The Erdös distance problem

by Garibaldi, Julia

Type Book

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Title Statements

Full title :The Erdös distance problem / Julia Garibaldi, Alex Iosevich, Steven Senger.

Summary

The Erdős problem asks, What is the smallest possible number of distinct distances between points of a large finite subset of the Euclidean space in dimensions two and higher? The main goal of this book is to introduce the reader to the techniques, ideas, and consequences related to the Erdős problem. The authors introduce these concepts in a concrete and elementary way that allows a wide audience—from motivated high school students interested in mathematics to graduate students specializing in combinatorics and geometry—to absorb the content and appreciate its far-reaching implications. In the process, the reader is familiarized with a wide range of techniques from several areas of mathematics and can appreciate the power of the resulting symbiosis. The book is heavily problem oriented, following the authors' firm belief that most of the learning in mathematics is done by working through the exercises. Many of these problems are recently published results by mathematicians working in the area. The order of the exercises is designed both to reinforce the material presented in the text and, equally importantly, to entice the reader to leave all worldly concerns behind and launch head first into the multifaceted and rewarding world of Erdős combinatorics. --

Edition Statements

Publication Date:©2011.

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, R.I
Language:eng
Publication Date:©2011.

The Physical Object

Description:xii, 150 pages : : illustrations ; : 22 cm.

Edition Identifiers

ISBN:9780821852811, 0821852817
oclc:ocn657223794
LC Classification:QA164
Dewey Decimal:511/.6

1. The [square root of n] theory -- 2. The [n to the 2/3 power] theory -- 3. The Cauchy-Schwarz inequality -- 4. Graph theory and incidences -- 5. The [n to the 4/5 power] theory -- 6. The [n to the 6/7 power] theory -- 7. Beyond [n to the 6/7 power] -- 8. Information theory -- 9. Dot products -- 10. Vector spaces over finite fields -- 11. Distances in vector spaces over finite fields.

Subjects

Analyse combinatoire Analyse harmonique Combinatorial analysis Combinatorial geometry Combinatorics Computational complexity Fourier analysis Geometrie geometry Harmonic analysis Harmonic analysis on Euclidean spaces Harmonische Analyse Kombinatorik Kombinatorische Analysis Number theory Théorie des nombres ZAHLENTHEORIE