Combinatorics: Ancient & Modern

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Robin Wilson (, Emeritus Professor of Pure Mathematics, The Open University, UK and a Visiting Professor in the History of Mathematics at the London School of Economics.) John J. Watkins (, Emeritus Professor of Mathematics, Colorado College)

Combinatorics

Ancient & Modern

Robin Wilson (, Emeritus Professor of Pure Mathematics, The Open University, UK and a Visiting Professor in the History of Mathematics at the London School of Economics.), John J. Watkins (, Emeritus Professor of Mathematics, Colorado College)

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English

Oxford University Press
12 March 2015

Mathematics & Sciences; Discrete mathematics; Combinatorics & graph theory; History of mathematics

Who first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.)

The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

Edited by: Robin Wilson ( Emeritus Professor of Pure Mathematics The Open University UK and a Visiting Professor in the History of Mathematics at the London School of Economics.), John J. Watkins (, Emeritus Professor of Mathematics, Colorado College)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 160mm, Spine: 21mm
Weight: 1g
ISBN: 9780198739050
ISBN 10: 0198739052
Pages: 400
Publication Date: 12 March 2015
Audience: College/higher education , Further / Higher Education
Format: Paperback
Publisher's Status: Active

INTRODUCTION DONALD E. KNUTH: Two Thousand Years of Combinatorics PART I: ANCIENT COMBINATORICS 1: TAKANORI KUSUBA and KIM PLOFKER: Indian Combinatorics 2: ANDREA BRÉARD: China 3: AHMED DJEBBAR: Islamic Combinatorics 4: VICTOR J. KATZ: Jewish Combinatorics 5: EBERHARD KNOBLOCH: Renaissance Combinatorics 6: EBERHARD KNOBLOCH: The Origins of Modern Combinatorics 7: A. W. F. EDWARDS: The Arithmetical Triangle PART II: MODERN COMBINATORICS 8: ROBIN WILSON: Early Graph Theory 9: GEORGE E. ANDREWS: Partitions 10: NORMAN BIGGS and ROBIN WILSON: Block Designs 11: LARS DØVLING ANDERSEN: Latin Squares 12: E. KEITH LLOYD: Enumeration (18th-20th Centuries) 13: IAN ANDERSON: Combinatorial Set Theory 14: LOWELL BEINEKE and ROBIN WILSON: Modern Graph Theory AFTERMATH PETER J. CAMERON: A Personal View of Combinatroics

John J. Watkins is an Emeritus Professor of Mathematics at Colorado College, USA. He received his doctorate from the University of Kansas, specializing in commutative ring theory. His main research interest, however, has been in graph theory and he has published mainly in this area, including many papers with undergraduates as co-authors. He has written several books, including Graphs: An Introductory Approach, Across the Board: The Mathematics of Chessboard Problems, and Topics in Commutative Ring Theory, and has recently finished his latest book, Elementary Number Theory. Colorado College presented John Watkins with the 2005 Boettcher Award for Faculty Excellence.