An Introduction to Algebraic Structures

by Joseph Landin

As the author notes in the preface, "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.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 skills. 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.

Genres: Mathematics

275 pages, Kindle Edition

First published March 1, 1989

Reviews

[Steven Harmon · Rating 3 out of 5]

Pretty inaccessible for an introduction

[Nick Black · Rating 4 out of 5]

A happy little read -- truly merely an introduction to abstract algebra -- that'll light your fire for operation structures. Rings, groups, fields, hurrah! You cannot understand the mathematics of the last two centuries without a deeper comprehension of algebra than Landin provides here, but it's a good starting place. This is probably one of the five most readable selections from the Dover Mathematics imprint for those of you without mathematical training.