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Spectrum Ser.: Proofs and Confirmations : The Story of the Alternating-Sign Matrix Conjecture by David M. Bressoud (1999, Trade Paperback)
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- Buy It NowProofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-100521666465
ISBN-139780521666466
eBay Product ID (ePID)734236
Product Key Features
Number of Pages292 Pages
Publication NameProofs and Confirmations : the Story of the Alternating-Sign Matrix Conjecture
LanguageEnglish
SubjectMechanics / General, Logic
Publication Year1999
TypeTextbook
Subject AreaMathematics, Science
AuthorDavid M. Bressoud
SeriesSpectrum Ser.
FormatTrade Paperback
Dimensions
Item Height0.7 in
Item Weight15.2 Oz
Item Length9 in
Item Width6 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN99-020232
Reviews"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 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, '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, '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, '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, "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, ‘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, ‘I strongly recommend the book as an account of a remarkable mathematical development.’P. J. Cameron, Proceedings of the Edinburgh Mathematical Society, ‘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 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, 'I strongly recommend the book as an account of a remarkable mathematical development.' P. J. Cameron, Proceedings of the Edinburgh Mathematical Society, "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, 'I strongly recommend the book as an account of a remarkable mathematical development.'P. J. Cameron, Proceedings of the Edinburgh Mathematical Society, '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
Dewey Edition21
IllustratedYes
Dewey Decimal512.9/434
Table Of Content1. The conjecture; 2. Fundamental structures; 3. Lattice paths and plane partitions; 4. Symmetric functions; 5. Hypergeometric series; 6. Explorations; 7. Square ice.
SynopsisThis 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., An introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses., 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., 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 formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While apparent that the conjecture must be true, the proof was elusive. Researchers became drawn to this problem, making connections to aspects of invariant theory, to symmetric functions, to hypergeometric and basic hypergeometric series, and, finally, to the six-vertex model of statistical mechanics. All these threads are brought together in Zeilberger's 1996 proof of the original conjecture. The book is accessible to anyone with a knowledge of linear algebra. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something new here.
LC Classification NumberQA188 .B73 1999
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