How to Count: An Introduction to Combinatorics and Its Applications by Robert A. BeelerHow to Count: An Introduction to Combinatorics and Its Applications by Robert A. Beeler

How to Count: An Introduction to Combinatorics and Its Applications

byRobert A. Beeler

Hardcover | March 27, 2015

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Providing a self-contained resource for upper undergraduate courses in combinatorics, this text emphasizes computation, problem solving, and proof technique. In particular, the book places special emphasis the Principle of Inclusion and Exclusion and the Multiplication Principle. To this end, exercise sets are included at the end of every section, ranging from simple computations (evaluate a formula for a given set of values) to more advanced proofs. The exercises are designed to test students' understanding of new material, while reinforcing a working mastery of the key concepts previously developed in the book. Intuitive descriptions for many abstract techniques are included. Students often struggle with certain topics, such as generating functions, and this intuitive approach to the problem is helpful in their understanding. When possible, the book introduces concepts using combinatorial methods (as opposed to induction or algebra) to prove identities. Students are also asked to prove identities using combinatorial methods as part of their exercises. These methods have several advantages over induction or algebra.
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 ...
Title:How to Count: An Introduction to Combinatorics and Its ApplicationsFormat:HardcoverDimensions:361 pages, 23.5 × 15.5 × 0.01 inPublished:March 27, 2015Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:331913843X

ISBN - 13:9783319138435


Table of Contents

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.

Editorial Reviews

"The book is an excellent introduction tocombinatorics. . The author uses a clear language and often provides an easyintuitive access to abstract subjects. The presentation is well motivated, theexplanations are transparent and illustrated by carefully selected examples.Each section ends with a list of well formulated exercises which make the bookideally suited for self-instruction." (Astrid Reifegerste, zbMATH 1328.05001,2016)"This book by Beeler . is an excellent introductorytext on combinatorics. The author gives the right balance of theory,computation, and applications, and he presents introductory-level topics, suchas the multiplication principle, binomial theorem, and distribution problems ina clear manner. . Summing Up: Highly recommended. Upper-division undergraduatesthrough researchers and faculty." (S. L. Sullivan, Choice, Vol. 53 (1),September, 2015)