AN INTRODUCTION TO
by Joseph Landin
As the author notes in the reface, "The purpose of this book is to acquaint a broad spectrum of students with what is today known as abstract algebra."' Written for a one-semester course, this self-contained text includes numerous examples designed to base the definitions and theorems on experience, to illustrate the theory with concrete examples in familiar contexts, and to give the student extensive computational practice.
I. Sets and Numbers 1. The Elements of Set Theory 2. The Real Numbers II. The Theory of Groups III. Group Isomorphism and Homomorphism IV. The Theory of Rings V. Polynomial Rings
The first three chapters progress in a relatively leisurely fashion and include abundant detail to make them as comprehensible as possible. Chapter One provides a short course in sets and numbers for students lacking those prerequisites, rendering the book largely self-contained. While Chapters Four and Five are more challenging, they are well within the reach of the serious student.
The exercises have been carefully chosen for maximum usefulness. Some are formal and manipulative, illustrating the theory and helping to develop computational skill. Others constitute an integral part of the theory, by asking the student to supply proofs or parts of proofs omitted from the text. Still others stretch mathematical imaginations by calling for both conjectures and proofs.
Taken together, text and exercises comprise an excellent introduction to the power and elegance of abstract algebra. Now available in this inexpensive edition, the book is accessible to a wide range of students, who will find it an exceptionally valuable resource.
Dr. Landin is Professor Emeritus, University of Illinois at Chicago, and was Head of the Department of Mathematics for ten years.
Copyright © 1996-2017 Alexander Bogomolny