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Visual Group Theory (MAA Classroom Resource Materials) (MAA Problem Book Series) [Hardcover]

Nathan Carter
4.4 out of 5 stars  See all reviews (7 customer reviews)

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Book Description

May 12, 2009 088385757X 978-0883857571 1

Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts. But its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective.

The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.


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Visual Group Theory (MAA Classroom Resource Materials) (MAA Problem Book Series) + A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)
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Editorial Reviews

Review

Carter presents the grojp theory portion of abstract algebra in a way that allows student to actually see, using a multitute of examples and applications, the basic concepts of group theory...The numerous images (more than 300) are the heart of the text. As this work enables readers to see, experiment with, and understand the significance of groups, they will accumulate examples of groups and their properties that will serve them well in future endeavors in mathematics. Recommended --J. T. Zerger, Choice

If you teach abstract algebra, then this book should be a part of the resources you use. While the phrase "visual abstract algebra" may seem to be a contradiction, the diagrams in this book are an existence proof to the contrary. They are clear, colorful and concise very easy to understand and sure to aid the students that have difficulty in internalizing the abstract nature of the subject matter. Especially appealing are the colorized tables of groups and their operations.

The approach is a very slow one in the sense that a foundation of common operations and rearrangements that are groups that are first examined with text and images. A large number of exercises are included at the end of each chapter and detailed solutions with colored images found in an appendix.

this book could also serve as a text in a first course in abstract algebra provided that the course is limited to groups only or you used supplementary material for rings and fields. If your course is restricted to groups only, then this is the best book available. --Charles Ashbacher, Journal of Recreational Mathematics

Book Description

This text approaches the learning of group theory visually. It allows the student to see groups, experiment with groups and understand their significance. It is ideal as a supplement for a first course in group theory or alternatively as recreational reading.

Product Details

  • Series: MAA Problem Book Series
  • Hardcover: 297 pages
  • Publisher: The Mathematical Association of America; 1 edition (May 12, 2009)
  • Language: English
  • ISBN-10: 088385757X
  • ISBN-13: 978-0883857571
  • Product Dimensions: 7.2 x 10.5 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #205,715 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
43 of 46 people found the following review helpful
4.0 out of 5 stars I really wanted to love this book but... May 7, 2010
By sp
Format:Hardcover|Verified Purchase
...I only like it. Given that I am not a fan of the formal turgid theorem/proof type of math text, I waited with much
anticipation to get a copy of this text. Without a doubt, this is a very original and fun text that presents a novel
approach to teaching group theory. However, if I had come to group theory with this text as my first
introduction, I do not think it would have been effective and I would have quickly become frustrated. Simply put, the author
goes to far to build up intuition about groups before he actually defines a group mathematically.
I think it would have been better to define a group early and then start to build up
intuition after the definition is secure. Sort of "Here is the abstract definition, lets now start to understand why anyone would want to define a group in the first place and lets see some examples involving symmetry and other physical situations where groups arise".

A better choice for the absolute novice in group theory is the book Groups by Jordan and Jordan. This book is not well known in the USA but is simple, intuitive, and
well-written.
For the person interested in exploring the entire landscape of abstract algebra (groups, rings, fields, Galois theory)
"A Book of Abstract Algebra" by Pinter is unmatched for its clarity. I also recommend the older book by Keesee "Elementary Abstract Algebra".

In summary, I cannot recommend Visual Group Theory as a textbook for a course in group theory although some might find it a refreshing supplement to an overly formal abstract algebra text/course. I think its target audience
falls outside workers in the mathematical sciences and is geared toward chemists, molecular biologists, future/current
high school math teachers, and weekend math warriors
who are looking for intellectual stimulation.
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10 of 10 people found the following review helpful
5.0 out of 5 stars Cracking the tough Nut of Abstract Group February 18, 2011
By Wu Bing
Format:Hardcover
I am reading this book half way through, it is amazing how 'readable' this book is compared to other Abstract Algebra books. Although this book inherits much ideas and notations from the other older book: "Groups and Their Graphs" by Grossman and Magnus, it elaborates with more Cayley Diagrams (over 300 of them) and more detailed explanations.

The book is well written and well illustrated. I took one night to read through the first 5 chapters, that shows how easy it is to understand the concepts. (It helps, may be, because I had read the Grossman and Magnus book, however the later is not a pre-requisite reading).

I am also very pleased that the author uses Cayley diagrams to show how Subgroups, Cosets and Normal Subgroups could be visualized. This is a real break-through in teaching abstract stuff like Group Theory - a real tough nut to crack for most Math students. Don't forget the inventor of Group - Evariste Galois - had hard time making himself understood by even the greatest mathematicians of his time - Cauchy, Fourier, Poisson, etc.

This is the book to read before anyone attempting to study Group Theory in a formal textbook way.
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4 of 4 people found the following review helpful
5.0 out of 5 stars Great so far, through ~5/6 chapters December 25, 2011
By Andrew
Format:Hardcover|Verified Purchase
I was a physics B.S. who is now pursuing a Ph.D. in applied physics. Was very intimidated by the very math-y and formal books on group theory. Have been working through all the problems through the first 5/6 chapters so far, the ones whose answers are in the back of the book. Already feel much more confident about the fundamentals of group theory. The referenced software the author created is also very helpful and creative. Plan to continue to work problems all the way to the end, after which I'm confident I'll feel like I've got a solid grasp on group theory.
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1 of 1 people found the following review helpful
5.0 out of 5 stars Great book for introducing group theory October 15, 2012
Format:Hardcover
If you teach abstract algebra, then this book should be a part of the resources you use. While the phrase "visual abstract algebra" may seem to be a contradiction, the diagrams in this book are an existence proof to the contrary. They are clear, colorful and concise, very easy to understand and sure to aid the students that have difficulty in internalizing the abstract nature of the subject matter. Especially appealing are the colorized tables of groups and their operations.
The approach is a very slow one in the sense that a foundation of common operations and rearrangements that are groups are first examined with text and images. A large number of exercises are included at the end of each chapter and detailed solutions with colored images found in an appendix.
This book could also serve as a text in a first course in abstract algebra provided that the course is limited to groups only or you used supplementary material for rings and fields. If your course is restricted to groups only, then this is the best book available.

Published in Journal of Recreational Mathematics, reprinted with permission
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