Student Mathematical Library 2003; 148 pp; softcover Volume: 23 ISBN10: 0821834819 ISBN13: 9780821834817 List Price: US$32 Member Price: US$25.60 Order Code: STML/23
 This book introduces readers to the language of generating functions, which nowadays, is the main language of enumerative combinatorics. The book starts with definitions, simple properties, and numerous examples of generating functions. It then discusses topics such as formal grammars, generating functions in several variables, partitions and decompositions, and the exclusioninclusion principle. In the final chapter, the author describes applications to enumeration of trees, plane graphs, and graphs embedded in twodimensional surfaces. Throughout the book, the author motivates readers by giving interesting examples rather than general theories. It contains numerous exercises to help students master the material. The only prerequisite is a standard calculus course. The book is an excellent text for a onesemester undergraduate course in combinatorics. Readership Advanced undergraduates, graduate students, and research mathematicians interested in modern methods of combinatorics. Reviews "A crisp and sophisticated text ... More examples than general theory. Covers standard material, but digs deeper ... An enjoyable read for professionals."  MAA Monthly "(This book) is driven by very, very interesting problems and examples."  MAA Reviews Table of Contents  Formal power series and generating functions. Operations with formal power series. Elementary generating functions
 Generating functions for wellknown sequences
 Unambiguous formal grammars. The Lagrange theorem
 Analytic properties of functions represented as power series and their asymptotics of their coefficients
 Generating functions of several variables
 Partitions and decompositions
 Dirichlet generating functions and the inclusionexclusion principle
 Enumeration of embedded graphs
 Final and bibliographical remarks
 Bibliography
 Index
