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Jan 05, Charles rated it liked it. Inaccurate to describe this as a book in popular mathematics A simple examination of the title and the cover leads you to believe that this is a book about the visual aspects of symmetry and how it is generated mathematically. However, there are only two images, one of a tetrahedron and the other of a sphere. The best way to describe the book is that it is a short and detailed journey through the mathematical background needed to explain representation theory, reciprocity rules, Galois theory an Inaccurate to describe this as a book in popular mathematics A simple examination of the title and the cover leads you to believe that this is a book about the visual aspects of symmetry and how it is generated mathematically.

## Fearless Symmetry: Exposing the Hidden Patterns of Numbers by Avner Ash,Robert Gross

The third and last part deals with topics that only people with a significant background in mathematics will understand. Other sections in parts one and two would also be difficult for the person not well schooled in mathematics to understand. In the foreword the authors recommend that the reader has studied calculus. I consider this too weak a background, the absolute minimum would be someone well-schooled in calculus.

However, it will not be easy.

- Fearless Symmetry: Exposing the Hidden Patterns of Numbers.?
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This book was made available for free for review purposes and this review also appears on Amazon Jun 09, Ramesh Abhiraman rated it it was amazing. Ash and Gross have written a hand-holding book for non-mathematicians, with absolute rigor, walking them through the Galois group and Galois theory SYMMETRY of solutions over Fp of polynomial equations , as well as the mysterious and not-so-mysterious underpinnings of the Legendre symbol and quadratic reciprocity, in chapters 6 and 7 respectively. The concept of varieties is introduced earlier. After elliptic curves Please note: I discovered Ash and Gross for their famous popular book on ellipti Ash and Gross have written a hand-holding book for non-mathematicians, with absolute rigor, walking them through the Galois group and Galois theory SYMMETRY of solutions over Fp of polynomial equations , as well as the mysterious and not-so-mysterious underpinnings of the Legendre symbol and quadratic reciprocity, in chapters 6 and 7 respectively.

After elliptic curves Please note: I discovered Ash and Gross for their famous popular book on elliptic curves are introduced in Chapter 9 This is stand-alone, you dont need their other book , one is led through group representations and characters albeit briefly in Chapter 15, the complicated concepts of Frobenius elements are introduced in chapter Z-varieties and the reciprocity law in context of Frobenius are re-explained in the penultimate chapter. The last chapter takes off in a way to show that math is a evolving area of research.

THe book boasts excellent credentials including a preface by Barry Mazur. View 2 comments. Apr 21, Jonathan Chuang rated it liked it Shelves: mathematics.

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Even though I probably wouldn't have understood it anyway, added with the fact that after a few chapters I stopped seriously working on any of the example problems, I felt that overall it wasn't very well explained. I sort of got the sense of what the Galois group is, but didn't really understand quadratic reciprocity. I guess it was a good jumping off point cos I found out about those things ever so dimly on my own.

But it could've been better explained with more diagrams a Even though I probably wouldn't have understood it anyway, added with the fact that after a few chapters I stopped seriously working on any of the example problems, I felt that overall it wasn't very well explained. But it could've been better explained with more diagrams and narrative.

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May 06, Erickson rated it it was amazing Shelves: mathematics. A rare book attempting to explain Galois theory and representation theory, to the extent of trying to illustrate how Fermat's Last Theorem and reciprocity laws are formulated. I personally find this book too difficult for laymen, though it does try to make it accessible by not skipping basic definitions and explanations.

### About this book

Overall, enlightening but difficult read despite the intended reader being general audience. Jul 17, Michael rated it it was ok. Relatively fearless for the first 16 chapters, but by the time it gets to Frobenius and linear Galois representations to show reciprocity it becomes quite fearful.

An interesting if underdeveloped incite into what mathematicians find wonderful about pure math and number theory that doesn't really achieve its goal. Nov 30, Achilleas rated it it was amazing. Excellent introduction to Galois theory and representation theory. Not for all audiences though.

Some general knowledge of maths and ideally Algebra is a must to understand the material presented in this book. Those who can approach this material will enjoy the beauty of modern mathematics.

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Jan 20, Gus rated it liked it. Interesting stuff.

## Fearless Symmetry: Exposing the Hidden Patterns of Numbers - PDF Free Download

The first have about p-adic numbers and all that was really interesting. The last half was way over my head though. Not a book for "lay" people, more for less-than-casual number-theory enthusiasts. Dec 18, Paul is currently reading it. Jan 08, MathMonk rated it really liked it. Try to cover very advanced topic in popular math fashion.

A partial success. Part 3 of book is very very difficult to understand and is the main motivation for the book. Sep 24, Fredrik rated it it was amazing Shelves: matematikk , fakta. Books will be free of page markings. Some pages may be slightly dog-eared through previous use.

The spine may show some creasing through previous use. Ultimately we would never send any book we would not pick up and read ourselves. All new books sold by AwesomeBooks:Will be completely new and unfolded. Wrapped carefully to prevent damage or curling of book edges. If you are not happy then neither are we. Return Policy At AwesomeBooks, we believe our customers should feel free to order any of our products in the knowledge that they can return anything back within 30 days of purchasing an item for any reason.

We will not make it awkward, if you want to return something then all you have to do is ask! Simply drop us an email to the address given on your order confirmation email or login to your paypal account used for payment and send us an email from there. Ant leads Gnam via a number of theories, and jointly, they placed the theories into action—applying linear diophantine equations to soccer scoring, utilizing a black-magic machine to simplify difficulties in modular buildings, and constructing exciting ameliorations to the foundations of chess.

Il libro tratta di metodi di crittografia e sistemi, con particolare enfasi alla teoria dei numeri. Download PDF sample. Skip to content. A Course in p-adic Analysis Graduate Texts in Mathematics Came upon on the flip of the twentieth century, p-adic numbers are often utilized by mathematicians and physicists. Elliptic Tales: Curves, Counting, and Number Theory Elliptic stories describes the newest advancements in quantity idea by way of some of the most interesting unsolved difficulties in modern mathematics—the Birch and Swinnerton-Dyer Conjecture.