Rings, Fields and Groups

By Reg Allenby

"'Rings, Fields and Groups' gives a stimulating and unusual introduction to the results, methods and ideas now commonly studied on abstract algebra courses at undergraduate level. The author provides a mixture of informal and formal material which help to stimulate the enthusiasm of the student, whilst still providing the essential theoretical concepts necessary for serious study.

Retaining the highly readable style of its predecessor, this second edition has also been thoroughly revised to include a new chapter on Galois theory plus hints and solutions to many of the 800 exercises featured."

• Format: Paperback
• Language: English
• ISBN: 0340544406
• ISBN13: 9780340544402
• Release Date: August 1991
• Publisher: Butterworth-Heinemann
• Length: 416 Pages
• Weight: 1.55 lbs.
• Dimensions: 0.8" x 6.1" x 9.2"

Customer Reviews

Good for self-study

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.

Algebra for advanced beginners

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.