This book is designed to make "Abstract Algebra" as down-to-earth as possible. Before getting into the deep theoretical stuff, we first take a look at algebraic systems beyond the real numbers that are widely used in practical applications of mathematics. These include the complex numbers, integers mod n, polynomials, symmetries, and permutations. We then use these examples to motivate and illustrate the beautifully general ideas of the theory of groups, rings, and fields. Along the way, we give applications to signal processing, cryptography and coding theory, as well as making connections with other branches of mathematics such as geometry and number theory.
The textbook is provided in three different formats: hyperlinked online version, pdf, and spiral bound copy (printme1.com is recommended for on-demand printing). The online version is from 2020, and is no longer updated. For the most updated copy, use the pdf.
An instructor's manual with solutions is available for instructors. Please see the 'For Instructors' page.
Online version
(HTML)
(No longer maintained: last update 2020)
Full textbook in PDF
(Free download--current version)
Spiral bound copy
(on-demand printing)