Modern Algebra: An Introduction

Written to help students learn the basic concepts of modern algebra and how to handle abstract ideas and proofs. Begins by introducing readers to the mechanics of proofs such as implications, contrapositives, converses, quantifiers and more. The fundamental concepts of groups, rings and fields are presented, along with the use of these concepts through other math courses, by characterizing each of the basic number systems--integers, rational, real and complex numbers. Packed with examples and problems, it includes a variety of applications to both motivate and show the usefulness of modern algebra.