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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

BooksJournals

    • Probabilistic Programming

      • 1st Edition
      • July 3, 2014
      • S. Vajda
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 7 8 6 1
      • eBook
        9 7 8 1 4 8 3 2 6 8 3 7 8
      Probabilistic Programming discusses a high-level language known as probabilistic programming. This book consists of three chapters. Chapter I deals with “wait-and-see” problems that require waiting until an observation is made on the random elements, while Chapter II contains the analysis of decision problems, particularly of so-called two-stage problems. The last chapter focuses on “chance constraints,” such as constraints that are not expected to be always satisfied, but only in a proportion of cases or “with given probabilities.” This text specifically deliberates the decision regions for optimality, probability distributions, Kall's Theorem, and two-stage programming under uncertainty. The complete problem, active approach, quantile rules, randomized decisions, and nonzero order rules are also covered. This publication is suitable for developers aiming to define and automatically solve probability models.

    • Fixed Effects Analysis of Variance

      • 1st Edition
      • July 3, 2014
      • Lloyd Fisher + 1 more
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 4 4 3 7
      • eBook
        9 7 8 1 4 8 3 2 1 7 8 6 4
      Fixed Effects Analysis of Variance covers the mathematical theory of the fixed effects analysis of variance. The book discusses the theoretical ideas and some applications of the analysis of variance. The text then describes topics such as the t-test; two-sample t-test; the k-sample comparison of means (one-way analysis of variance); the balanced two-way factorial design without interaction; estimation and factorial designs; and the Latin square. Confidence sets, simultaneous confidence intervals, and multiple comparisons; orthogonal and nonorthologonal designs; and multiple regression analysis and related matters are also encompassed. Mathematicians, statisticians, and students taking related courses will find the book useful.

    • Probability Algebras and Stochastic Spaces

      • 1st Edition
      • July 3, 2014
      • Demetrios A. Kappos
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 5 0 7 6
      • eBook
        9 7 8 1 4 8 3 2 1 8 5 0 2
      Probability Algebras and Stochastic Spaces explores the fundamental notions of probability theory in the so-called “point-free” way. The space of all elementary random variables defined over a probability algebra in a “point-free” way is a base for the stochastic space of all random variables, which can be obtained from it by lattice-theoretic extension processes. This book is composed of eight chapters and begins with discussions of the definition, properties, scope, and extension of probability algebras. The succeeding chapters deal with the Cartesian product of probability algebras and the principles of stochastic spaces. These topics are followed by surveys of the expectation, moments, and spaces of random variables. The final chapters define generalized random variables and the Boolean homomorphisms of these variables. This book will be of great value to mathematicians and advance mathematics students.

    • Fourier Transforms of Distributions and Their Inverses

      • 1st Edition
      • July 3, 2014
      • Fritz Oberhettinger
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 5 5 9 5
      • eBook
        9 7 8 1 4 8 3 2 1 9 0 2 8
      Fourier Transforms of Distributions and Their Inverses: A Collection of Tables is a collection of tables on the integrals of Fourier transforms of distributions and their inverses involving the class of functions which are nonnegative and integrable over the interval. The emphasis is on the probability densities, and a number of examples are provided. This book is organized into two parts and begins with an introduction to those properties of characteristic functions which are important in probability theory, followed by a description of the tables and their use. The first three tables contain Fourier transforms of absolutely continuous distribution functions, namely, even functions (including Legendre functions); functions vanishing identically for negative values of the argument (including arbitrary powers); and functions that do not belong to either of the above classes. The transform pairs are numbered consecutively and arranged systematically according to the analytical character of the frequency function. The next two tables give the inverse transforms of the functions listed in the first and third tables, respectively. This monograph will appeal to students and specialists in the fields of probability and mathematical statistics.

    • Real Analysis and Probability

      • 1st Edition
      • July 3, 2014
      • Robert B. Ash
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 7 5 6 1 4
      • eBook
        9 7 8 1 4 8 3 1 9 1 4 2 3
      Real Analysis and Probability provides the background in real analysis needed for the study of probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability. The interplay between measure theory and topology is also discussed, along with conditional probability and expectation, the central limit theorem, and strong laws of large numbers with respect to martingale theory. Comprised of eight chapters, this volume begins with an overview of the basic concepts of the theory of measure and integration, followed by a presentation of various applications of the basic integration theory. The reader is then introduced to functional analysis, with emphasis on structures that can be defined on vector spaces. Subsequent chapters focus on the connection between measure theory and topology; basic concepts of probability; and conditional probability and expectation. Strong laws of large numbers are also examined, first from the classical viewpoint, and then via martingale theory. The final chapter is devoted to the one-dimensional central limit problem, paying particular attention to the fundamental role of Prokhorov's weak compactness theorem. This book is intended primarily for students taking a graduate course in probability.

