Sequences, Discrepancies and Applications PDF Download

Author: Michael Drmota
Publisher: Springer
ISBN: 354068333X
Category : Mathematics
Languages : en
Pages : 517

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Book Description
The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.

Author: ERDÖS
Publisher: Birkhäuser
ISBN: 3034854382
Category : Science
Languages : en
Pages : 741

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Book Description
This volume, written by his friends, collaborators and students, is offered to the memory of Paul Tunin. Most of the papers they contributed discuss subjects related to his own fields of research. The wide range of topics reflects the versatility of his mathematical activity. His work has inspired many mathematicians in analytic number theory, theory of functions of a complex variable, interpolation and approximation theory, numerical algebra, differential equations, statistical group theory and theory of graphs. Beyond the influence of his deep and important results he had the exceptional ability to communicate to others his enthusiasm for mathematics. One of the strengths of Turan was to ask unusual questions that became starting points of many further results, sometimes opening up new fields of research. We hope that this volume will illustrate this aspect of his work adequately. Born in Budapest, on August 28, 1910, Paul Turan obtained his Ph. D. under L. Fejer in 1935. His love for mathematies enabled him to work even under inhuman circumstances during the darkest years of the Second World War. One of his major achievements, his power sum method originated in this period. After the war he was visiting professor in Denmark and in Princeton. In 1949 he became professor at the Eotvos Lorand University of Budapest, a member of the Hungarian Academy of Sciences and a leading figure of the Hungarian mathematical community.

Author: Dmitriy Bilyk
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110652587
Category : Mathematics
Languages : en
Pages : 225

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Book Description
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: E. Keith Lloyd
Publisher: Cambridge University Press
ISBN: 0521275520
Category : Mathematics
Languages : en
Pages : 271

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Book Description
This volume contains the invited papers from the 1983 British Combinatorial Conference. Several distinguished mathematicians were invited to give a lecture and write a paper for the conference volume. The papers cover a broad range of combinatorial topics, including enumeration, finite geometries, graph theory and permanents.

Author: Hugh L. Montgomery
Publisher: American Mathematical Soc.
ISBN: 1470424444
Category : Education
Languages : en
Pages : 242

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Book Description
This book contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. This book would be an excellent resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in nu.

Author: Ian Anderson
Publisher: Cambridge University Press
ISBN: 0521315247
Category : Mathematics
Languages : en
Pages : 181

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Book Description
This volume contains the invited papers at the 1985 British Combinatorial Conference presented by several distinguished mathematicians.

Author: Giancarlo Travaglini
Publisher: Cambridge University Press
ISBN: 1139992821
Category : Mathematics
Languages : en
Pages : 251

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Book Description
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: Jiri Matousek
Publisher: Springer Science & Business Media
ISBN: 3642039421
Category : Mathematics
Languages : en
Pages : 293

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Book Description
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: H. Jager
Publisher: Springer
ISBN: 3540389067
Category : Mathematics
Languages : en
Pages : 306

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Book Description

Author: William Chen
Publisher: Springer
ISBN: 3319046969
Category : Mathematics
Languages : en
Pages : 708

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Book Description
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.