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How to count :an introduction to com...

Beeler, Robert A.

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 :Robert A. Beeler.
其他題名:	an introduction to combinatorics and its applications /
作者:	Beeler, Robert A.
出版者:	Cham :Springer,c2015.
面頁冊數:	xv, 361 p. :ill. ;25 cm.
標題:	Combinatorial analysis.
ISBN:	9783319138435 (hbk.) :

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

How to count :an introduction to combinatorics and its applications /Robert A. Beeler. - Cham :Springer,c2015. - xv, 361 p. :ill. ;25 cm.

Includes bibliographical references and index.

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: 9783319138435 (hbk.) :NT$1383Subjects--Topical Terms:

182280
Combinatorial analysis.

LC Class. No.: QA164 / .B44 2015

Dewey Class. No.: 511/.6

How to count :an introduction to combinatorics and its applications /
LDR:02184cam a2200229 a 4500 001 457894
003 OCoLC
005 20150728105327.0
008 150922s2015 sz a b 001 0 eng d
020 $a 9783319138435 (hbk.) : $c NT$1383
020 $a 331913843X (hbk.)
020 $z 9783319138442 (ebk.)
035 $a (OCoLC)894745613
035 $a 894745613
040 $a YDXCP $b eng $c YDXCP $d BTCTA $d OCLCQ $d OCLCO $d NHM $d CDX $d DXU $d UtOrBLW
050 4 $a QA164 $b .B44 2015
082 0 4 $a 511/.6 $2 23
100 1 $a Beeler, Robert A. $3 709057
245 1 0 $a How to count : $b an introduction to combinatorics and its applications / $c Robert A. Beeler.
260 $a Cham : $b Springer, $c c2015.
300 $a xv, 361 p. : $b ill. ; $c 25 cm.
504 $a Includes bibliographical references and index.
505 0 $a 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.
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.
650 0 $a Combinatorial analysis. $3 182280