How to Count

Robert A. Beeler is an Associate Professor of Mathematics at East Tennessee State University. His research interests include enumerative combinatorics and graph theory; edge decompositions of graphs, graceful labelings on graphs, intersection/representation theory, and combinatorial designs; combinatorial games and games on graphs. He is a member of the Mathematics Association of America, the American Mathematical Society, and the Institute of Combinatorics and its Applications.

Preliminaries.- Basic Counting.- The Binomial Coefficient.- Distribution Problems.- Generating Functions.- Recurrence Relations.- Advanced Counting - Inclusion and Exclusion.- Advanced Counting - Polya Theory.- Application: Probability.- Application: Combinatorial Designs.- Application: Graph Theory.- Appendices.

"The book is an excellent introduction to combinatorics. ... The author uses a clear language and often provides an easy intuitive access to abstract subjects. The presentation is well motivated, the explanations are transparent and illustrated by carefully selected examples. Each section ends with a list of well formulated exercises which make the book ideally suited for self-instruction." (Astrid Reifegerste, zbMATH 1328.05001, 2016)

"This book by Beeler ... is an excellent introductory text on combinatorics. The author gives the right balance of theory, computation, and applications, and he presents introductory-level topics, such as the multiplication principle, binomial theorem, and distribution problems in a clear manner. ... Summing Up: Highly recommended. Upper-division undergraduates through researchers and faculty." (S. L. Sullivan, Choice, Vol. 53 (1), September, 2015)