Convex And Discrete Geometry

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Convex and Discrete Geometry

Peter M. Gruber
Convex and Discrete Geometry Book PDF

Author : Peter M. Gruber
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 47,8 Mb
Release : 2007-05-17
Category : Mathematics
ISBN : 9783540711339

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Convex and Discrete Geometry by Peter M. Gruber Pdf

Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers, and useful to people working in the applied fields.

The Cube-A Window to Convex and Discrete Geometry

Chuanming Zong
The Cube A Window to Convex and Discrete Geometry Book PDF

Author : Chuanming Zong
Publisher : Cambridge University Press
Page : 196 pages
File Size : 45,9 Mb
Release : 2006-02-02
Category : Mathematics
ISBN : 0521855357

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The Cube-A Window to Convex and Discrete Geometry by Chuanming Zong Pdf

Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory.

Lectures on Discrete Geometry

Jiri Matousek
Lectures on Discrete Geometry Book PDF

Author : Jiri Matousek
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 42,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461300397

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Lectures on Discrete Geometry by Jiri Matousek Pdf

The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.

Lectures on Convex Geometry

Daniel Hug,Wolfgang Weil
Lectures on Convex Geometry Book PDF

Author : Daniel Hug,Wolfgang Weil
Publisher : Springer Nature
Page : 287 pages
File Size : 42,7 Mb
Release : 2020-08-27
Category : Mathematics
ISBN : 9783030501808

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Lectures on Convex Geometry by Daniel Hug,Wolfgang Weil Pdf

This book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.

Convexity and Discrete Geometry Including Graph Theory

Karim Adiprasito,Imre Bárány,Costin Vilcu
Convexity and Discrete Geometry Including Graph Theory Book PDF

Author : Karim Adiprasito,Imre Bárány,Costin Vilcu
Publisher : Springer
Page : 280 pages
File Size : 50,9 Mb
Release : 2016-05-02
Category : Mathematics
ISBN : 9783319281865

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Convexity and Discrete Geometry Including Graph Theory by Karim Adiprasito,Imre Bárány,Costin Vilcu Pdf

This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.

Classical Topics in Discrete Geometry

Károly Bezdek
Classical Topics in Discrete Geometry Book PDF

Author : Károly Bezdek
Publisher : Springer Science & Business Media
Page : 171 pages
File Size : 52,8 Mb
Release : 2010-06-23
Category : Mathematics
ISBN : 9781441906007

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Classical Topics in Discrete Geometry by Károly Bezdek Pdf

Geometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast developing eld called discrete geometry. One can brie y describe this branch of geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, also includes the theory of polytopes and tilings in addition to the theory of packing and covering. D- crete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mat- matics, including convex and combinatorial geometry, coding theory, calculus of variations, di erential geometry, group theory, and topology, as well as geometric analysis and number theory.

Foundations of Convex Geometry

W. A. Coppel
Foundations of Convex Geometry Book PDF

Author : W. A. Coppel
Publisher : Cambridge University Press
Page : 236 pages
File Size : 49,5 Mb
Release : 1998-03-05
Category : Mathematics
ISBN : 0521639700

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Foundations of Convex Geometry by W. A. Coppel Pdf

This book on the foundations of Euclidean geometry aims to present the subject from the point of view of present day mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here real affine space is characterised by a small number of axioms involving points and line segments making the treatment self-contained and thorough, many results being established under weaker hypotheses than usual. The treatment should be totally accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.

Convex and Discrete Geometry

Peter Gruber
Convex and Discrete Geometry Book PDF

Author : Peter Gruber
Publisher : Springer
Page : 580 pages
File Size : 44,9 Mb
Release : 2009-09-02
Category : Mathematics
ISBN : 3540835903

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Convex and Discrete Geometry by Peter Gruber Pdf

Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers, and useful to people working in the applied fields.

Research Problems in Discrete Geometry

Peter Brass,William O. J. Moser,János Pach
Research Problems in Discrete Geometry Book PDF

Author : Peter Brass,William O. J. Moser,János Pach
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 43,6 Mb
Release : 2006-01-27
Category : Mathematics
ISBN : 9780387299297

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Research Problems in Discrete Geometry by Peter Brass,William O. J. Moser,János Pach Pdf

This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.

