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Author: L. Kuipers Publisher: Courier Corporation ISBN: 0486149994 Category : Mathematics Languages : en Pages : 416
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: L. Kuipers Publisher: Courier Corporation ISBN: 0486149994 Category : Mathematics Languages : en Pages : 416
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: Michael Drmota Publisher: Springer ISBN: 354068333X Category : Mathematics Languages : en Pages : 517
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: Graham Everest Publisher: American Mathematical Soc. ISBN: 1470423154 Category : Mathematics Languages : en Pages : 338
Book Description
Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
Author: M. R. Leadbetter Publisher: Springer Science & Business Media ISBN: 1461254493 Category : Mathematics Languages : en Pages : 344
Book Description
Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.
Author: Barry C. Arnold Publisher: SIAM ISBN: 0898716489 Category : Mathematics Languages : en Pages : 291
Book Description
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: Murray Rosenblatt Publisher: Springer Science & Business Media ISBN: 1461251567 Category : Mathematics Languages : en Pages : 253
Book Description
This book has a dual purpose. One of these is to present material which selec tively will be appropriate for a quarter or semester course in time series analysis and which will cover both the finite parameter and spectral approach. The second object is the presentation of topics of current research interest and some open questions. I mention these now. In particular, there is a discussion in Chapter III of the types of limit theorems that will imply asymptotic nor mality for covariance estimates and smoothings of the periodogram. This dis cussion allows one to get results on the asymptotic distribution of finite para meter estimates that are broader than those usually given in the literature in Chapter IV. A derivation of the asymptotic distribution for spectral (second order) estimates is given under an assumption of strong mixing in Chapter V. A discussion of higher order cumulant spectra and their large sample properties under appropriate moment conditions follows in Chapter VI. Probability density, conditional probability density and regression estimates are considered in Chapter VII under conditions of short range dependence. Chapter VIII deals with a number of topics. At first estimates for the structure function of a large class of non-Gaussian linear processes are constructed. One can determine much more about this structure or transfer function in the non-Gaussian case than one can for Gaussian processes. In particular, one can determine almost all the phase information.
Author: Albert Edward Ingham Publisher: Cambridge University Press ISBN: 9780521397896 Category : Mathematics Languages : en Pages : 140
Book Description
Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field.
Author: C. Ding Publisher: Springer Science & Business Media ISBN: 1447105516 Category : Computers Languages : en Pages : 404
Book Description
This book contains survey papers and research papers by leading experts on sequences and their applications. It discusses both the theory of sequences and their applications in cryptography, coding theory, communications systems, numerical computation and computer simulation. Sequences have important applications in ranging systems, spread spectrum communication systems, multi-terminal system identification, code division multiply access communications systems, global positioning systems, software testing, circuit testing, computer simulation, and stream ciphers. The papers contained in this volume bring together experts from discrete mathematics, computer science and communications engineering, and help to bridge advances in these different areas.
Author: Marco Taboga Publisher: Createspace Independent Publishing Platform ISBN: 9781981369195 Category : Mathematical statistics Languages : en Pages : 670
Book Description
The book is a collection of 80 short and self-contained lectures covering most of the topics that are usually taught in intermediate courses in probability theory and mathematical statistics. There are hundreds of examples, solved exercises and detailed derivations of important results. The step-by-step approach makes the book easy to understand and ideal for self-study. One of the main aims of the book is to be a time saver: it contains several results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books. The topics covered by the book are as follows. PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions. PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions. PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions. PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart. PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions. PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutsky's Theorem. PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.
Author: L. Kuipers
Author: L. Kuipers
Author: Michael Drmota
Author: Graham Everest
Author: M. R. Leadbetter
Author: Barry C. Arnold
Author: Murray Rosenblatt
Author: Albert Edward Ingham
Author: C. Ding
Author: El Mustapha Ait Ben Hassi
Author: Marco Taboga