Visual Group Theory (Classroom Resource Materials)

I really enjoyed reading this book. It is an introduction to group theory, and could be read and enjoyed by anyone with minimal background in mathematics. I studied Group Theory for my PhD (although that was more than ten years ago now) but even so, I still learnt things from this book. The tool most used in the book are Cayley diagrams, and the diagrams in the book are wonderfully clear. The goal is to explain the basic concepts of group theory, and to build up the reader's intuition about groups - essential in what can often be a very dry and abstract subject. The book achieves this goal brilliantly, and several ideas and results become essentially obvious. The introduction of semi-direct products is the best I have ever read, and why the fundamental theorem of abelian groups is true is made so obvious it is almost trivial. The final two chapters cover Sylow's Theorems and Galois Theory. The Sylow Theorems are clearly proved and groups up to order 15 are classified. The final chapter gives a brief introduction to Galois Theory. Little is proved in this chapter, but the reader is given a sketch of what the theory is about and roughly how it works. It is an excellent taster for further study. The book contains a multitude of exercises which are mostly fairly straight forward, and if I had to criticise the book it would be for the lack of stretching exercises, but this is a very minor criticism; there are many other books which can stretch a keen student of group theory. This is an excellent book, and would be perfect reading for anyone beginning their study of group theory.

Excellent! After searching so long for a good book that takes you from zero to significant understanding but in an intelligent way (visual here) I've found a book that does it. Writing is clear. Exercises are very well thought out and not there just to add volume to the book. You should do them. So much of mathematical/scientific writing is almost deliberately obscured by jargon or bad writing. In fact much of the material can be expressed to most intelligent or curious readers .. if it's presented and written well. Great book - and unlike some books this is printed very well on good materials. If I could have more I'd ask for more material on the symmetries in number theory.

I managed to pass the Group Theory module at the Open University but still hadn't got an intuitive feel for what cosets/ normal groups etc. were. This book really helps you get a gut feeling as to what the various aspects of group theory are and how they are useful. One point to readers: even if you think you know group theory, it is well worth (essential?) to got through the exercises.

I struggled with groups at university. Although I was able to stumble through questions and manipulate the algebra I didn't have any intuitive feel for what a group really 'was'. This book succeeds in providing that intuition.

I did a group theory course as an undergraduate mathematician 30 years ago. It was so dry and tedious that I never looked at abstract algebra again. I never really understood anything, even though I could hack my way through some of the early proofs, and I'd forgotten it all by the time I finished my degree. In later life, I've also occasionally tried to read more conventional books with titles like 'Groups, Rings and Fields', which have always had the same feeling of 'mysterious, pointless, and deeply boring'. I figured I just didn't have the right sort of intuition and wasn't any good at pushing symbols around. This is a pretty common experience, I think. Visual Group Theory has completely changed my mind. It's been fascinating from the start (I'm 8 chapters in). Groups are just the prettiest and most interesting things. How could anyone not love them?! What's really wonderful about this book is that it gives you tools to see the group structures, and intuition about how they work, and lots of really carefully chosen example problems that are well within your reach if you just draw enough pictures. No mysterious symbol pushing. Precious few symbols. There's nothing difficult or obscure here, I could have read this book as a twelve-year old. And yet it covers everything that was on my awful university course. I've been diligently doing every exercise, for fun, and I've found that I always pretty much already know what the next chapter is going to say, or at least, that the new ideas introduced look very much like the ideas I was having while tackling the exercises in the last chapter. I haven't enjoyed reading a book so much since Game of Thrones, and all five volumes of that only lasted a week. This has kept me entertained every day for nearly two months. This is pretty much the highest praise I can give for a book. What's really amazing is that as I've been going along, I've reconstructed all the usual dry algebraic stuff for myself, including lots of things I've never seen before and that aren't in this book, like 'Why you can't solve the general quintic equation', and 'Todd-Coxeter coset enumeration'. They've just seemed like fascinating and important things I would really like to understand, so I looked them up and worked them out. The usual style no longer holds any terrors for me. I know what those symbols *mean*.

bought this book after bothering many times with so called introductory text on group theory: incredible, the author manages to make you grasp and penetrate the most important concepts of the matter. incredibly enjoyable experience. absolutely suggested!