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How to Count

An Introduction to Combinatorics and Its Applications

Author: Robert A. Beeler  

Providing a self-contained resource for upper undergraduate courses in combinatorics, this text emphasizes computation, problem solving, and proof technique. When possible, the book introduces concepts using combinatorial methods (as opposed to induction or algebra) to prove identities.

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Summary

Providing a self-contained resource for upper undergraduate courses in combinatorics, this text emphasizes computation, problem solving, and proof technique. When possible, the book introduces concepts using combinatorial methods (as opposed to induction or algebra) to prove identities.

Read more

Description

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.

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Critic Reviews

“"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)”

“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)

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About the Author

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.

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Back Cover

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.

Read more

Product Details

Publisher
Springer International Publishing Ag | Springer International Publishing AG
Published
27th March 2015
Edition
2015th
Pages
361
ISBN
9783319138435

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