Abstract Algebra: Theory and Applications

Everything you wanted to know about abstract algebra, but were afraid to buy

Sage is an open-source program for doing mathematics and is the ideal companion to Abstract Algebra: Theory and Applications. Sage is designed to be a free, open source alternative to Magma, Maple, Mathematica and Matlab. It includes many mature and powerful open-source tools for mathematics, such as GAP for group theory. With a strength in number theory, Sage also has excellent support for rings and fields.

Rob Beezer has contributed extensive material about studying abstract algebra concepts with Sage, and instruction in the use of Sage itself. Each chapter (except one, Matrix Groups and Symmetry) has an extensive discussion of how to profitably use Sage. For most chapters (except two), these discussions are followed by classroom-tested exercises, ranging from very computational to open-ended guided explorations. In total there are 710 examples of Sage code and 121 exercises. These examples are run through automated testing twice a year using the latest stable version of Sage, so are highly reliable.

All of this material is included in the online version, where the Sage examples are executable and editable, via the free, zero-configuration Sage Cell server. The PDF download below is a static version of the online version and includes all the Sage material, where the examples have sample output included.

Abstract Algebra: Theory and Applications
Text by Tom Judson, Sage material by Rob Beezer
For Sage Version 9.6 and AATA Annual Edition 2022

[PDF: text and Sage material]

There was once a tutorial here, and we have left the PDF available. It is now obsolete and is no longer being maintained. If you have a link pointing here, you might wish to adjust the description of what is actually available.