Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications.

An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

Table of Contents

Chapter 1: Why Abstract Algebra?

Chapter 2: Operations

Chapter 3: The Definition of Groups

Chapter 4: Elementary Properties of Groups

Chapter 5: Subgroups

Chapter 6: Functions

Chapter 7: Groups of Permutations

Chapter 8: Permutations of A Finite Set

Chapter 9: Isomorphism

Chapter 10: Order of Group Elements

Chapter 11: Cyclic Groups

Chapter 12: Partitions and Equivalence Relations

Chapter 13: Counting Cosets

Chapter 14: Homomorphisms

Chapter 15: Quotient Groups

Chapter 16: The Fundamental Homomorphism Theorem

Chapter 17: Ring- Definitions and Elementary Properties

Chapter 18: Ideals and Homomorphisms

Chapter 19: Quotient Rings

Chapter 20: Integral Domains

Chapter 21: The Integers

Chapter 22: Factoring Into Primes

Chapter 23: Elements of Number Theory

Chapter 24: Rings of Polynomials

Chapter 25: Factoring Polynomials

Chapter 26: Substitution in Polynomials

Chapter 26: Extentions of Fields

Chapter 28: Vector Spaces

Chapter 29: Degrees of Field Extentions

Chapter 30: Ruler and Compass

Chapter 31: Galois Theory- Preamble

Chapter 32: Galois Theory- The Heart of The Matter

Chapter 33: Solving Equations by Radicals

About the Author

Charles C. Pinter is Professor Emeritus of Mathematics at Bucknell University.