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Fearless Symmetry: Exposing the Hidden Patterns of Numbers [Paperback]

Avner Ash , Robert Gross
3.6 out of 5 stars  See all reviews (5 customer reviews)
RRP: 19.95
Price: 17.23 & FREE Delivery in the UK. Details
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Book Description

24 Aug 2008

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 évariste 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.

Frequently Bought Together

Fearless Symmetry: Exposing the Hidden Patterns of Numbers + Elliptic Tales: Curves, Counting, and Number Theory + The Irrationals: A Story of the Numbers You Can't Count On
Price For All Three: 47.69

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Product details

  • Paperback: 312 pages
  • Publisher: Princeton University Press; New edition (24 Aug 2008)
  • Language: English
  • ISBN-10: 0691138710
  • ISBN-13: 978-0691138718
  • Product Dimensions: 22.9 x 15.2 x 2.3 cm
  • Average Customer Review: 3.6 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Bestsellers Rank: 575,127 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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"The authors are to be admired for taking a very difficult topic and making it . . . more accessible than it was before."--Timothy Gowers, Nature

"The authors . . . outline current research in mathematics and tell why it should hold interest even for people outside scientific and technological fields."--Science News

"The book . . . does a remarkable job in making the work it describes accessible to an audience without technical training in mathematics, while at the same time remaining faithful to the richness and power of this work. I recommend it to mathematicians and nonmathematicians alike with any interest in this subject."--William M. McGovern, SIAM Review

"Unique. . . . [T]his book is an amazing attempt to provide to a mathematically unsophisticated reader a realistic impression of the immense vitality of this area of mathematics."--Lindsay N. Childs, Mathematical Reviews

"To borrow one of the authors' favorite words, this book is an amazing attempt to provide to a mathematically unsophisticated reader a realistic impression of the immense vitality of this area of mathematics. But I think the book has another useful role. With a very broad brush, it paints a beautiful picture of one of the main themes of the Langlands program."--Lindsay N. Childs, MathSciNet

From the Inside Flap

"All too often, abstract mathematics, one of the most beautiful of human intellectual creations, is ground into the dry dust of drills and proofs. Useful, yes; exciting, no. Avner Ash and Robert Gross have done something different--by focusing on the ideas that modern mathematicians actually care about. Fearless Symmetry is a book about detecting hidden patterns, about finding definitions that clarify, about the study of numbers that has entranced some of our great thinkers for thousands of years. It is a book that takes on number theory in a way that a nonmathematician can follow-systematically but without a barrage of technicalities. Ash and Gross are two terrific guides who take the reader, scientist or layman, on a wonderful hike through concepts that matter, culminating in the extraordinary peaks that surround the irresistible, beckoning claim of Fermat's Last Theorem."--Peter Galison, Harvard University

--This text refers to an out of print or unavailable edition of this title.

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Customer Reviews

Most Helpful Customer Reviews
6 of 6 people found the following review helpful
Whether you like this book or not, you cannot deny that the authors have been very brave to write a popular mathematics book on one of the most abstract parts of mathematics. The central topic of this book is Galois Theory. This theory was developed by Evariste Galois to show that it was possible to solve equations of one variable using addition, subtraction, multiplication, division, and the extraction of roots only for equations of order less than five. This theory has led to what is now called modern or abstract algebra, which probably ties together more areas of mathematics than any other. The problem is that it deals with many highly abstract mathematical objects. Equations, complex numbers, modular arithmetic, and permutations on the one hand are not so difficult to explain and understand. It is however very different for symmetry, groups and their representations, and elliptic curves. It is amazing how far the authors can reduce the complexity of the mathematics, but the book is not an easy one to read. However, if you are looking for an introductory book on abstract algebra, then this is certainly one to consider.
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4 of 4 people found the following review helpful
3.0 out of 5 stars Good attempt but falls short 13 May 2012
Firstly, this book is not for the layman. This is despite the opening line on the back cover of the book. It may be the intention of the authors that this book is for everyone, but the level is far too high (even graduates and quite possibly maths professors outside of pure mathematics). The actual subject matter is an attempt to explain the proof of Andrew Wiles's proof of Fermat's Last Theorem. This greatly relies upon groups, and hence symmetry which is how the name of the book came about.

It could be that the publisher has prevented the book from being much longer but I could imagine a book twice the size being more fitting. The content of the book is incredibly interesting and is something I want to pursue. There is no shying away from algebra at all and there are no stories about the life of mathematicians. That, for me, is a big selling point. There are many more books out there that cover the lives of mathematicians past and present. This book just sticks to the mathematics, which is something I'd like to see more of going forward. I don't think that just sticking to mathematics means that a book has to be presented at academic research level. If it is possible for this book to be re-published with fuller explanations then it would be one of the greatest books ever: it explains a fascinating and difficult topic of mathematics in logically inductive way using clear examples that are simple to follow. That is the intention of this book, but it doesn't quite get there.

This book is getting a lot of high ratings on Amazon but I'm going to be bold and suggest the reason for the high ratings is due to the authors' *attempt* to delve into some incredibly interesting mathematics, but not based upon the actual delivery of the content.
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5.0 out of 5 stars Gallois Theory for the timid 25 Feb 2014
By Albear
Format:Paperback|Verified Purchase
Having studied group theory in its more basic aspects, I felt lacking in knowing nothing about Gallois theory. Having read various articles exhorting me to 'permute the roots of the equation' I felt I would get nowhere until I read this text. The skill and effort these experts put into making their subject accessible is exceptional. With a journey mapped out over interesting foothills, the reader is lead to higher peaks without any feeling of vertigo. Many concepts which previously had just been mysterious words now have meaning. Wonderful explanation.
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4 of 6 people found the following review helpful
5.0 out of 5 stars Review from an 'amateur' mathematician 28 Oct 2009
Let me say at the outset that I have not read all of this book. That's because I keep going back a chapter to make sure I have understood what has gone before.
I can only say that this book has taken me further than any other into the world of advanced pure mathematics. The text is pervaded with a sense that the authors really want the reader to understand this difficult and esoteric subject. What more can I say? Buy a copy. Some day it will be a classic.
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0 of 1 people found the following review helpful
Format:Paperback|Verified Purchase
This is a comment on the "New Edition" by Princeton University Press. The print is truly rotten.

Entire chapters are missing, pp. 85-118, are missing from the copy I was sent. Looking at where the text stops and where it starts again, I think probably the entire printed batch, and not just my copy, is defective.

Shame on Princeton University Press to send out such a defective product. Apparently they use the shoddiest cheapest printer out there and have no quality control whatsoever in place.

Shame on Princeton University Press! Disgraceful! Moneygrabbers without the least ethical conviction! Amateurs!
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