Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks. This book is offered as a manual to a new way of thinking. The author aims to instill the desire to understand the material, to encourage more discovery, and to appreciate the subject for its own sake.

Steve Rosenberg is a professor in the Mathematics and Computer Science Department at the University of Wisconsin-Superior. He received his Ph.D. from the Ohio State University. As an educator, Dr. Rosenberg has both developed and taught a wide array of courses in mathematics and computer science. As a researcher, he has published results in the areas of algebraic number theory, cryptographic protocols, and combinatorial designs, among others. As a software developer, his clients included Coca-Cola Enterprises and the pension agency of Cook County Illinois. He has extensive experience in computer science and software engineering.

Preface
Symbols
1.Review of Sets, Functions, and Proofs
2.Introduction: A Number Game
3.Groups
4.Subgroups
5.Symmetry
6.Free Groups
7.Group Homomorphisms
8.Lagrange's Theorem
9.Special Types of Homomorphisms
10.Making Groups
11.Rings
12.Results on Commutative Rings
13.Vector Spaces
14.Polynomial Rings
15.Field Theory
16.Galois Theory
17.Direct Sums and Direct Products
18.The Structure of Finite Abelian Groups
19.Group Actions
20.Learning from Z
21.The Problems of the Ancients
22.Solvability of Polynomial Equations by Radicals
23.Projects
Bibliography
Index