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Author: L. Kuipers
Publisher: Courier Corporation
ISBN: 0486149994
Category : Mathematics
Languages : en
Pages : 416
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Book Description
The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of both methods and their underlying principles. A practical introduction for students of number theory and analysis as well as a reference for researchers in the field, this book covers uniform distribution in compact spaces and in topological groups, in addition to examinations of sequences of integers and polynomials. Notes at the end of each section contain pertinent bibliographical references and a brief survey of additional results. Exercises range from simple applications of theorems to proofs of propositions that expand upon results stated in the text.
Author: Lauwerens Kuipers
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 410
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Book Description
The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916 and ultimately provided common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of methods as well as their underlying principles. 1974 edition.
Author: W. Narkiewicz
Publisher: Springer
ISBN: 3540390634
Category : Mathematics
Languages : en
Pages : 133
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Book Description
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: L. Kuipers
Publisher: Courier Corporation
ISBN: 0486149994
Category : Mathematics
Languages : en
Pages : 416
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Book Description
The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of both methods and their underlying principles. A practical introduction for students of number theory and analysis as well as a reference for researchers in the field, this book covers uniform distribution in compact spaces and in topological groups, in addition to examinations of sequences of integers and polynomials. Notes at the end of each section contain pertinent bibliographical references and a brief survey of additional results. Exercises range from simple applications of theorems to proofs of propositions that expand upon results stated in the text.
Author: Oto Strauch
Publisher: Peter Lang Publishing
ISBN:
Category : Mathematics
Languages : en
Pages : 576
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Book Description
The monograph covers material scattered throughout books and journals and focuses on the distribution properties of sequences which may be expressed in terms of distribution function, upper and lower distribution function, the discrepancy, diaphony, dispersion etc. The individual character of sequences reflected in their distribution properties may be an object of study from various points of view, and as such they are often the primary goal of investigation. In that case the studied properties are caught in separate results and are consequently accessible in a displayed form. On the other hand, the various distribution properties of sequences play only a subsidiary role in proofs and thus remain often hidden and are not manifested in a visible form. The enormous wealth of information contained in both cases may be of value not only to those working directly in the field, but also to those working in related branches of number theory, combinatorics, real or numerical analysis in the process of finding sequence possessing the required properties. Last, but not least browsing throughout the book may provide the impetus for prospective further research. This is what we hope may address a wide class of working mathematicians.
Author:
Publisher:
ISBN: 9780387138725
Category :
Languages : en
Pages :
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Book Description
Author: Wadysaw Narkiewicz
Publisher:
ISBN: 9783662192191
Category :
Languages : en
Pages : 140
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Book Description
Author: Charles Vanden Eynden
Publisher:
ISBN:
Category : Number theory
Languages : en
Pages : 48
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Book Description
Author: Edmund Hlawka
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 160
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Book Description
Author: Rachel M. Andriunas
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This report is an exploration into the basics of the uniform distribution of sequences and a proof of Weyl's Criterion. After describing what it means for a sequence to be uniformly distributed, we develop the tools to prove Weyl's Criterion. In order to do this, we split Weyl's Criterion into two theorems and prove each of them. Finally, we will show an example which applies Weyl's Criterion to prove that a certain sequence of irrational numbers is uniformly distributed.
