How to Count

! 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 Completely revised, the book shows how to solve numerous classic and other interesting combinatorial problems. ! The reading list at the end of the book gives direction to exploring more complicated counting problems as well as other areas of combinatorics. --Zentralblatt MATH 1197