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 Discrete Geometry
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Editorial Reviews
Review
From the reviews: "Discrete geometry is not quite a newcomer on the stage of mathematics. … The book under review covers … a gap in the pedagogical literature, providing an expository treatment of a wide range of topics in discrete geometry, without assuming too many prerequisites from the reader. … it will be ideal to be used both as a textbook and for self-study. … In fact … this book can be used as a ‘mathematical companion’ to a textbook on computational geometry … ." (Paul A. Blaga, Studia Universitatis Babes-Bolyai Mathematica, Vol. XLVIII (1), March, 2004) "Matoušek’s excellent new book concerns discrete geometry. … The style is clear and pleasant; things are streamlined and collected in one place, and are explained on simple, concrete examples. … a final chapter on ‘What was it about? An informal summary’ was an innovation that I found to be an excellent idea. Lectures on discrete geometry is a splendid book. I recommend it both to students and researchers in the field, as well as to those who like mathematics for its own inherent beauty." (Imre Bárány, Bulletin of the London Mathematical Society, Issue 35, 2003) "This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections, and thus, it can serve as a collection of surveys in several narrower subfields." (L’ENSEIGNEMENT MATHEMATIQUE, Vol. 48 (3-4), 2002) "This is an introduction to the field of discrete geometry understood as the investigation of combinatorial properties of configurations of (usually finitely many) geometric objects … . The book is written in a lively and stimulating but very precise style and contains many figures. It gives a good impression of the richness and the relevance of the field." (Johann Linhart, Zentralblatt Math, Vol. 999 (24), 2002)
From the Back Cover
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics 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; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Computer Science at Charles University in Prague. His research has contributed to several of the considered areas and to their algorithmic applications. This is his third book.
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Inside This Book
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First Sentence:
Linear subspaces. Let Rd denote the d-dimensional Euclidean space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
halving edges, ill general position, cutting lemma, first selection lemma, flattening lemma, algebraic surface patches, general posit ion, zone theorem, upper hound theorem, perfect graph conjecture, enclosing ellipsoid, point line incidences, hamming cube, blue facets, epsilon nets, cyclic polytope, disjoint convex sets, finite metric spaces, net theorem, vent ices, convex position, lowest vertex, vert ices, lower envelope, finite point set Key Phrases - Capitalized Phrases (CAPs): (learn more)
Davenport Schinzel, Exercises Let, Brunn Minkowski, Tight Lower Bound, Use Ramsey New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Linear subspaces. Let Rd denote the d-dimensional Euclidean space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
halving edges, ill general position, cutting lemma, first selection lemma, flattening lemma, algebraic surface patches, general posit ion, zone theorem, upper hound theorem, perfect graph conjecture, enclosing ellipsoid, point line incidences, hamming cube, blue facets, epsilon nets, cyclic polytope, disjoint convex sets, finite metric spaces, net theorem, vent ices, convex position, lowest vertex, vert ices, lower envelope, finite point set Key Phrases - Capitalized Phrases (CAPs): (learn more)
Davenport Schinzel, Exercises Let, Brunn Minkowski, Tight Lower Bound, Use Ramsey New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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30
books
cite this book:
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- Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang in Back Matter (1), Back Matter (2), and Back Matter (3)
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Front Matter, and Back Matter
- An Introduction to Algebraic Topology (Graduate Texts in Mathematics) by Joseph J. Rotman in Back Matter (1), and Back Matter (2)
- A Short Course on Spectral Theory by William Arveson in Back Matter
- Galois Theory (Graduate Texts in Mathematics) by Harold M. Edwards in Back Matter
See all 100 books this book cites
- Convex Polytopes (Graduate Texts in Mathematics) by Branko Grunbaum in Back Matter (1), and Back Matter (2)
- Introduction to Smooth Manifolds by John M. Lee in Back Matter
- Partial Differential Equations by Jürgen Jost in Back Matter
- Elliptic Curves (Graduate Texts in Mathematics) by Dale Husemöller in Back Matter
- Smooth Manifolds and Observables by Jet Nestruev in Back Matter
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