Strange Phenomena in Convex and Discrete Geometry

Chuanming Zong
Strange Phenomena in Convex and Discrete Geometry Book PDF

Author : Chuanming Zong
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461384816

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Strange Phenomena in Convex and Discrete Geometry by Chuanming Zong Pdf

Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can explain many of its problems, even the most difficult - such as the sphere-packing problem (what is the densest possible arrangement of spheres in an n-dimensional space?) and the Borsuk problem (is it possible to partition any bounded set in an n-dimensional space into n+1 subsets, each of which is strictly smaller in "extent" than the full set?) - in terms that a layman can understand; and one can reasonably make conjectures about their solutions with little training in mathematics.

Geometry - Intuitive, Discrete, and Convex

Imre Bárány,Károly Jr. Böröczky,Gábor Fejes Tóth,Janos Pach
Geometry Intuitive Discrete and Convex Book PDF

Author : Imre Bárány,Károly Jr. Böröczky,Gábor Fejes Tóth,Janos Pach
Publisher : Springer
Page : 367 pages
File Size : 43,5 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9783642414985

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Geometry - Intuitive, Discrete, and Convex by Imre Bárány,Károly Jr. Böröczky,Gábor Fejes Tóth,Janos Pach Pdf

The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth.

Discrete Geometry

Andras Bezdek
Discrete Geometry Book PDF

Author : Andras Bezdek
Publisher : CRC Press
Page : 492 pages
File Size : 49,9 Mb
Release : 2003-02-04
Category : Mathematics
ISBN : 0203911210

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Discrete Geometry by Andras Bezdek Pdf

Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analy

Selected Topics in Convex Geometry

Maria Moszynska
Selected Topics in Convex Geometry Book PDF

Author : Maria Moszynska
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 52,7 Mb
Release : 2006-11-24
Category : Mathematics
ISBN : 9780817644512

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Selected Topics in Convex Geometry by Maria Moszynska Pdf

Examines in detail those topics in convex geometry that are concerned with Euclidean space Enriched by numerous examples, illustrations, and exercises, with a good bibliography and index Requires only a basic knowledge of geometry, linear algebra, analysis, topology, and measure theory Can be used for graduates courses or seminars in convex geometry, geometric and convex combinatorics, and convex analysis and optimization

Bodies of Constant Width

Horst Martini,Luis Montejano,Déborah Oliveros
Bodies of Constant Width Book PDF

Author : Horst Martini,Luis Montejano,Déborah Oliveros
Publisher : Springer
Page : 486 pages
File Size : 50,6 Mb
Release : 2019-03-16
Category : Mathematics
ISBN : 9783030038687

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Bodies of Constant Width by Horst Martini,Luis Montejano,Déborah Oliveros Pdf

This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from several points of view, and, in doing so, shows surprising connections between various areas of mathematics. Concise explanations and detailed proofs demonstrate the many interesting properties and applications of these bodies. Numerous instructive diagrams are provided throughout to illustrate these concepts. An introduction to convexity theory is first provided, and the basic properties of constant width bodies are then presented. The book then delves into a number of related topics, which include Constant width bodies in convexity (sections and projections, complete and reduced sets, mixed volumes, and further partial fields) Sets of constant width in non-Euclidean geometries (in real Banach spaces, and in hyperbolic, spherical, and further non-Euclidean spaces) The concept of constant width in analysis (using Fourier series, spherical integration, and other related methods) Sets of constant width in differential geometry (using systems of lines and discussing notions like curvature, evolutes, etc.) Bodies of constant width in topology (hyperspaces, transnormal manifolds, fiber bundles, and related topics) The notion of constant width in discrete geometry (referring to geometric inequalities, packings and coverings, etc.) Technical applications, such as film projectors, the square-hole drill, and rotary engines Bodies of Constant Width: An Introduction to Convex Geometry with Applications will be a valuable resource for graduate and advanced undergraduate students studying convex geometry and related fields. Additionally, it will appeal to any mathematicians with a general interest in geometry.

Handbook of Convex Geometry

Bozzano G Luisa
Handbook of Convex Geometry Book PDF

Author : Bozzano G Luisa
Publisher : Elsevier
Page : 769 pages
File Size : 54,9 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080934402

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Handbook of Convex Geometry by Bozzano G Luisa Pdf

Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.