Combinatorics: Ancient & Modern

Combinatorics is the branch of discrete mathematics that studies (and counts) permutations, combinations, and arrangements of sets of elements. This book constitutes the first book-length survey of the history of combinatorics and uniquely assembles research in the area that would otherwise be inaccessible to the general reader.

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 is currently President of the British Society for the History of Mathematics. He has written and edited many books on graph theory, including Introduction to Graph Theory and Four Colours Suffice, and on the history of mathematics, including Lewis Carroll in Numberland. He is involved with the popularization and communication of mathematics and its history, and was awarded a Pólya prize by the Mathematical Association of America for 'outstanding expository writing'.
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.

- INTRODUCTION
- 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
- A Personal View of Combinatroics