Combinatorics: Ancient and Modern

Paperback | March 11, 2015

EditorRobin Wilson, John J. Watkins

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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 sixteenexperts. 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 sevenchapters 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 distinguishedcombinatorialist, 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 ofmathematics 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.

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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 subj...

Robin Wilson is an Emeritus Professor of Pure Mathematics at the Open University, Emeritus Professor of Geometry at Gresham College, London, and a former Fellow of Keble College, Oxford. He was President of the British Society for the History of Mathematics from 2012 to 2014s. He has written and edited many books on graph theory, incl...

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Format:PaperbackDimensions:400 pages, 9.21 × 6.14 × 0.81 inPublished:March 11, 2015Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198739052

ISBN - 13:9780198739050

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Table of Contents

INTRODUCTIONDONALD E. KNUTH: Two Thousand Years of CombinatoricsPART I: ANCIENT COMBINATORICS1. TAKANORI KUSUBA and KIM PLOFKER: Indian Combinatorics2. ANDREA BREARD: China3. AHMED DJEBBAR: Islamic Combinatorics4. VICTOR J. KATZ: Jewish Combinatorics5. EBERHARD KNOBLOCH: Renaissance Combinatorics6. EBERHARD KNOBLOCH: The Origins of Modern Combinatorics7. A. W. F. EDWARDS: The Arithmetical TrianglePART II: MODERN COMBINATORICS8. ROBIN WILSON: Early Graph Theory9. GEORGE E. ANDREWS: Partitions10. NORMAN BIGGS and ROBIN WILSON: Block Designs11. LARS DOVLING ANDERSEN: Latin Squares12. E. KEITH LLOYD: Enumeration (18th-20th Centuries)13. IAN ANDERSON: Combinatorial Set Theory14. LOWELL BEINEKE and ROBIN WILSON: Modern Graph TheoryAFTERMATHPETER J. CAMERON: A Personal View of Combinatroics