Combinatorial Geometry

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9780471588900: Combinatorial Geometry
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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

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From the Publisher:

A broad perspective on an area of discrete mathematics, combinatorial geometry demonstrates that important results in many areas of number theory can be established by easy geometric arguments. This book is a comprehensive overview of the field. Includes numerous exercises and solutions.

From the Inside Flap:

How many objects of a given shape and size can be packed into alarge box of fixed volume? Can one plant n trees in an orchard, notall along the same line, so that every line determined by two treeswill pass through a third? These questions, raised by Hilbert andSylvester roughly one hundred years ago, have generated a lot ofinterest among professional and amateur mathematicians andscientists. They have led to the birth of a new mathematicaldiscipline with close ties to classical geometry and number theory,and with many applications in coding theory, potential theory,computational geometry, computer graphics, robotics , etc.Combinatorial Geometry offers a self-contained introduction to thisrapidly developing field, where combinatorial and probabilistic(counting) methods play a crucial role. This book has grown out ofthe material of both undergraduate and graduate courses inmathematics and computer science given by János Pach at theCourant Institute of Mathematical Sciences, New York University.Divided into two parts— Arrangements of Convex Sets andArrangements of Points and Lines—it presents and explains someof the most important and ingenious results in combinatorialgeometry, including:

  • Dowker’s theorems
  • Fáry’s theorem
  • Fejes Tóth’ stheorems
  • Methods of Blichtfeldt and Rogers
  • Minkowski—Hlawka theorem
  • Koebe’s representation theorem
  • Lipton—Tarjan separator theorem
  • Theorems of Erd???s, Turán, and Ramsey
  • Szemerédi’s regularity lemma
  • Szemerédi—Trotter theorems
  • Methods of Clarkson, Edelsbrunner, Guibas, Sharir, andWelzl
  • Counterexample to Borsuk’s conjecture

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Janos Pach, Pankaj K. Agarwal
Published by John Wiley and Sons Ltd, United States (1995)
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Book Description John Wiley and Sons Ltd, United States, 1995. Hardback. Condition: New. Language: English. Brand new Book. A complete, self-contained introduction to a powerful and resurging mathematical discipline . Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Toth, Rogers, and Erd???s. Nearly half the results presented in this book were discovered over the past twenty years, and most have never before appeared in any monograph. Combinatorial Geometry will be of particular interest to mathematicians, computer scientists, physicists, and materials scientists interested in computational geometry, robotics, scene analysis, and computer-aided design. It is also a superb textbook, complete with end-of-chapter problems and hints to their solutions that help students clarify their understanding and test their mastery 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. Seller Inventory # AAH9780471588900

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Book Description John Wiley and Sons Ltd, United States, 1995. Hardback. Condition: New. Language: English. Brand new Book. A complete, self-contained introduction to a powerful and resurging mathematical discipline . Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Toth, Rogers, and Erd???s. Nearly half the results presented in this book were discovered over the past twenty years, and most have never before appeared in any monograph. Combinatorial Geometry will be of particular interest to mathematicians, computer scientists, physicists, and materials scientists interested in computational geometry, robotics, scene analysis, and computer-aided design. It is also a superb textbook, complete with end-of-chapter problems and hints to their solutions that help students clarify their understanding and test their mastery 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. Seller Inventory # AAH9780471588900

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Book Description John Wiley and Sons Ltd, United States, 1995. Hardback. Condition: New. Language: English. Brand new Book. A complete, self-contained introduction to a powerful and resurging mathematical discipline . Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Toth, Rogers, and Erd???s. Nearly half the results presented in this book were discovered over the past twenty years, and most have never before appeared in any monograph. Combinatorial Geometry will be of particular interest to mathematicians, computer scientists, physicists, and materials scientists interested in computational geometry, robotics, scene analysis, and computer-aided design. It is also a superb textbook, complete with end-of-chapter problems and hints to their solutions that help students clarify their understanding and test their mastery 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. Seller Inventory # LIE9780471588900

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