Author : Jiri Matousek
Publisher : Springer Science & Business Media
Page : 293 pages
File Size : 44,96 MB
Release : 2009-12-02
Category : Mathematics
ISBN : 3642039421
What is the "most uniform" way of distributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribution? This book is an accessible and lively introduction to the area of geometric discrepancy theory, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research.
Author : Giancarlo Travaglini
Publisher : Cambridge University Press
Page : 251 pages
File Size : 33,48 MB
Release : 2014-06-12
Category : Mathematics
ISBN : 1139992821
The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory, Fourier analysis and geometric discrepancy theory, and the relations between them, at the advanced undergraduate or beginning graduate level. It starts as a traditional course in elementary number theory, and introduces the reader to subsequent material on uniform distribution of infinite sequences, and discrepancy of finite sequences. Both modern and classical aspects of the theory are discussed, such as Weyl's criterion, Benford's law, the Koksma–Hlawka inequality, lattice point problems, and irregularities of distribution for convex bodies. Fourier analysis also features prominently, for which the theory is developed in parallel, including topics such as convergence of Fourier series, one-sided trigonometric approximation, the Poisson summation formula, exponential sums, decay of Fourier transforms, and Bessel functions.
Author : Csaba D. Toth
Publisher : CRC Press
Page : 1928 pages
File Size : 40,4 MB
Release : 2017-11-22
Category : Computers
ISBN : 1498711421
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Author : Dmitriy Bilyk
Publisher : Walter de Gruyter GmbH & Co KG
Page : 225 pages
File Size : 39,43 MB
Release : 2020-01-20
Category : Mathematics
ISBN : 3110652587
The contributions in this book focus on a variety of topics related to discrepancy theory, comprising Fourier techniques to analyze discrepancy, low discrepancy point sets for quasi-Monte Carlo integration, probabilistic discrepancy bounds, dispersion of point sets, pair correlation of sequences, integer points in convex bodies, discrepancy with respect to geometric shapes other than rectangular boxes, and also open problems in discrepany theory.
Author : Giancarlo Travaglini
Publisher : Cambridge University Press
Page : 251 pages
File Size : 50,72 MB
Release : 2014-06-12
Category : Mathematics
ISBN : 1107044030
Classical number theory is developed from scratch leading to geometric discrepancy theory, with Fourier analysis introduced along the way.
Author : Jiří Matoušek
Publisher :
Page : 296 pages
File Size : 30,92 MB
Release : 2009
Category : Irregularities of distribution (Number theory)
ISBN :
What is the "most uniform" way of distributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribution? Such questions are treated in geometric discrepancy theory. The book is an accessible and lively introduction to this area, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research. Including a wide variety of mathematical techniques (from harmonic analysis, combinatorics, algebra etc.) in action on non-trivial examples, the book is suitable for a "special topic" course for early graduates in mathematics and computer science. Besides professional mathematicians, it will be of interest to specialists in fields where a large collection of objects should be "uniformly" represented by a smaller sample (such as high-dimensional numerical integration in computational physics or financial mathematics, efficient divide-and-conquer algorithms in computer science, etc.). From the reviews: " ... The numerous illustrations are well placed and instructive. The clear and elegant exposition conveys a wealth of intuitive insights into the techniques utilized. Each section usually consists of text, historical remarks and references for the specialist, and exercises. Hints are provided for the more difficult exercises, with the exercise-hint format permitting inclusion of more results than otherwise would be possible in a book of this size ..." Allen D. Rogers, Mathematical Reviews Clippings (2001).
Author : William Chen
Publisher : Springer
Page : 708 pages
File Size : 30,52 MB
Release : 2014-10-07
Category : Mathematics
ISBN : 3319046969
This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions. It consists of several chapters, written by experts in their respective fields and focusing on the different aspects of the theory. Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling and is currently located at the crossroads of number theory, combinatorics, Fourier analysis, algorithms and complexity, probability theory and numerical analysis. This book presents an invitation to researchers and students to explore the different methods and is meant to motivate interdisciplinary research.
Author : Bernard Chazelle
Publisher : American Mathematical Soc.
Page : 480 pages
File Size : 39,55 MB
Release : 1999
Category : Mathematics
ISBN : 0821806742
This volume is a collection of refereed expository and research articles in discrete and computational geometry written by leaders in the field. Articles are based on invited talks presented at the AMS-IMS-SIAM Summer Research Conference, "Discrete and Computational Geometry: Ten Years Later", held in 1996 at Mt. Holyoke College (So.Hadley, MA). Topics addressed range from tilings, polyhedra, and arrangements to computational topology and visibility problems. Included are papers on the interaction between real algebraic geometry and discrete and computational geometry, as well as on linear programming and geometric discrepancy theory.
Author : Library of Congress. Cataloging Policy and Support Office
Publisher :
Page : 1688 pages
File Size : 38,26 MB
Release : 2009
Category : Subject headings, Library of Congress
ISBN :
Author : Library of Congress
Publisher :
Page : 1606 pages
File Size : 29,54 MB
Release : 1975
Category : Subject headings
ISBN :
