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Combinatorics: A Guided Tour(AMS/MAA Textbooks Vol. 55) H 390 p. 20

Combinatorics: A Guided Tour(AMS/MAA Textbooks Vol. 55) H 390 p. 20

著者:Mazur, David R.


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内容の説明

Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Polya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470. Most sections conclude with Travel Notes that add color to the material of the section via anecdotes, open problems, suggestions for further reading, and biographical information about mathematicians involved in the discoveries.

登録情報

商品コード:1031289186
出版社: Mathematical Association of America
出版年月: 2020/02
ISBN-10: 1470453002
ISBN-13: 978-1-4704-5300-8
出版国: アメリカ合衆国
装丁: hardcover/Geb./rel.
媒体: 冊子
ページ数: 390 p.
ジャンル: 数学基礎論



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