Research Problems in Discrete Geometry

by Peter Brass, William O. J. Moser, Jïnos Pach

Overview

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.

Product Details

ISBN-13:	9781441920164
Publisher:	Springer New York
Publication date:	10/29/2010
Edition description:	Softcover reprint of hardcover 1st ed. 2005
Pages:	500
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

About the Author

Pach is a distinguished researcher at NYU, his book "Combinatorial Geometry," 1995, Wiley, is considered "the bible" in the area of discrete geometry. He has also published several books with Springer-Verlag.

William O.J. Moser is a Springer author as well. He has been awarded the CMS 2003 Distinguished Service Award for his sustained and significant contributions to the Canadian mathematical community.

Table of Contents

Preface.- 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.- Author Index.- Subject Index.

Editorial Reviews

From the reviews:

"Research Problems in Discrete Geometry has recently been released by Springer. This book collects hundreds of questions and open conjectures in the field, and discusses partial results … . The book very efficiently and clearly describes the relevant definitions … . The book is very well annotated, with a comprehensive bibliography after every set of problems … . Brass, Moser, and Pach have done a very nice job in putting this collection together … an excellent addition to any library or math department lounge." (Daren Glass, MathDL – Online, October, 2006)

"Many problems in discrete geometry have an intuitive appeal … . This book is a large collection of such problems … . the collection is quite impressive and is likely to be appreciated by a large audience of mathematicians … . an up-to-date bibliography is given, making this book a valuable source of reference. The whole text is written in a pleasant, easy to read style. The great number of beautiful illustrations help with the explanations and make the book even more attractive." (W. Kuperberg, Mathematical Reviews, 2006 i)

"The book is written in the style of Paul Erdös’s problem articles. … Each section is a self-contained essay that provides the history of a problem, known partial results, motivation and bibliography – everything needed for the reader, especially a young mathematician seeking a problem to conquer … . Professionals will find the book to be a valuable encyclopedic source for their research. Indeed, this is an exceptional book, a must for all active mathematicians." (Alexander Soifer, Zentralblatt MATH, Vol. 1086, 2006)

"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 historicaldetails 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." (L'Enseignement Mathématique, Vol. 52 (2), 2006)

"The origin of this book is an informal list of problems, first distributed by Leo Moser (1921-1970) in 1963 (in Boulder, Colorado) and then in 1977 (in Oberwolfach). It soon became famous in the discrete geometry community, was widely distributed and updated several times. … this is a ‘long-awaited’ book which turns out to be not only a valuable source for researchers, but is also a very readable panorama of discrete geometry for all who are interested in this subject." (P. Schmitt, Monatshefte für Mathematik, Vol. 151 (4), 2007)

"This is a book that gathers together an enormous number of open problems in Discrete Geometry. … The intended audience is both researchers and graduate students … . This is a very nice collection of problems. If you want to learn some open problems in Discrete Geometry this is clearly the book to go to. … An interested undergraduate, or someone in a different field, can get a start in this field through this book." (William Gasarch, SIGACT News, Vol. 38 (4), 2007)

From the Publisher