Ebook: Abstract Algebra: An Introduction

ABSTRACT ALGEBRA: AN INTRODUCTION, 3E, It is intended for a first undergraduate course in modern abstract algebra. The flexible design of the text 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 emphasis is on clarity of exposition. The thematic development and organizational overview is what sets this book apart. The chapters are organized around three themes: arithmetic, congruence, and abstract structures. Each theme is developed first for the integers, then for polynomials, and finally for rings and groups. This enables students to see where many abstract concepts come from, why they are important, and how they relate to one another. Features The flexible design of the text makes it suitable for courses of various lengths and different levels of mathematical sophistication flavor. The emphasis of this text is on clarity of exposition. The chapters are organized around three themes: arithmetic, congruence, and abstract structures. The interconnections of the basic areas of algebra are frequently pointed out in the text and in the Thematic Table of Contents.

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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: 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 13% more exercises.