Mathematical Groups (Teach Yourself)

Rating:
Summary: Well done explanations of basic group theory
Review: The study of abstract algebra begins with the study of groups and that starts with the basics of mathematical proof, sets and binary operations. This book begins with those basics and then steps through the fundamental concepts of group theory. The chapters on groups are:

*) Groups
*) Subgroups
*) Cyclic groups
*) Products of groups
*) Isomorphisms
*) Permutation groups
*) Dihedral groups
*) Cosets
*) Groups of orders up to 8
*) Quotient groups
*) Homomorphisms

which covers all the introductory material that would be included in a first course in abstract algebra. A set of exercises is included at the end of each chapter and complete solutions to all of them are found in the last chapter.
The explanations of the principles of group theory are very well done, better than those found in most abstract algebra textbooks. Therefore, this book could also be used in a course of self-study. It has been a long time since I last taught abstract algebra, but if I do so again, I will either make a reserve copy of this book available or recommend it as an optional, supplementary text.


Rating:
Summary: This book is ok.
Review: I would not advise buying this book.Most students buy this book only because their lecturers say it's a good book; afterwards they discover that the book isn't as good as was first claimed to be.The first ten chapters are well-written, but the following chapters are difficult to understand. All the students studying Abstract Algebra have admitted that they had difficulties with this book. Get a copy from the library and see what you think.

Rating:
Summary: A very fine introduction
Review: I'm learning group theory in order to use it in physics. I found this book very good for a first introduction to the subject. It starts with pretty simple stuff and then proceeds with more serious matters. I find the example very clear, and I especially appreciate that full solutions to the exercises are provided, so that you can check your own findings. There are a few easy to amend typos, and I think the demonstration on page 46, theorem 20, part (2) is false. Finding another demo was a good exercise !
I went through that book twice, before moving to Burn's "Groups : a path to geometry".
All in all, it deserves 5 stars because it succeeds in delivering the reader what it promises.

Rating:
Summary: A pleasant surprise
Review: Many books on algebra lose sight of the basic underlying ideas when the author gets caught up in the formalism. Formalism is good but, as Bourbaki has demonstrated, it isn't always the best thing for teaching newcomers.

This little book is a gem. I bought it on a whim - curious that such a format would be applied to such a subject. I was pleasantly surprised. It pares the subject down to the minimal essentials without losing anything of central importance in the process. There are books that cost 10 times - even 20 times as much that don't do half as good a job.

IF you take the trouble to actually read the book, listen to what the authors are saying, do their exercises and THINK about what you are doing, you can learn an awful lot very quickly. The authors know how to blend formalism with intuition - a mark of the true teacher.