory and Applications

Thomas W. Judson’s Abstract Algebra: Theory and Applications is an open source textbook designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. Rob Beezer has contributed complementary material using the open source system, Sage.

The latest and most up-to-date version of Abstract Algebra: Theory and Applications can be found at HTML Edition (updated August 1, 2024). There is also a Runestone Version and a Spanish Language edition.

We recommend the online version in Runestone, since it contains working Sage cells and allows students to respond to reading questions directly in the textbook. The Runestone version of Abstract Algebra: Theory and Applications is updated weekly.

A nicely printed and bound (hardcover or paperback) copy of the 2023 Edition of AATA can be purchased at a reasonable price—about $18 for paperback edition and $25 for the hardbound edition (price at the start of the Fall 2023 semester). It is available at your favorite online retailer (Amazon or Barnes and Noble) or by special order from your local or college bookstore. This is a service provided by Lon Mitchell of Orthogonal Publishing. The author, while supportive of this edition, is not involved directly in any way, including financially. The ISBNs for the 2023 Edition are: 9781944325183 (paperback) and 9781944325190 (hardcover). The next print edition will be August 2025. After 2025, print editions will be every four years—2029, 2033, etc.

The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.

The book’s strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. Technology is integrated into the textbook using the open source system, Sage. In addition, there are reading questions and class activities in each section. Reading questions are intended to be completed prior to class. These questions provide an opportunity for students to familiarize themselves with the material before it is covered in class. Reading questions also allow the instructor a chance to modify a lesson according to the student responses.

Abstract Algebra: Theory and Applications is written in PreTeXt. PreTeXt is an authoring and publishing system for authors of textbooks, research articles, and monographs, especially in STEM disciplines. Once a book has been written in PreTeXt different outputs can be produced such as PDF, HTML, EPUB, Jupyter Notebooks, and even braille. The PreTeXt source for Abstract Algebra: Theory and Applications is available at GitHub. Abstract Algebra: Theory and Applications has received support from the National Science Foundation (Awards #DUE-1020957, #DUE–1625223, and #DUE–1821329).