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Groups and Symmetry (Undergraduate Texts in Mathematics) Hardcover – 1 Apr 1997

4.3 out of 5 stars 3 customer reviews

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Product details

  • Hardcover: 204 pages
  • Publisher: Springer; 1988. Corr. 2nd edition (1 April 1997)
  • Language: English
  • ISBN-10: 0387966757
  • ISBN-13: 978-0387966755
  • Product Dimensions: 15.6 x 1.3 x 23.4 cm
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Bestsellers Rank: 91,854 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description


M.A. Armstrong

Groups and Symmetry

"This book is a gentle introductory text on group theory and its application to the measurement of symmetry. It covers most of the material that one might expect to see in an undergraduate course . . . The theory is amplified, exemplified and properly related to what this part of algebra is really for by discussion of a wide variety of geometrical phenomena in which groups measure symmetry. Overall, the author’s plan, to base his treatment on the premise that groups and symmetry go together, is a very good one, and the book deserves to succeed."―MATHEMATICAL REVIEWS

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Customer Reviews

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Top Customer Reviews

Format: Hardcover
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.
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Format: Hardcover
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.
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By A Customer on 21 Oct. 2000
Format: Hardcover
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.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 3.9 out of 5 stars 11 reviews
13 of 14 people found the following review helpful
5.0 out of 5 stars Excellent introduction to abstract algebra through group theory 13 Sept. 2005
By Alexander C. Zorach - Published on Amazon.com
Format: Hardcover
This was the textbook for my first course in abstract algebra and the first "yellow book" that I read. I found it an excellent book: rather than starting with axioms and dryly deriving everything, it gets one to contemplate the meaning and motivation behind the axioms. This book will encourage you to play around with mathematics on paper and in your mind, helping you to get a concrete feel for a subject that many people view as painfully abstract.

The prose is clear and well-written: there is just the right amount of discussion to elucidate necessary points, while allowing the book to remain fairly compact. Exercises are fun but difficult and many require genuine creativity.

I also really like the choice of topics: although this book is introductory (with respect to abstract algebra, it presupposes some knowledge of linear algebra), because it focuses only on groups (as opposed to also trying to handle rings & fields) it is able to get into some more advanced and very interesting topics and applications in later chapters. This book will give you a lot more than can be covered in a single semester undergrad course, and while it doesn't exactly make the best reference text, it will be a book you will want to keep coming back to, if only to study some of the more advanced material.

There are differing perspectives on the teaching of abstract algebra: some people like to start with group theory exclusively in a first course, and treat rings, fields, and other structures in later courses. Other people recommend more integrated approaches, or approaches starting from rings. While I can't say that either approach is better, I can say that this book takes the first approach, focusing exclusively on groups and assuming little prior background..and for a first course in abstract algebra, this book is an excellent choice.
10 of 11 people found the following review helpful
4.0 out of 5 stars A good introductory text 25 Oct. 2007
By Ramsharan Rangarajan - Published on Amazon.com
Format: Hardcover
I'm using this book for a first course in Group theory and it makes a good introductory text. Topics are neatly arranged and follow an order that makes reading easy. But it is definitely not a text for any sort of rigorous proofs. Rather, it focuses on learning from examples.
12 of 14 people found the following review helpful
5.0 out of 5 stars Excellent introduction to group theory 2 Nov. 2004
By Martin P. Cohen - Published on Amazon.com
Format: Hardcover
Please note that the other reviews here are obviously for some other book. This is not an advanced text on bifurcations and stability. It is an introductory book on group theory. I have been using this book for self study. It is well suited to this purpose. The book uses symmetry to unify and motivate the study of groups. The discussion of the symmetry groups of Platonic solids is both enjoyable in itself and useful for visualizing groups. The chapters are very short. The exercises are well suited to gaining insight into the material.
2 of 2 people found the following review helpful
5.0 out of 5 stars Great Intro 13 July 2011
By Gnugs - Published on Amazon.com
Format: Paperback
Some authors like to expound, some like to dazzle and some like to teach. Armstrong falls easily into the latter category. If you are looking for a clear and motivating book to start learning about group theory, you will not find a better book. It is a short book but covers the essentials. The range of topics covers the necessary ground for an introduction: Sylow's theorems, free groups, matrix groups, presentations are all there with a strong geometric content. He even proves the Nielsen-Schrier Theorem in an accessible manner. All you really need to know is some basic undergraduate algebra to understand this little gem and it will certainly give you the foundation to move deeper. Highly recommended for a starting point.
2 of 2 people found the following review helpful
3.0 out of 5 stars Good book for a specific audience 4 Feb. 2016
By Dylan - Published on Amazon.com
Format: Hardcover Verified Purchase
I used this book for my introductory group theory class (Math 109 at Stanford). The book is alright, but the entire thing is written in the style of a proof. Theorems are introduced, then promptly proven. As a result, the exercises are often dramatically more difficult than material covered in the corresponding chapters. Another result of this style is extreme concision. Be prepared to read every sentence twice. This is a good book, but be comfortable with proofs and discrete math before attempting to read it.
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