Combinatorics: A Guided Tour (MAA Textbooks)

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9780883857625: Combinatorics: A Guided Tour (MAA Textbooks)

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, Pólya 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.

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Book Description:

Combinatorics is the mathematics of counting. This text presents the topics covered in undergraduate courses in combinatorics and advanced discrete mathematics, as well as in some introductory graduate courses. Uniquely, it features over 350 reading questions that provide checkpoints for learning and prepare the reader for the end-of-section exercises.

About the Author:

David Mazur is Associate Professor of Mathematics at Western New England College in Springfield, Massachusetts. He received his undergraduate degree in mathematics from the University of Delaware in 1993. He then began graduate study at The Johns Hopkins University where he earned a Master's in 1996 and a Ph.D. in 1999, focusing on operations research, integer programming, and polyhedral combinatorics. He was a 2000-2001 Project NExT fellow and continues to be active in the Mathematical Association of America.

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Book Description Mathematical Association of America, United States, 2010. Hardback. Book Condition: New. Language: English . Brand New Book. 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. 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. It also features 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. Bookseller Inventory # AAA9780883857625

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Book Description Mathematical Association of America, United States, 2010. Hardback. Book Condition: New. UK ed.. Language: English . Brand New Book. 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. 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. It also features 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. Bookseller Inventory # AAA9780883857625

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