Overview

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.

Full Product Details

9781420082609

Table of Contents

Reviews

! 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

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

Author Information

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.

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available