Combinatorics: A Guided Tour - Rilegato

Mazur, David R.

Rilegato

ISBN 10: 0883857626 ISBN 13: 9780883857625

Casa editrice: The Mathematical Association of America, 2010

Riassunto

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. 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.

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Descrizione del libro:

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.

L'autore:

David R. Mazur is Associate Professor of Mathematics at Western New England College in Springfield, Massachusetts. He was born on October 23, 1971 in Washington, D.C. He received his undergraduate degree in Mathematics from the University of Delaware in 1993, and also won the Department of Mathematical Sciences' William D. Clark prize for 'unusual ability' in the major that year. He then received two fellowships for doctoral study in the Department of Mathematical Sciences (now the Department of Applied Mathematics and Statistics) at The Johns Hopkins University. From there he received his Master's in 1996 and his Ph.D. in 1999 under the direction of Leslie A. Hall, focusing on operations research, integer programming, and polyhedral combinatorics. His dissertation, 'Integer Programming Approaches to a Multi-Facility Location Problem', won first prize in the 1999 joint United Parcel Service/INFORMS Section on Location Analysis Dissertation Award Competition. The competition occurs once every two years to recognize outstanding dissertations in the field of location analysis. Professor Mazur began teaching at Western New England College in 1999 and received tenure and promotion to Associate Professor in 2005. He was a 2000–2001 Project NExT fellow and continues to serve this program as a consultant. He is an active member of the Mathematical Association of America, having co-organized several sessions at national meetings. He currently serves on the MAA's Membership Committee.

Su questa edizione

• Editore: The Mathematical Association of America
• Data di pubblicazione: 2010
• ISBN 10: 0883857626
• ISBN 13: 9780883857625
• Rilegatura: Copertina rigida
• Numero di pagine: 410