Abstract Algebra: An Introduction

ABSTRACT ALGEBRA: AN INTRODUCTION is intended for a first undergraduate course in modern abstract algebra. Its flexible design makes it suitable for courses of various lengths and different levels of mathematical sophistication, ranging from a traditional abstract algebra course to one with a more applied flavor. The book is organized around two themes: arithmetic and congruence. Each theme is developed first for the integers, then for polynomials, and finally for rings and groups, so students can see where many abstract concepts come from, why they are important, and how they relate to one another. New Features: A groups-first option that enables those who want to cover groups before rings to do so easily. Proofs for beginners in the early chapters, which are broken into steps, each of which is explained and proved in detail. In the core course (chapters 1-8), there are 35% more examples and 13% more exercises.