Lectures on Discrete Geometry (Graduate Texts in Mathematics, 212) by Jiri (PDF)

Description

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.

User’s Reviews

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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a well written book on the geometry that is critical to so many different fields of math, including combinatorial optimization and linear optimization.

⭐

⭐hi,i’d like to thank you for excellent product and service.i got the book very shortly after ordering it, and much time(!) before your commitment.i found this book very helpful for my studies.thanks again,shai

⭐This is an excellent book. I read completely and carefully the last chapter on embeddings of metric spaces and some portions of previous chapters. It was a really enjoyable reading. Also it was the only book among those which I read so far for which I was unable to resist the temptation to solve all the exercises, at least those which have rank 3 and higher. (Reading some of the books I do not have such temptation at all.) It is unfortunate that the author updated the book only for the Japanese translation and the notes which he posted on his web page. It would be nice if the author will publish a new updated edition.

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Free Download Lectures on Discrete Geometry (Graduate Texts in Mathematics, 212) in PDF format
Lectures on Discrete Geometry (Graduate Texts in Mathematics, 212) PDF Free Download
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Lectures on Discrete Geometry (Graduate Texts in Mathematics, 212) 2002 PDF Free Download
Download Lectures on Discrete Geometry (Graduate Texts in Mathematics, 212) PDF
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