How to Count

An Introduction to Combinatorics, Second Edition

R.B.J.T. Allenby, Alan Slomson

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Hardback

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English

Chapman and Hall
12 August 2010

Mathematics & Sciences; Combinatorics & graph theory

Suitable for self-study or a first course in combinatorics at the undergraduate level, How to Count: An Introduction to Combinatorics, Second Edition follows a similar approach to its predecessor. This second edition continues to focus on counting problems and emphasize a problem solving approach. It includes a new chapter on graph theory and many more exercises, some with full solutions or hints. The authors provide proofs of all significant results and illustrate applications from other areas of mathematics, such as elementary ideas from analysis in proving Stirling's formula. A solutions manual is available for qualifying instructors.

By: R.B.J.T. Allenby, Alan Slomson
Imprint: Chapman and Hall
Country of Publication: United Kingdom
Edition: 2nd New edition
Volume: v. 60
Dimensions: Height: 254mm, Width: 178mm, Spine: 25mm
Weight: 964g
ISBN: 9781420082609
ISBN 10: 1420082604
Pages: 444
Publication Date: 12 August 2010
Audience: College/higher education , A / AS level
Replaced By: 9781138093881
Format: Hardback
Publisher's Status: Active

What’s It All About?. Permutations and Combinations. Occupancy Problems. The Inclusion-Exclusion Principle. Stirling and Catalan Numbers. Partitions and Dot Diagrams. Generating Functions and Recurrence Relations. Partitions and Generating Functions. Introduction to Graphs. Trees. Groups of Permutations. Group Actions. Counting Patterns. Pólya Counting. Dirichlet’s Pigeonhole Principle. Ramsey Theory. Rook Polynomials and Matchings. Solutions to the A Exercises. Books for Further Reading. Index.

Alan Slomson taught mathematics at the University of Leeds from 1967 to 2008. He is currently the secretary of the United Kingdom Mathematics Trust. R.B.J.T. Allenby taught mathematics at the University of Leeds from 1965 to 2007.

Reviews for How to Count: An Introduction to Combinatorics, Second Edition

! thoughtfully written, contain[s] plenty of material and exercises ! very readable and useful ! --MAA Reviews, February 2011 The reasons I adopted this book are simple: it's the best one-volume book on combinatorics for undergraduates. It begins slowly and gently, but does not avoid subtleties or difficulties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence. Enumerative combinatorics is developed rather fully, through Stirling and Catalan numbers, for example, before generating functions are introduced. Thus this tool is very much appreciated and its 'naturalness' is easier to comprehend. Likewise, partitions are introduced in the absence of generating functions, and then later generating functions are applied to them: again, a wise pedagogical move. The ordering of chapters is nicely set up for two different single-semester courses: one that uses more algebra, culminating in Polya's counting theorem; the other concentrating on graph theory, ending with a variety of Ramsey theory topics. ! I was very much impressed with the first edition when I encountered it in 1994. I like the second edition even more. ! --Paul Zeitz, University of San Francisco, California, USA