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Computing the Continuous Discretely: Integer-point Enumeration in Polyhedra (Undergraduate Texts in Mathematics) - Softcover
Synopsis
This much-anticipated textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. It weaves a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory.
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From the Back Cover
This much-anticipated textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. Because there is no other book that puts together all of these ideas in one place, this text is truly a service to the mathematical community.
We encounter here a friendly invitation to the field of "counting integer points in polytopes," also known as Ehrhart theory, and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant, and the authors' engaging style encourages such participation. The many compelling pictures that accompany the proofs and examples add to the inviting style.
For teachers, this text is ideally suited as a capstone course for undergraduate students or as a compelling text in discrete mathematical topics for beginning graduate students. For scientists, this text can be utilized as a quick tooling device, especially for those who want a self-contained, easy-to-read introduction to these topics.
About the Author
Matthias Beck is Professor of Mathematics at San Francisco State University. Sinai Robins is Associate Professor of Mathematics at Nanyang Technological University, Singapore.
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- PublisherSpringer
- Publication date2010
- ISBN 10 1441921192
- ISBN 13 9781441921192
- BindingPaperback
- LanguageEnglish
- Number of pages244
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Computing the Continuous Discretely
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of 'counting integer points in polytopes', and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant. 244 pp. Englisch. Seller Inventory # 9781441921192
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - The world is continuous, but the mind is discrete. David Mumford We seek to bridge some critical gaps between various elds of mathematics by studying the interplay between the continuous volume and the discrete v- ume of polytopes. Examples of polytopes in three dimensions include crystals, boxes, tetrahedra, and any convex object whose faces are all at. It is amusing to see how many problems in combinatorics, number theory, and many other mathematical areas can be recast in the language of polytopes that exist in some Euclidean space. Conversely, the versatile structure of polytopes gives us number-theoretic and combinatorial information that ows naturally from their geometry. Fig. 0. 1. Continuous and discrete volume. The discrete volume of a body P can be described intuitively as the number of grid points that lie inside P, given a xed grid in Euclidean space. The continuous volume of P has the usual intuitive meaning of volume that we attach to everyday objects we see in the real world. VIII Preface Indeed, the di erence between the two realizations of volume can be thought of in physical terms as follows. On the one hand, the quant- level grid imposed by the molecular structure of reality gives us a discrete notion of space and hence discrete volume. On the other hand, the N- tonian notion of continuous space gives us the continuous volume. Seller Inventory # 9781441921192
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The authors write with flair and have chosen a unique set of topicsPlaces a strong emphasis on computational techniquesContains more than 200 exercises and has been heavily class-testedIncludes hints to selected exercisesT. Seller Inventory # 4172652
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