Customer Reviews

Introduction to Algebra

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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 theory

This 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.

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).

This is not a bad book but not more than an average text. The introduction is grafted on summary of high school algebra that isn't very cohesive or structured.

The presentations are rigorous but most modern math books are as well. The presentation is dry. I like math and math texts. Some add humor, some add history, and some add examples of applications to make things more interesting. This book could serve as the basis for a good course if the lecturer was dynamic but as a read it is only average.