Groups and Symmetry (Undergraduate Texts in Mathematics) [Hardcover]

M. A. Armstrong (Author)

Book Description

ISBN-10: 0387966757 | ISBN-13: 978-0387966755 | Publication Date: October 25, 1988

This is a gentle introduction to the vocabulary and many of 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 a new idea. Includes more than 300 exercises and approximately 60 illustrations.

Editorial Reviews

Review

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

Product Details

• Hardcover: 186 pages
• Publisher: Springer (October 25, 1988)
• Language: English
• ISBN-10: 0387966757
• ISBN-13: 978-0387966755
• Product Dimensions: 9.4 x 6.3 x 0.7 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #241,799 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

10 of 10 people found the following review helpful:

5.0 out of 5 stars Excellent introduction to abstract algebra through group theory, September 13, 2005

By 

Alexander C. Zorach "Alex Zorach" (Lancaster, PA) - See all my reviews
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This review is from: Groups and Symmetry (Undergraduate Texts in Mathematics) (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 10 people found the following review helpful:

5.0 out of 5 stars Excellent introduction to group theory, November 1, 2004

By 

Martin P. Cohen "Seeker" (Langhorne, PA USA) - See all my reviews
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This review is from: Groups and Symmetry (Undergraduate Texts in Mathematics) (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.

6 of 6 people found the following review helpful:

4.0 out of 5 stars A good introductory text, October 25, 2007

By 

Ramsharan Rangarajan "Ramsharan" (Stanford, CA) - See all my reviews
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This review is from: Groups and Symmetry (Undergraduate Texts in Mathematics) (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.