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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

    • Mathematical Statistics

      • 1st Edition
      • July 10, 2014
      • Thomas S. Ferguson
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 7 8 0 3
      • eBook
        9 7 8 1 4 8 3 2 2 1 2 3 6
      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.

    • Strong Approximations in Probability and Statistics

      • 1st Edition
      • July 10, 2014
      • M. Csörgo + 1 more
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 3 7 8 3 1
      • eBook
        9 7 8 1 4 8 3 2 6 8 0 4 0
      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.

    • The Expected-Outcome Model of Two-Player Games

      • 1st Edition
      • July 10, 2014
      • Bruce Abramson
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 8 9 8 1
      • eBook
        9 7 8 1 4 8 3 2 5 8 9 5 9
      The Expected-Outcome Model of Two-Player Games deals with the expected-outcome model of two-player games, in which the relative merit of game-tree nodes, rather than board positions, is considered. The ambiguity of static evaluation and the problems it generates in the search system are examined and the development of a domain-independent static evaluator is described. Comprised of eight chapters, this book begins with an overview of the rationale for the mathematical study of games, followed by a discussion on some previous artificial intelligence (AI) research efforts on game-trees. The next section opens with the definition of a node's expected-outcome value as the expected value of the leaves beneath it. The expected-outcome model is outlined, paying particular attention to the expected-outcome value of a game-tree node. This model was implemented on some small versions of tic-tac-toe and Othello. The book also presents results that offer strong support for both the validity of the expected-outcome model and the rationality of its underlying assumptions. This monograph is intended for specialists in AI and computer science.

    • TREAT

      • 1st Edition
      • July 10, 2014
      • Daniel P. Miranker
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 8 9 9 8
      • eBook
        9 7 8 1 4 8 3 2 5 8 8 9 8
      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.

    • Introduction to Stochastic Dynamic Programming

      • 1st Edition
      • July 10, 2014
      • Sheldon M. Ross
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 5 7 7 5
      • eBook
        9 7 8 1 4 8 3 2 6 9 0 9 2
      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.

    • Martingale Limit Theory and Its Application

      • 1st Edition
      • July 10, 2014
      • P. Hall + 1 more
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 0 2 4 4
      • eBook
        9 7 8 1 4 8 3 2 6 3 2 2 9
      Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.

    • Measure and Integral

      • 1st Edition
      • July 10, 2014
      • Konrad Jacobs
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 1 0 4 3
      • eBook
        9 7 8 1 4 8 3 2 6 3 0 4 5
      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.

    • Nonparametric Functional Estimation

      • 1st Edition
      • July 10, 2014
      • B. L. S. Prakasa Rao
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 4 9 4 5
      • eBook
        9 7 8 1 4 8 3 2 6 9 2 3 8
      Nonparametric Functional Estimation is a compendium of papers, written by experts, in the area of nonparametric functional estimation. This book attempts to be exhaustive in nature and is written both for specialists in the area as well as for students of statistics taking courses at the postgraduate level. The main emphasis throughout the book is on the discussion of several methods of estimation and on the study of their large sample properties. Chapters are devoted to topics on estimation of density and related functions, the application of density estimation to classification problems, and the different facets of estimation of distribution functions. Statisticians and students of statistics and engineering will find the text very useful.

    • Lattice Path Counting and Applications

      • 1st Edition
      • July 10, 2014
      • Gopal Mohanty
      • Z. W. Birnbaum + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 5 3 7 3
      • eBook
        9 7 8 1 4 8 3 2 1 8 8 0 9
      Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Lattice Path Counting and Applications focuses on the principles, methodologies, and approaches involved in lattice path counting and applications, including vector representation, random walks, and rank order statistics. The book first underscores the simple and general boundaries of path counting. Topics include types of diagonal steps and a correspondence, paths within general boundaries, higher dimensional paths, vector representation, compositions, and domination, recurrence and generating function method, and reflection principle. The text then examines invariance and fluctuation and random walk and rank order statistics. Discussions focus on random walks, rank order statistics, Chung-Feller theorems, and Sparre Andersen's equivalence. The manuscript takes a look at convolution identities and inverse relations and discrete distributions, queues, trees, and search codes, as well as discrete distributions and a correlated random walk, trees and search codes, convolution identities, and orthogonal relations and inversion formulas. The text is a valuable reference for mathematicians and researchers interested in in lattice path counting and applications.

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

      • 1st Edition
      • July 3, 2014
      • K. A. Karpov
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 1 1 4 6
      • eBook
        9 7 8 1 4 8 3 2 1 4 5 7 3
      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.

Related subjects

Mathematics and applied mathematics

Statistics and probability