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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.

  • Mathematical Statistics

    A Decision Theoretic Approach
    • 1st Edition
    • Thomas S. Ferguson
    • Z. W. Birnbaum + 1 more
    • English
    Mathematical Statistics: A Decision Theoretic Approach presents an investigation of the extent to which problems of mathematical statistics may be treated by decision theory approach. This book deals with statistical theory that could be justified from a decision-theoretic viewpoint. Organized into seven chapters, this book begins with an overview of the elements of decision theory that are similar to those of the theory of games. This text then examines the main theorems of decision theory that involve two more notions, namely the admissibility of a decision rule and the completeness of a class of decision rules. Other chapters consider the development of theorems in decision theory that are valid in general situations. This book discusses as well the invariance principle that involves groups of transformations over the three spaces around which decision theory is built. The final chapter deals with sequential decision problems. This book is a valuable resource for first-year graduate students in mathematics.

  • Design Problem Solving

    Knowledge Structures and Control Strategies
    • 1st Edition
    • David C. Brown + 1 more
    • English
    Design Problem Solving: Knowledge Structures and Control Strategies describes the application of the generic task methodology to the problem of routine design. This book discusses the generic task methodology and what constitutes the essence of the Al approach to problem solving, including the analysis of design as an information processing activity. The basic design problem solving framework, DSPL language, and AIR-CYL Air cylinder design system are also elaborated. Other topics include the high level languages based on generic tasks, structure of a Class 3 design problem solver, and failure handling in routine design. The conceptual structure for the air cylinder and improvements to DSPL system support are likewise covered in this text. This publication is beneficial to students and specialists concerned with solving design problems.

  • An Introduction to Mathematical Analysis

    • 1st Edition
    • Robert A. Rankin
    • English
    International Series of Monographs on Pure and Applied Mathematics, Volume 43: An Introduction to Mathematical Analysis discusses the various topics involved in the analysis of functions of a single real variable. The title first covers the fundamental idea and assumptions in analysis, and then proceeds to tackling the various areas in analysis, such as limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. The book will be most useful to undergraduate students of mathematical 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.

  • Stochastic Calculus and Stochastic Models

    • 1st Edition
    • E. J. McShane
    • Z. W. Birnbaum + 1 more
    • English
    Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Stochastic Calculus and Stochastic Models focuses on the properties, functions, and applications of stochastic integrals. The publication first ponders on stochastic integrals, existence of stochastic integrals, and continuity, chain rule, and substitution. Discussions focus on differentiation of a composite function, continuity of sample functions, existence and vanishing of stochastic integrals, canonical form, elementary properties of integrals, and the Itô-belated integral. The book then examines stochastic differential equations, including existence of solutions of stochastic differential equations, linear differential equations and their adjoints, approximation lemma, and the Cauchy-Maruyama approximation. The manuscript takes a look at equations in canonical form, as well as justification of the canonical extension in stochastic modeling; rate of convergence of approximations to solutions; comparison of ordinary and stochastic differential equations; and invariance under change of coordinates. The publication is a dependable reference for mathematicians and researchers interested in stochastic integrals.

  • Residuation Theory

    • 1st Edition
    • T. S. Blyth + 1 more
    • I. N. Sneddon + 1 more
    • English
    Residuation Theory aims to contribute to literature in the field of ordered algebraic structures, especially on the subject of residual mappings. The book is divided into three chapters. Chapter 1 focuses on ordered sets; directed sets; semilattices; lattices; and complete lattices. Chapter 2 tackles Baer rings; Baer semigroups; Foulis semigroups; residual mappings; the notion of involution; and Boolean algebras. Chapter 3 covers residuated groupoids and semigroups; group homomorphic and isotone homomorphic Boolean images of ordered semigroups; Dubreil-Jacotin and Brouwer semigroups; and lolimorphisms. The book is a self-contained and unified introduction to residual mappings and its related concepts. It is applicable as a textbook and reference book for mathematicians who plan to learn more about the subject.

  • 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.

  • Representations of Commonsense Knowledge

    • 1st Edition
    • Ernest Davis
    • Ronald J. Brachman
    • English
    Representations of Commonsense Knowledge provides a rich language for expressing commonsense knowledge and inference techniques for carrying out commonsense knowledge. This book provides a survey of the research on commonsense knowledge. Organized into 10 chapters, this book begins with an overview of the basic ideas on artificial intelligence commonsense reasoning. This text then examines the structure of logic, which is roughly analogous to that of a programming language. Other chapters describe how rules of universal validity can be applied to facts known with absolute certainty to deduce other facts known with absolute certainty. This book discusses as well some prominent issues in plausible inference. The final chapter deals with commonsense knowledge about the interrelations and interactions among agents and discusses some issues in human and social interactions that have been studied in the artificial intelligence literature. This book is a valuable resource for students on a graduate course on knowledge representation.

  • Interpretation of Visual Motion

    A Computational Study
    • 1st Edition
    • Muralidhara Subbarao
    • English
    Interpretation of Visual Motion: A Computational Study provides an information processing point of view to the phenomenon of visual motion. This book discusses the computational theory formulated for recovering the scene from monocular visual motion, determining the local geometry and rigid body motion of surfaces from spatio-temporal parameters of visual motion. This compilation also provides a theoretical and computational framework for future research on visual motion, both in human vision and machine vision areas. Other topics include the computation of image flow from intensity derivatives, instantaneous image flow due to rigid motion, time and space-time derivatives of image flow, and estimation of maximum absolute error. This publication is recommended for professionals and non-specialists intending to acquire knowledge of visual motion.

  • 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.

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