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Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture (Spectrum) Paperback – 13 Aug 1999


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'Proofs and Confirmations is one of the most brilliant examples of mathematical exposition that I have encountered, in many years of reading the same. This is not for the faint-hearted, nor is Proofs and Confirmations a book that can be read in an easy chair, like a novel; it demands active participation by the reader. But Bressoud rewards such readers with a panorama of combinatorics today and with renewed awe at the human ability to penetrate the deeply hidden mysteries of pure mathematics.' Herbert S. Wilf, Science

'The unexpected twists and turns will hardly be matched in any novel - this book allows us all to share in the excitement … a brilliant book.' Alun O. Morris

'I strongly recommend the book as an account of a remarkable mathematical development.' P. J. Cameron, Proceedings of the Edinburgh Mathematical Society

'This is an excellent book which can be recommended without hesitation, not only to specialists in the field, but to any mathematician with time to read something interesting and nicely written.' EMS

Book Description

This is an introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. The author recounts the story of the search for and discovery of a proof of a counting formula conjectured in the late 1970s with connections to disparate topics in mathematics and physics including partition theory, symmetric functions, hypergeometric series, and statistical mechanics.

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Conjectures are the warp upon which we weave mathematics. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Amazon.com: 3 reviews
20 of 20 people found the following review helpful
Amazing book on how mathematical research is actually done 30 Jan 2000
By Peter W. Shor - Published on Amazon.com
Format: Paperback
This book tells the story of one of the more important areas of research in algebraic combinatorics in the last few years. Not only does it tell the story of how the relevant conjectures were proposed, and how they were eventually proved (including some of the blind alleys and several cases where surprising connections were discovered), but it also contains a beautiful exposition of the relevant mathematics, at a level which a reader with no more than a reasonable background in linear algebra can follow. The history is fascinating and the mathematics is beautiful. If you want to know what research in mathematics is really like, this is the book to read.
15 of 16 people found the following review helpful
Fantastic! 30 May 2000
By Sen Peng Eu - Published on Amazon.com
Format: Paperback Verified Purchase
Everyone wants to know what mathematicians do should read this book. Yes, only very few among people can get familiar or endure gorgeous complicated formulas here, But even scan or skim this book one will learn much more than he predicted. The goal of this book is simple enough: To prove a conjecture (surely when proved, it becomes a theorem) But the structure and details are well selected and carefully designed. First it introduces and explains the original problem, than talk about it's history, how it does connect with other branches of math, what these branches is about, and what the other mathematicians do on this conjecture, and at last the most exciting: how these results all bringed together and then solve this 20-year-long famous conjecture in combinatorics. There are exercises after every chapter. so this is NOT merely a history survey (as most books do). Indeed it is a textbook and contains some very excellent introductions to some branches(for example, plane partition). And I think this is THE correct style to populating mathematics--- Do not afraid of formulas, just show readers the signs, the terrible formulas, show them how and what mathematicians study and think! Every student major in mathematics should read it, and it surely is a must-have for reseachers in combinatorics.
14 of 15 people found the following review helpful
Massterpiece of Mathematical Exposition 1 Oct 1999
By A Customer - Published on Amazon.com
Format: Paperback Verified Purchase
Dave Bressoud tells, in his wonderful gripping style, the fascinating recent history of the proof of the alternating sign matrix conjecture, and the not-so-recent background that lead to it. The book can be read on many levels, and is full of fascinating historical tidbits. This book is a must to anyone who wants to know how math is actually done, and who wants to share in the excitement of discovery.
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