- Paperback: 292 pages
- Publisher: Cambridge University Press; 1 edition (Aug 13 1999)
- Language: English
- ISBN-10: 0521666465
- ISBN-13: 978-0521666466
- Product Dimensions: 2.3 x 1.5 x 0.2 cm
- Shipping Weight: 318 g
- Average Customer Review: 5.0 out of 5 stars See all reviews (4 customer reviews)
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Amazon Bestsellers Rank:
#759,822 in Books (See Top 100 in Books)
- #51 in Books > Science > Mathematics > Matrices
- See Complete Table of Contents
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Product Details |
Product Description
Review
"Bressoud has created a beautiful new genre of mathematical exposition. It is neither popular mathematics, nor textbook, nor research monograph, nor problem book. It is all these and much more: a historical novel, a detective story and, implicitly, a philosophical manifesto. Yet the mathematics is deep, and all the proofs are complete...Proofs and Confirmations is destined to be a classic." American Mathematical Monthly
"Bressoud's book provides an opportunity to learn about all the mainstays of combinatorics like partitions, lattice paths, plane partitions, and hypergeometric functions by tracing a narrative that reads like a taut detective novel." Choice
"Bressoud has done a very nice job of presenting us with a readable book which delivers a self-contained look at some current mathematics. And he's done a wonderful job at exposing the flavor of research mathematics. Take a look." MAA Online
"the book will appeal to anyone who likes algebra and combinatorics, and is curious as to what is currently going on at intersection of these two disciplines." William Gasarch
"Bressoud's book provides an opportunity to learn about all the mainstays of combinatorics like partitions, lattice paths, plane partitions, and hypergeometric functions by tracing a narrative that reads like a taut detective novel." Choice
"Bressoud has done a very nice job of presenting us with a readable book which delivers a self-contained look at some current mathematics. And he's done a wonderful job at exposing the flavor of research mathematics. Take a look." MAA Online
"the book will appeal to anyone who likes algebra and combinatorics, and is curious as to what is currently going on at intersection of these two disciplines." William Gasarch
Product Description
This introduction to recent developments in algebraic combinatorics illustrates how research in mathematics actually progresses. The author recounts the dramatic search for and discovery of a proof of a counting formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While it was apparent that the conjecture must be true, the proof was elusive. As a result, researchers became drawn to this problem and made connections to aspects of the invariant theory of Jacobi, Sylvester, Cayley, MacMahon, Schur, and Young; to partitions and plane partitions; to symmetric functions; to hypergeometric and basic hypergeometric series; and, finally, to the six-vertex model of statistical mechanics. This volume is accessible to anyone with a knowledge of linear algebra, and it includes extensive exercises and Mathematica programs to help facilitate personal exploration. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something unique within Proofs and Confirmations.
Inside This Book
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First Sentence
Conjectures are the warp upon which we weave mathematics. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Conjectures are the warp upon which we weave mathematics. Read the first page
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Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most helpful customer reviews
5.0 out of 5 stars
Fantastic!,
By
This review is from: Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture (Paperback)
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.
5.0 out of 5 stars
Amazing book on how mathematical research is done,
By
This review is from: Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture (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 calculus and 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.
5.0 out of 5 stars
Amazing book on how mathematical research is done,
By
This review is from: Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture (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.
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