Product Description

This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside’s paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.

Product Details

• Amazon Sales Rank: #204566 in Books
• Published on: 2001-10-18
• Original language: English
• Number of items: 1
• Binding: Paperback
• 458 pages

Review
‘… this reviewer regards the second printing of the book as a gem in studying representation theory of finite groups.’ R. W. van der Wall, Zentralblatt für Mathematik

'This is a beautiful well-balanced introduction to representations and characters of finite groups over the complex field, suitable for advanced undergraduate and beginning graduate students. The reviewer enjoyed the exposition tremendously and strongly recommends this already popular book both as a textbook and for self-study.' EMS

'For me, the attractive features are the short chapters (substantial but bite-sized), the motivational comments throughout the book and useful summaries at the end of each chapter, the wealth of detailed examples which break up and illuminate the theory, and full solutions to all the exercises.' The Mathematical Gazette

'The review found this to be a clearly and carefully written book, which he will recommend to all students seeking an introduction to group representation theory. the authors write in a down-to-earth style, provide a large number of examples throughout, and give very useful content summaries at the end of each chapter … In summary, the additions to the second edition only improve what was already an excellent text.’ Proceedings of the Edinburgh Mathematical Society

Customer Reviews

Very Good Introduction to Representation Theory
This book deals with introductory representation theory very well, introducing the often difficult-to-grasp concept of a module very well, considering. However, although the proofs are slicker, I would prefer at least a small matrix-leaning for the uninitiated. Considering they assume almost no group theory whatsoever, to introduce modules that quickly seems like a bit of lopsidedness in the prerequisites. Having said that, this is my only grumble with this book. Well planned and with a leisurely pace, this book should keep most people, at least through the first two-thirds of the book. I would recommend this book - I learned (basic) representation theory solely from this book, and it hasn't done me any harm!

A Nice Introduction to Representation Theory
This book has one of the clearest and simplest
exposition of the theory of group representations.

There is little fuss or abstract formalism that
might obscure the meaning of the fundamental
concepts and theorems. The material is clearly
written and very well organized. The chapters
are very short, thankfully, and the best thing
is that there are complete worked solutions to
all the chapter exercises.

The book ends with a nice application of the
theory to molecular vibration.

(As always, it helps to know the basic facts
about groups, and linear algebra - vector
spaces, linear transformations, matrices etc.)

An excellent book!

An enjoyable Maths Book!
I found the book easy to start with a cursory cursory read through to get an overview. I needed to re-read each chapter carefully to get to grips with the content. The contents fared well under scrutiny with neat concise proofs. Whether my linear algebra and group theory would stand the strain was always a worry, but the style of the writing kept me reassured, a compliment to the authors. The result is that I now have a fairly good idea of the subject.

An enjoyable learning experience!