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How to Count = An Introduction to Co...
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How to Count = An Introduction to Combinatorics and Its Applications /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
How to Count/ by Robert A. Beeler.
其他題名:
An Introduction to Combinatorics and Its Applications /
作者:
Beeler, Robert A.
面頁冊數:
XV, 361 p. 61 illus., 2 illus. in color.online resource. :
Contained By:
Springer Nature eBook
標題:
Combinatorics. -
電子資源:
https://doi.org/10.1007/978-3-319-13844-2
ISBN:
9783319138442
How to Count = An Introduction to Combinatorics and Its Applications /
Beeler, Robert A.
How to Count
An Introduction to Combinatorics and Its Applications /[electronic resource] :by Robert A. Beeler. - 1st ed. 2015. - XV, 361 p. 61 illus., 2 illus. in color.online resource.
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.
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.
ISBN: 9783319138442
Standard No.: 10.1007/978-3-319-13844-2doiSubjects--Topical Terms:
669353
Combinatorics.
LC Class. No.: QA164-167.2
Dewey Class. No.: 511.6
How to Count = An Introduction to Combinatorics and Its Applications /
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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.
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