Combinatorics: A Guided Tour

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Combinatorics: A Guided Tour

⑂ Combinatorics: A Guided Tour textCombinatorics: A Guided Tour ⑫ Kindle Ebook Author David R Mazur ┍ 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, P lya 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.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. 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