    • Stochastic Convergence

      • 2nd Edition
      • July 3, 2014
      • Eugene Lukacs
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 5 1 5 1
      • eBook
        9 7 8 1 4 8 3 2 1 8 5 8 8
      Stochastic Convergence, Second Edition covers the theoretical aspects of random power series dealing with convergence problems. This edition contains eight chapters and starts with an introduction to the basic concepts of stochastic convergence. The succeeding chapters deal with infinite sequences of random variables and their convergences, as well as the consideration of certain sets of random variables as a space. These topics are followed by discussions of the infinite series of random variables, specifically the lemmas of Borel-Cantelli and the zero-one laws. Other chapters evaluate the power series whose coefficients are random variables, the stochastic integrals and derivatives, and the characteristics of the normal distribution of infinite sums of random variables. The last chapter discusses the characterization of the Wiener process and of stable processes. This book will prove useful to mathematicians and advance mathematics students.

    • Probability Measures on Metric Spaces

      • 1st Edition
      • July 3, 2014
      • K. R. Parthasarathy
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 1 1 8 2 4
      • eBook
        9 7 8 1 4 8 3 2 2 5 2 5 8
      Probability Measures on Metric Spaces presents the general theory of probability measures in abstract metric spaces. This book deals with complete separable metric groups, locally impact abelian groups, Hilbert spaces, and the spaces of continuous functions. Organized into seven chapters, this book begins with an overview of isomorphism theorem, which states that two Borel subsets of complete separable metric spaces are isomorphic if and only if they have the same cardinality. This text then deals with properties such as tightness, regularity, and perfectness of measures defined on metric spaces. Other chapters consider the arithmetic of probability distributions in topological groups. This book discusses as well the proofs of the classical extension theorems and existence of conditional and regular conditional probabilities in standard Borel spaces. The final chapter deals with the compactness criteria for sets of probability measures and their applications to testing statistical hypotheses. This book is a valuable resource for statisticians.

    • Probability Theory

      • 1st Edition
      • July 3, 2014
      • L. E. Maistrov
      • Samuel Kotz
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 5 2 0 5
      • eBook
        9 7 8 1 4 8 3 2 1 8 6 3 2
      Probability Theory: A Historical Sketch covers the probability theory, mainly axiomatization problems. The book discusses the prehistory of the probability theory; the first stage in the development of probability theory; and the development of probability theory to the middle of the 19th century. The text also describes the probability theory in the second half of the 19th century; and the axiomatic foundations of the probability theory. Historians and mathematicians will find the book invaluable.

    • Statistics of Directional Data

      • 1st Edition
      • July 3, 2014
      • K. V. Mardia
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 5 2 3 6
      • eBook
        9 7 8 1 4 8 3 2 1 8 6 6 3
      Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Statistics of Directional Data aims to provide a systematic account of statistical theory and methodology for observations which are directions. The publication first elaborates on angular data and frequency distributions, descriptive measures, and basic concepts and theoretical models. Discussions focus on moments and measures of location and dispersion, distribution function, corrections for grouping, calculation of the mean direction and the circular variance, interrelations between different units of angular measurement, and diagrammatical representation. The book then examines fundamental theorems and distribution theory, point estimation, and tests for samples from von Mises populations. The text takes a look at non-parametric tests, distributions on spheres, and inference problems on the sphere. Topics include tests for axial data, point estimation, distribution theory, moments and limiting distributions, and tests of goodness of fit and tests of uniformity. The publication is a dependable reference for researchers interested in probability and mathematical statistics.

    • Classical and Modern Integration Theories

      • 1st Edition
      • July 3, 2014
      • Ivan N. Pesin
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 4 7 3 0
      • eBook
        9 7 8 1 4 8 3 2 6 8 6 9 9
      Classical and Modern Integration Theories discusses classical integration theory, particularly that part of the theory directly associated with the problems of area. The book reviews the history and the determination of primitive functions, beginning from Cauchy to Daniell. The text describes Cauchy's definition of an integral, Riemann's definition of the R-integral, the upper and lower Darboux integrals. The book also reviews the origin of the Lebesgue-Young integration theory, and Borel's postulates that define measures of sets. W.H. Young's work provides a construction of the integral equivalent to Lebesque's construction with a different generalization of integrals leading to different approaches in solutions. Young's investigations aim at generalizing the notion of length for arbitrary sets by means of a process which is more general than Borel's postulates. The text notes that the Lebesgue measure is the unique solution of the measure problem for the class of L-measurable sets. The book also describes further modifications made into the Lebesgue definition of the integral by Riesz, Pierpont, Denjoy, Borel, and Young. These modifications bring the Lebesgue definition of the integral closer to the Riemann or Darboux definitions, as well as to have it associated with the concepts of classical analysis. The book can benefit mathematicians, students, and professors in calculus or readers interested in the history of classical mathematics.

Related subjects

Mathematics and applied mathematics

Statistics and probability