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How to count = an introduction to co...

Beeler, Robert A.

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How to count = an introduction to combinatorics and its applications /

紀錄類型:	書目-電子資源 : 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.
出版者:	Cham :Springer International Publishing : : 2015.,
面頁冊數:	xv, 361 p. :ill. (some col.), digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Combinatorial analysis. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-13844-2
ISBN:	9783319138442 (electronic bk.)

How to count = an introduction to combinatorics and its applications /
Beeler, Robert A.

How to countan introduction to combinatorics and its applications /[electronic resource] :by Robert A. Beeler. - Cham :Springer International Publishing :2015. - xv, 361 p. :ill. (some col.), digital ;24 cm.

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 (electronic bk.)

Standard No.: 10.1007/978-3-319-13844-2doiSubjects--Topical Terms:

523878
Combinatorial analysis.

LC Class. No.: QA164

Dewey Class. No.: 511.6

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520 $a 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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