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How to Count [electronic resource] : An Introduction to Combinatorics and Its Applications / by Robert A. Beeler

Author
Beeler, Robert A.
Published
Cham : Springer International Publishing : Imprint: Springer, 2015.
Physical Description
XV, 361 pages 61 illustrations, 2 illustrations in color : online resource
Additional Creators
SpringerLink (Online service)
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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.
Summary
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.
Subject(s)
ISBN
9783319138442
Digital File Characteristics
text file PDF
Note
AVAILABLE ONLINE TO AUTHORIZED PSU USERS.
Part Of
Springer eBooks
View MARC record | catkey: 14701622