Research Problems in Discrete Geometry

Peter Brass, William Moser, Janos Pach

512 pages, parution le 04/11/2005

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Résumé

Although discrete geometry has a rich history extending more than 150 years, it abounds in open problems that even a high-school student can understand and appreciate. Some of these problems are notoriously difficult and are intimately related to deep questions in other fields of mathematics. But many problems, even old ones, can be solved by a clever undergraduate or a high-school student equipped with an ingenious idea and the kinds of skills used in a mathematical olympiad.

Research Problems in Discrete Geometry is the result of a 25-year-old project initiated by the late Leo Moser. It is 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.

Important features include:

More than 500 open problems, some old, others new and never before published;
Each chapter divided into self-contained sections, each section ending with an extensive bibliography;
A great selection of research problems for graduate students looking for a dissertation topic;
A comprehensive survey of discrete geometry, highlighting the frontiers and future of research;
More than 120 figures;
A preface to an earlier version written by the late Paul Erdos.

L'auteur - Peter Brass

Peter Brass is Associate Professor of Computer Science at the City College of New York.

L'auteur - William Moser

William O. J. Moser is Professor Emeritus at McGill University.

L'auteur - Janos Pach

Janos Pach is Distinguished Professor at The City College of New York, Research Professor at the Courant Institute, NYU, and Senior Research Fellow at the Rényi Institute, Budapest.

Sommaire

Preface to an earlier version by Paul Erdos
Definitions and Notations
Density Problems for Packings and Coverings
Structural Packing and Covering Problems
Packing and Covering with Homothetic Copies
Tiling Problems
Distance Problems
Problems on Repeated Subconfigurations
Incidence and Arrangement Problems
Problems on Points in General Position
Graph Drawing and Geometric Graphs
Lattice Point Problems
Geometric Inequalities

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Peter Brass, William Moser, Janos Pach
Parution	04/11/2005
Nb. de pages	512
Format	16 x 24
Couverture	Relié
Poids	840g
Intérieur	Noir et Blanc
EAN13	9780387238159
ISBN13	978-0-387-23815-9