Introduction to Algebra

by Peter J. Cameron

Book Overview

Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of...

• Format: Hardcover
• Language: English
• ISBN: 0198569130
• ISBN13: 9780198569138
• Release Date: February 2008
• Publisher: OUP Oxford
• Length: 354 Pages
• Weight: 1.05 lbs.
• Dimensions: 1.0" x 6.3" x 9.2"

Customer Reviews

Best Abstract Algebra book for undergrads

Cameron's 2nd Edition is the first book I have seen in the market which is remarkably better than other similar "Intro" to Abstract Algebra for teaching undergrads who have never been exposed to New Math: 1) He places Rings (chap 2) before Groups (chap 3)- this is a very bold idea and I think very logical. Rings (like Z) are very familiar to normal high school students, so easier to understand than the more abstract Group theory. Starting from Ring to learn factor ring, ideals, Laws of Isomorphism and other concepts, then revisit them later in Group will help to reinforce understanding. 2) He uses simple layman languages to explain complex concepts. For example: Homomorphism vs Isomorphism is akin to seeing things by short-sighted person without glasses (look similar) vs with glasses (exact image 1:1).

2nd Edition is Better

A nice thing about the new edition is the greatly expanded preliminary chapter which covers most of what a good advanced high school algebra course contains, plus a bit more. Depending on the reader's background, this may be very valuable. Also, this book is surprisingly lightweight (literally), which is good for those of us who carry around a lot of books in our backpacks.

Excellent, concise introduction

Peter J. Cameron's "Introduction to Algebra" is exactly that, an introduction to algebra and a good one at that. I must confess that before reading this book had a very limited knowledge of abstract algebra however with a little bit of time and effort I am now quite comfertable with the subject thanks to this book."Algebra" is divided into a 8 sections: 1) Set Theory and Relation Theory 2) Ring Theory 3) Group Theory 4) Vector Spaces 5) Modules 6) Numbers 7) More Rings and Groups 8) Galois theory and coding theoryThis book succeeds by having an interesting writing style, not being dry, and at the same time being very rigorous. The rigor is always present and all proofs are carefully developed however the "feel" of the subject is never lost as Cameron strives to help the reader grasp the "shape" of the algebraic structures that he introduces.This book has a slightly wider scope than many introductory algebra books however it succeeds in covering all of its topics well although the sections on category theory and algebraic geometry are only a page or two long and thus are only present to whet the reader's interest. In addition, Cameron motivates the discussions by drawing the topics together in the end in the applications chapter. This chapter covers the basics of the commonly known Galois theory and the less covered Coding theory which is one of the backbones of the internet.Final: Buy this book for a good introduction. I have borrowed a number of other introductory books from the university up the hill but this one was the clearest for me.