Customer Reviews

Rings, Fields and Groups: An Introduction to Abstract Algebra

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I used this book as a supplement to a course in algebra at master level. Allenby uses a simple step by step approach to the subject supplied with simple examples and some exercises (not that simple).

What I realy like with this book is the historical tour of algebra and the brief presentation of many of the worlds famoust mathematicians.

I think the simple approach and the historical elements is main reason for still using this book when I am plying with the math.

For the most part, this book is a clear and concise introduction to abstract algebra. The prose is lucid and the author's notes and remarks give some intuitive rationale behind several of the results. The exercises are well-thought out, and in some cases they expound on an idea touched on earlier in the chapter.

On the other hand, a few of the chapters went over my head. The Prologue, for example, cites the major contributions of the key figures in the historical development of algebra. Since I was still an algebra novice when I read the Prologue, I found it hard to follow. Moreover, Chapter 5 on Group Theory begins with an introduction that summarizes two methods of solving the cubic. I had a lot of trouble following this section as well. In his description of Tchirnhaus' method, he brings up a simultaneous equation involving a cubic and quadratic but skips over some calculations. I spent 2 days trying to fill in the gaps, only to throw my 20 pages of scribble into the wastebasket in frustration. If you are not as obsessive as I am, then you might be ok with skipping over topics or exercises that are too advanced.

Having done every exercise up to Chapter 5, I've found about 5-6 typos in the print, which is decent for a math text. Brief solutions for most problems are in the back, which makes this book ideal for self-study.