Combinatorial Geometry with Applications to Field Theory, Second Edition, graduate textbook in mathematics PDF Download

Author: Linfan Mao
Publisher: Infinite Study
ISBN: 159973155X
Category : Combinatorial geometry
Languages : en
Pages : 502

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Author: Linfan Mao
Publisher:
ISBN: 9781461914068
Category : Combinatorial geometry
Languages : en
Pages : 484

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Author: János Pach
Publisher: John Wiley & Sons
ISBN: 1118031369
Category : Mathematics
Languages : en
Pages : 376

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Book Description
A complete, self-contained introduction to a powerful and resurgingmathematical discipline . Combinatorial Geometry presents andexplains with complete proofs some of the most important resultsand methods of this relatively young mathematical discipline,started by Minkowski, Fejes Toth, Rogers, and Erd???s. Nearly halfthe results presented in this book were discovered over the pasttwenty years, and most have never before appeared in any monograph.Combinatorial Geometry will be of particular interest tomathematicians, computer scientists, physicists, and materialsscientists interested in computational geometry, robotics, sceneanalysis, and computer-aided design. It is also a superb textbook,complete with end-of-chapter problems and hints to their solutionsthat help students clarify their understanding and test theirmastery of the material. Topics covered include: * Geometric number theory * Packing and covering with congruent convex disks * Extremal graph and hypergraph theory * Distribution of distances among finitely many points * Epsilon-nets and Vapnik--Chervonenkis dimension * Geometric graph theory * Geometric discrepancy theory * And much more

Author: Linfan Mao
Publisher: Infinite Study
ISBN: 1599731002
Category : Mathematics
Languages : en
Pages : 499

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This monograph is motivated with surveying mathematics and physics by CC conjecture, i.e., a mathematical science can be reconstructed from or made by combinatorialization. Topics covered in this book include fundamental of mathematical combinatorics, differential Smarandache n-manifolds, combinatorial or differentiable manifolds and submanifolds, Lie multi-groups, combinatorial principal fiber bundles, gravitational field, quantum fields with their combinatorial generalization, also with discussions on fundamental questions in epistemology. All of these are valuable for researchers in combinatorics, topology, differential geometry, gravitational or quantum fields.

Author: Herbert Edelsbrunner
Publisher: Springer Science & Business Media
ISBN: 9783540137221
Category : Computers
Languages : en
Pages : 446

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Book Description
Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.

Author: Jacob E. Goodman
Publisher: Cambridge University Press
ISBN: 9780521848626
Category : Computers
Languages : en
Pages : 640

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Book Description
This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.

Author: Ezra Miller
Publisher: American Mathematical Soc.
ISBN: 0821837362
Category : Combinatorial analysis
Languages : en
Pages : 705

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Book Description
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.

Author: Günter Ewald
Publisher: Springer Science & Business Media
ISBN: 1461240441
Category : Mathematics
Languages : en
Pages : 378

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Book Description
The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties. The first part of the book covers the theory of polytopes and provides large parts of the mathematical background of linear optimization and of the geometrical aspects in computer science. The second part introduces toric varieties in an elementary way.

Author: Vladimir Boltyanski
Publisher: Springer Science & Business Media
ISBN: 3642592376
Category : Mathematics
Languages : en
Pages : 428

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siehe Werbetext.

Author: Linfan MAO
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 35

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The universality of contradiction and connection of things in nature implies that a thing is nothing else but a labeled topological graph GL with a labeling map L.