Fearless Symmetry: Exposing the Hidden Patterns of Numbers | 
 enlarge | Authors: Avner Ash, Robert Gross
Publisher: Princeton University Press
Category: Book
List Price: $24.95
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Rating:  15 reviews
Sales Rank: 516510
Media: Hardcover
Pages: 302
Number Of Items: 1
Shipping Weight (lbs): 1.4
Dimensions (in): 9.3 x 6.4 x 1.2
ISBN: 0691124922
Dewey Decimal Number: 512.7
EAN: 9780691124926
Publication Date: May 22, 2006
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Product Description
Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them. Hidden symmetries were first discovered nearly two hundred years ago by French mathematician Evariste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination. The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.
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| Customer Reviews: Read 10 more reviews...
 Excellent discussion of mathematical symmetry June 5, 2006
Mike Birman (Brooklyn, New York USA)
62 out of 64 found this review helpful
We may be entering a golden age of popularized mathematics literature. On the heels of John Derbyshire's recent superb book about Algebra, which alternates historical discussion with mathematical primers that illuminate rather than confuse, comes this excellent book that covers the fascinating topic of mathematical symmetry: especially Evariste Galois' final frenzied creation, Group Theory. From its birth to a productive maturity in Number Theory; where it has found extensive practical usage in acoustics, radar, codes and ciphers (and of course particle physics), Fearless Symmetry unfurls the threads of Galois Theory and follows their path through several branches of mathematics. It doesn't utilize Derbyshire's stark method of alternating chapters between history and mathematics. Rather, it enfolds the historical narrative into a clear presentation of the requisite mathematics.
Simplified abstraction, is probably the best explanation of the author's technique. Group Theory discussion leads to Andrew Wiles and Fermat's Last Theorem, Fibonacci numbers, Pythagorean Triples and the Riemann Hypothesis. In the process, Fearless Symmetry becomes the first popularized exposition of representation theory and reciprocity laws. It also discusses how mathematicians prove theorems and solve problems. The all-important rules of mathematics are also discussed. This is a wide-ranging work that manages to avoid the obfuscation often found in math books. A willingness to solve problems that are simply and clearly posed are all that's required from the reader. The authors even suggest that readers disinclined to solve problems can skip them. That would be a severe loss given the nature of this book. In any case, the problems are not difficult, offer instantaneous feedback as to the reader's understanding of the material and are an extension of the text. Mathematicians may enjoy the book for its elegance in uniting so many disparate topics. As a non-mathematician (a molecular biologist by training), I can attest to the clarity of the discussion. I found the book fascinating, truly informative, endlessly challenging to my own assumptions of the way math is done. If you don't mind some mathematics on the printed page, this book may provide several hours of sheer intelligent pleasure. Strongly recommended.
Mike Birman
Superb September 21, 2006
Dr. Lee D. Carlson (Saint Louis, Missouri USA)
32 out of 35 found this review helpful
In both the physics and mathematics community something very exciting is happening. Highly competent physicists and mathematicians have for the last six or seven years been writing books that give deep insight into the concepts and intuition behind their specialties. A voluminous literature of course exists that is written for the specialist in the field of relevance, and these are written in a high-level, formal style, and no motivation, either historically or technically is given. Those interested in entering the field will have to rely on getting verbal explanations from the researchers themselves, which may be difficult if they are not close to them in a geographical sense. This is also another reminder that there is definitely an oral tradition in mathematics, and experts it seems are reluctant to explain themselves to newcomers. Physicists are particularly sensitive to this state of affairs. They need to not only understand a large amount of material in physics, but they require deep insight into the mathematical tools that must be used to formulate their theories, and this insight must be obtained rather quickly. They do not have time to wait until the mathematical concepts "come to them."
This book gives a great deal of this insight in the field of Galois theory, the theory of equations, and algebraic number theory. But the reader also gets a taste of such esoteric topics such as etale cohomology and the proof of Fermat's Last Theorem. The authors pull all of this off in 267 pages, an amazing feat considering the nature of the subject matter. The book can be best appreciated by the advanced undergraduate student or graduate student of mathematics, but even professional mathematicians in other fields of mathematics will no doubt find the book helpful in introducing them to the subject. High-energy physicists will love the book, even the parts that are really a review of some elementary linear algebra.
The authors know when to stop when discussing a topic, so as to not lead the unprepared reader into a morass of highly technical argumentation. But they wet the reader's appetite enough to motivate them to consult the references for further reading. This book, and others like it thankfully are becoming more prevalent. Mathematicians are realizing that there is nothing wrong in engaging in a little hand waving in order to explain their ideas. This has enormous didactic power, and one can only imagine the ramifications of a large number of these kinds of books appearing in the next few years. With the deep insights they grant to aspiring mathematicians, this reviewer predicts an enormous explosion of new mathematics in the next decades, even greater than the current rate of progress, incredible as it is.
quite possibly the best recreational math book explaining groups July 3, 2008
marion buehring (Fairbanks, Alaska)
2 out of 2 found this review helpful
Fearless Symmetry is an engaging, entertaining, wonderful piece of literary mathematics. It gives a concise view of number theory without the dryness of a textbook. The authors do a wonderful job of explaining and solidifying the abstraction in mathematics, bringing the average non-mathematically minded reader into the realm of modern mathematics.
This book is a 'must read' for any undergraduate student of mathematics who may be experiencing difficulty understanding the basic concepts of modern algebra.
outstanding June 27, 2007
parmenides
4 out of 6 found this review helpful
This is a very good introduction to arithmetic that everyone wanting to be initiated in this important branch of mathematics should read.
The authors achieved something remarkable: they were able to communicate with accuracy the deepest concepts of arithmetic without the boring style of many mathematics textbooks. The book is very engaging, with nice reflections about the nature of mathematical thought, as well as the motivations behind the concepts.
The authors managed to have a gradual build up of difficulty of topics all the way
to the proof of Fermat's last Theorem. Unlike other introductory texts that let you down
because in their effort to be more engaging, end up too elementary, this one is perfectly balanced. I will also recommend the "Calculus Gallery" as a second outstanding book introducing Analysis.
It would be great if other branches of mathematics like dynamics, algebra, informatics etc had the privilege of such well balanced and insightful introductions.
Well done!
Rare - a well written book about math May 29, 2007
Chris R (Virginia)
2 out of 5 found this review helpful
Unlike most math books, Fearless symmetry is well written. Key concepts from prior chapters are reemphasized in subsequent chapters so readers are less likely to get lost. This is the first book on groups and representation theory that made clear sense to me. I can see where galois therory is going and now have an understanding of the basic form of the proof of Fermat's last theorem.
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