Uniform Distribution Of Sequences
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| Author | : L. Kuipers |
| Publisher | : Courier Corporation |
| Total Pages | : 416 |
| Release | : 2012-05-24 |
| Genre | : Mathematics |
| ISBN | : 0486149994 |
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 |
| Total Pages | : 410 |
| Release | : 1974 |
| Genre | : Mathematics |
| ISBN | : |
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 | : Michael Drmota |
| Publisher | : Springer |
| Total Pages | : 517 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 354068333X |
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 | : W. Narkiewicz |
| Publisher | : Springer |
| Total Pages | : 133 |
| Release | : 2006-12-08 |
| Genre | : Mathematics |
| ISBN | : 3540390634 |
| Author | : Oto Strauch |
| Publisher | : Peter Lang Pub Incorporated |
| Total Pages | : 543 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 9783631540138 |
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 | : Gunther Leobacher |
| Publisher | : Springer |
| Total Pages | : 206 |
| Release | : 2014-09-12 |
| Genre | : Mathematics |
| ISBN | : 3319034251 |
This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive treatment of the subject with detailed explanations comprises, for example, lattice rules, digital nets and sequences and discrepancy theory. It also presents methods currently used in research and discusses practical applications with an emphasis on finance-related problems. Each chapter closes with suggestions for further reading and with exercises which help students to arrive at a deeper understanding of the material presented. The book is based on a one-semester, two-hour undergraduate course and is well-suited for readers with a basic grasp of algebra, calculus, linear algebra and basic probability theory. It provides an accessible introduction for undergraduate students in mathematics or computer science.
| Author | : Edmund Hlawka |
| Publisher | : |
| Total Pages | : 160 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Jiri Matousek |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 310 |
| Release | : 1999-05-19 |
| Genre | : Mathematics |
| ISBN | : 9783540655282 |
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 | : Barry C. Arnold |
| Publisher | : SIAM |
| Total Pages | : 291 |
| Release | : 2008-09-25 |
| Genre | : Mathematics |
| ISBN | : 0898716489 |
This updated classic text will aid readers in understanding much of the current literature on order statistics: a flourishing field of study that is essential for any practising statistician and a vital part of the training for students in statistics. Written in a simple style that requires no advanced mathematical or statistical background, the book introduces the general theory of order statistics and their applications. The book covers topics such as distribution theory for order statistics from continuous and discrete populations, moment relations, bounds and approximations, order statistics in statistical inference and characterisation results, and basic asymptotic theory. There is also a short introduction to record values and related statistics. The authors have updated the text with suggestions for further reading that may be used for self-study. Written for advanced undergraduate and graduate students in statistics and mathematics, practising statisticians, engineers, climatologists, economists, and biologists.
| Author | : Rick Durrett |
| Publisher | : Cambridge University Press |
| Total Pages | : |
| Release | : 2010-08-30 |
| Genre | : Mathematics |
| ISBN | : 113949113X |
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
