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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.

  • Multivariate Statistical Inference

    • 1st Edition
    • Narayan C. Giri
    • Z. W. Birnbaum + 1 more
    • English
    Multivariate Statistical Inference is a 10-chapter text that covers the theoretical and applied aspects of multivariate analysis, specifically the multivariate normal distribution using the invariance approach. Chapter I contains some special results regarding characteristic roots and vectors, and partitioned submatrices of real and complex matrices, as well as some special theorems on real and complex matrices useful in multivariate analysis. Chapter II deals with the theory of groups and related results that are useful for the development of invariant statistical test procedures, including the Jacobians of some specific transformations that are useful for deriving multivariate sampling distributions. Chapter III is devoted to basic notions of multivariate distributions and the principle of invariance in statistical testing of hypotheses. Chapters IV and V deal with the study of the real multivariate normal distribution through the probability density function and through a simple characterization and the maximum likelihood estimators of the parameters of the multivariate normal distribution and their optimum properties. Chapter VI tackles a systematic derivation of basic multivariate sampling distributions for the real case, while Chapter VII explores the tests and confidence regions of mean vectors of multivariate normal populations with known and unknown covariance matrices and their optimum properties. Chapter VIII is devoted to a systematic derivation of tests concerning covariance matrices and mean vectors of multivariate normal populations and to the study of their optimum properties. Chapters IX and X look into a treatment of discriminant analysis and the different covariance models and their analysis for the multivariate normal distribution. These chapters also deal with the principal components, factor models, canonical correlations, and time series. This book will prove useful to statisticians, mathematicians, and advance mathematics students.

  • Introduction to Stochastic Dynamic Programming

    • 1st Edition
    • Sheldon M. Ross
    • Z. W. Birnbaum + 1 more
    • English
    Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist—providing counterexamples where appropriate—and then presents methods for obtaining such policies when they do. In addition, general areas of application are presented. The final two chapters are concerned with more specialized models. These include stochastic scheduling models and a type of process known as a multiproject bandit. The mathematical prerequisites for this text are relatively few. No prior knowledge of dynamic programming is assumed and only a moderate familiarity with probability— including the use of conditional expectation—is necessary.

  • Machine Vision

    Theory, Algorithms, Practicalities
    • 1st Edition
    • E. R. Davies
    • P. G. Farrell + 1 more
    • English
    Machine Vision: Theory, Algorithms, Practicalities covers the limitations, constraints, and tradeoffs of vision algorithms. This book is organized into four parts encompassing 21 chapters that tackle general topics, such as noise suppression, edge detection, principles of illumination, feature recognition, Bayes’ theory, and Hough transforms. Part 1 provides research ideas on imaging and image filtering operations, thresholding techniques, edge detection, and binary shape and boundary pattern analyses. Part 2 deals with the area of intermediate-level vision, the nature of the Hough transform, shape detection, and corner location. Part 3 demonstrates some of the practical applications of the basic work previously covered in the book. This part also discusses some of the principles underlying implementation, including on lighting and hardware systems. Part 4 highlights the limitations and constraints of vision algorithms and their corresponding solutions. This book will prove useful to students with undergraduate course on vision for electronic engineering or computer science.

  • Foundations of Stochastic Analysis

    • 1st Edition
    • M. M. Rao
    • Z. W. Birnbaum + 1 more
    • English
    Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and measures. The applications of these conditional expectations and probabilities to Reynolds operators are also considered. The reader is then introduced to projective limits, direct limits, and a generalized Kolmogorov existence theorem, along with infinite product conditional probability measures. The book also considers martingales and their applications to likelihood ratios before concluding with a description of abstract martingales and their applications to convergence and harmonic analysis, as well as their relation to ergodic theory. This monograph should be of considerable interest to researchers and graduate students working in stochastic analysis.

  • TREAT

    A New and Efficient Match Algorithm for AI Production System
    • 1st Edition
    • Daniel P. Miranker
    • English
    TREAT: A New and Efficient Match Algorithm for AI Production Systems describes the architecture and software systems embodying the DADO machine, a parallel tree-structured computer designed to provide significant performance improvements over serial computers of comparable hardware complexity in the execution of large expert systems implemented in production system form. This book focuses on TREAT as a match algorithm for executing production systems that is presented and comparatively analyzed with the RETE match algorithm. TREAT, originally designed specifically for the DADO machine architecture, handles efficiently both temporally redundant and non-temporally redundant production system programs. This publication is suitable for developers and specialists interested in match algorithms for AI production systems.

  • Strong Approximations in Probability and Statistics

    • 1st Edition
    • M. Csörgo + 1 more
    • Z. W. Birnbaum + 1 more
    • English
    Strong Approximations in Probability and Statistics presents strong invariance type results for partial sums and empirical processes of independent and identically distributed random variables (IIDRV). This seven-chapter text emphasizes the applicability of strong approximation methodology to a variety of problems of probability and statistics. Chapter 1 evaluates the theorems for Wiener and Gaussian processes that can be extended to partial sums and empirical processes of IIDRV through strong approximation methods, while Chapter 2 addresses the problem of best possible strong approximations of partial sums of IIDRV by a Wiener process. Chapters 3 and 4 contain theorems concerning the one-time parameter Wiener process and strong approximation for the empirical and quantile processes based on IIDRV. Chapter 5 demonstrate the validity of previously discussed theorems, including Brownian bridges and Kiefer process, for empirical and quantile processes. Chapter 6 illustrate the approximation of defined sequences of empirical density, regression, and characteristic functions by appropriate Gaussian processes. Chapter 7 deal with the application of strong approximation methodology to study weak and strong convergence properties of random size partial sum and empirical processes. This book will prove useful to mathematicians and advance mathematics students.

  • Measure and Integral

    • 1st Edition
    • Konrad Jacobs
    • Z. W. Birnbaum + 1 more
    • English
    Probability and Mathematical Statistics: Measure and Integral provides information pertinent to the general mathematical notions and notations. This book discusses how the machinery of ?-extension works and how ?-content is derived from ?-measure. Organized into 16 chapters, this book begins with an overview of the classical Hahn–Banach theorem and introduces the Banach limits in the form of a major exercise. This text then presents the Daniell extension theory for positive ?-measures. Other chapters consider the transform of ?-contents and ?-measures by measurable mappings and kernels. This text is also devoted to a thorough study of the vector lattice of signed contents. This book discusses as well an abstract regularity theory and applied to the standard cases of compact, locally compact, and Polish spaces. The final chapter deals with the rudiments of the Krein–Milman theorem, along with some of their applications. This book is a valuable resource for graduate students.

  • Tables of the Function w (z)- e-z2 ? ex2 dx

    Mathematical Tables Series, Vol. 27
    • 1st Edition
    • K. A. Karpov
    • English
    Tables of the Function w(z) = e-z2 z?0ex2dx in the Complex Domain contains tables of the function in connection with the problem of the radio wave propagation. These tables are compiled in the Experimental-Computi... Laboratories of the Institute of Exact Mechanics and Computational Methods of the U.S.S.R. Academy of Sciences. The function w(z) is represented in the upper half-plane by the asymptotic series. Description of the tables and method of computation is provided. This book will prove useful to mathematicians and researchers.

  • Real Analysis and Probability

    Probability and Mathematical Statistics: A Series of Monographs and Textbooks
    • 1st Edition
    • Robert B. Ash
    • Z. W. Birnbaum + 1 more
    • English
    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.

  • Probabilistic Programming

    • 1st Edition
    • S. Vajda
    • Z. W. Birnbaum + 1 more
    • English
    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.

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