Introduction to Abstract Algebra: with Applications

Preface Preface

This text is intended for a one-semester introduction to abstract algebra, specifically Math 351 at the University of Tennessee. It is a condensed and rearranged version of Abstract Algebra: Theory and Applications² by Thomas Judson. I have tried to make the text flow as well as possible in its current form, but you may find discrepencies where the editing process is apparent.

Introductions to abstract algebra usually focus on two structures: groups and rings. It is traditional to teach these two structures in that order, as does Abstract Algebra: Theory and Applications. In some sense, groups are simpler, having only one operation, instead of the two operations in a ring. However, basic examples of rings are more familiar than for groups, and their theory has more parallels with results students are likely to have seen before. Some of the examples of groups are in fact coming from rings, and the restriction to only one of the operations can seem arbitrary. Therefore, this text treats rings first and uses the examples of rings to give some of our first examples of groups.

As the title suggests, an emphasis of the original text Abstract Algebra: Theory and Applications is to include applications of abstract algebra. This characteristic has been continued in the revised version, with chapters on cryptography and coding theory. Connections between abstract algebra and many areas of science have grown in the past several decades and this text gives a sample of that.