Product Details

• Amazon Sales Rank: #1744005 in Books
• Published on: 1997-12
• Original language: English
• Binding: Hardcover
• 197 pages

Synopsis
Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory. Written in an informal style, the material is divided into short sections each of which deals with an important result or idea. Throughout the book, the emphasis is placed on concrete examples, many of them geometrical in nature, so that finite rotation groups and the 17 wallpaper groups are treated in detail alongside theoretical results such as Lagrange's theorem, the Sylow theorems, and the classification theorem for finitely generated abelian groups. A novel feature at this level is a proof of the Nielsen-Schreier theorem, using group actions on trees. There are more than three hundred exercises to help develop the student's intuition.

Customer Reviews

Extremely concise and digestable.
After studying most of my semester course on group theory with another text book, I bought "Groups and Symmetry" despite being initially discouraged by the high price. The book is worth the cost however - if you are studying a first group theory module. The chapters are very short and hence can be worked through thoroughly, (perhaps without doing ALL of the exercises at the end), within an hour or two each. It was rewarding to be able to get through about ten chapters in one day of revision. I found it very valuable to have such a concise book on group theory, and my exam revision was aided greatly by it. Undoubtedly I will have to find a new group theory book if I am to study it in any further modules, (as I believe I intend to), as the book has almost nothing that would be irrelivant for a first group theory course at university, (perhaps it seemed to be particularly useful to me because my lecturer referred to it regularly I believe). I do think that the book is overpriced but it is difficult to say at what point the book would have been TOO overpriced, given how useful it has been to me. The book is written in informal and comfortable to read prose.

First hand information
I am a student studying mathematics at Durham University, and Dr Armstrong lectures me for Algebra and Number Theory. "Groups and Symmetry" is the recommended course text. I can say that Dr Armstrong is a fine lecturer with a remarkable grasp of the subject. He explains things very clearly and his book is an excellent example of his work, and will aid any second year student studying group theory.

An Easy Read
We used this book for a one quarter undergraduate class called Applied Groups. In retrospect, I should have just taken a proper algebra class as we spent too much time altogether on symmetries of dodecahedra (quite a pain to draw, BTW) and never got to point groups. But that isn't the fault of the book. It purports to cover 'groups and symmetry' after all and at that it does a relatively good job. On the whole, this book is easy to read. I would put it on a level with say, Griffiths' E and M text and Schroeder's thermo text, with Jackson's E and M text being at the other end of the scale. There are places where it gets denser for no good reason (steps left out or I could not see them) and other places where ideas and concepts are used that have not been defined. But these are few. The examples are for the most part non-trivial and illuminating. In summary, my sense is that this is an excellent way to get a foot in the door, but one would probably want to study more detailed texts later on.