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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.

  • Computer Chess

    • 1st Edition
    • Monroe Newborn
    • Thomas A. Standish
    • English
    Computer Chess deals with the history of computer chess games and the programming of computer chess. Topics covered include chess programs such as the one initiated by Richard Greenblatt and those launched by the United States and the USSR in 1966-1967. The United States Computer Chess Championships from 1970 to 1973 are also discussed. Comprised of 10 chapters, this book begins with a historical overview of the basic ideas underlying computer chess and several of the earliest computer games. The next chapter deals with the chess match held in 1966 pitting the Kotok-McCarthy Chess Program of the United States and the ITEP (Institute of Theoretical and Experimental Physics) Chess Program of the Soviet Union. The reader is then introduced to Greenblatt's program, named Mac Hack Six, the first chess program to compete respectably against humans in tournament play. Subsequent chapters focus on the U.S. Computer Chess Championships, from its first edition in New York in 1970 to the fourth, held in Atlanta in 1973. Russia's chess program called KAISSA, an improved version of the ITEP Chess Program, is also described. The final chapter is devoted to OSTRICH, a chess-playing program written by George Arnold in the Digital Computer Laboratory of Columbia University's Department of Electrical Engineering and Computer Science in 1971. This monograph will be of value to computer science and those interested in computer chess programs and in the broader field of artificial intelligence.

  • Ten-Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates

    Volume 33 in Mathematical Tables Series
    • 1st Edition
    • L. A. Lyusternik
    • English
    Ten-Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates contains Tables of mathematical functions up to ten-decimal value. These tables are compiled in the Department for Approximate Computations of the Institute of Exact Mechanics and Computational Methods of the U.S.S.R. Academy of Sciences. The computations are carried out by this department in conjunction with the Computational-Experi... Laboratory of the Institute. This book will be of value to mathematicians and researchers.

  • Decomposability

    Queueing and Computer System Applications
    • 1st Edition
    • P. J. Courtois
    • Robert L. Ashenhurst
    • English
    Decomposability: Queueing and Computer System Applications presents a set of powerful methods for systems analysis. This 10-chapter text covers the theory of nearly completely decomposable systems upon which specific analytic methods are based. The first chapters deal with some of the basic elements of a theory of nearly completely decomposable stochastic matrices, including the Simon-Ando theorems and the perturbation theory. The succeeding chapters are devoted to the analysis of stochastic queuing networks that appear as a type of key model. These chapters also discuss congestion problems in information processing systems, which could be studied by the queuing network models. A method of analysis by decomposition and aggregation for these models is proposed. Other chapters highlight the problem of computer system performance evaluation, specifically the analysis of hardware and software of the dynamic behavior of computer systems and user programs. These topics are followed by a description of an aggregative model of a typical multiprogramming time-sharing computer system. The last chapter examines the existing affinity between the concept of aggregate in nearly completely decomposable structures and the notions of module and level of abstraction so frequently invoked in computer system design and software engineering. This book will prove useful to both hardware and software designers and engineers, as well as scientists who are investigating complex systems.

  • Stochastic Integrals

    • 1st Edition
    • H. P. McKean
    • Z. W. Birnbaum + 1 more
    • English
    Stochastic Integrals discusses one area of diffusion processes: the differential and integral calculus based upon the Brownian motion. The book reviews Gaussian families, construction of the Brownian motion, the simplest properties of the Brownian motion, Martingale inequality, and the law of the iterated logarithm. It also discusses the definition of the stochastic integral by Wiener and by Ito, the simplest properties of the stochastic integral according to Ito, and the solution of the simplest stochastic differential equation. The book explains diffusion, Lamperti's method, forward equation, Feller's test for the explosions, Cameron-Martin's formula, the Brownian local time, and the solution of dx=e(x) db + f(x) dt for coefficients with bounded slope. It also tackles Weyl's lemma, diffusions on a manifold, Hasminski's test for explosions, covering Brownian motions, Brownian motions on a Lie group, and Brownian motion of symmetric matrices. The book gives as example of a diffusion on a manifold with boundary the Brownian motion with oblique reflection on the closed unit disk of R squared. The text is suitable for economists, scientists, or researchers involved in probabilistic models and applied mathematics.

  • Computability Theory

    An Introduction
    • 1st Edition
    • Neil D. Jones
    • Robert L. Ashenhurst
    • English
    Computability Theory: An Introduction provides information pertinent to the major concepts, constructions, and theorems of the elementary theory of computability of recursive functions. This book provides mathematical evidence for the validity of the Church–Turing thesis. Organized into six chapters, this book begins with an overview of the concept of effective process so that a clear understanding of the effective computability of partial and total functions is obtained. This text then introduces a formal development of the equivalence of Turing machine computability, enumerability, and decidability with other formulations. Other chapters consider the formulas of the predicate calculus, systems of recursion equations, and Post's production systems. This book discusses as well the fundamental properties of the partial recursive functions and the recursively enumerable sets. The final chapter deals with different formulations of the basic ideas of computability that are equivalent to Turing-computability... This book is a valuable resource for undergraduate or graduate students.

  • Sequential Statistical Procedures

    • 1st Edition
    • Z. Govindarajulu
    • Z. W. Birnbaum + 1 more
    • English
    Probability and Mathematical Statistics, Volume 26: Sequential Statistical Procedures provides information pertinent to the sequential procedures that are concerned with statistical analysis of data. This book discusses the fundamental aspects of sequential estimation. Organized into four chapters, this volume begins with an overview of the essential feature of sequential procedure. This text then examines the sequential probability ratio test procedure and provides a method of constructing a most powerful test for a simple hypothesis versus simple alternative-testing problem. Other chapters consider the problem of testing a composite hypothesis against a composite alternative. This book discusses as well the theory of sequential tests that is appropriate for distinguishing between two simple or composite hypotheses. The final chapter deals with the theory of sequential estimation. This book is a valuable resource for graduate students, research workers, and users of sequential procedures.

  • Computational Linguistics

    International Series in Modern Applied Mathematics and Computer Science
    • 1st Edition
    • Nick Cercone
    • English
    Computational Linguistics provides an overview of the variety of important research in computational linguistics in North America. This work is divided into 15 chapters and begins with a survey of the theoretical foundations and parsing strategies for natural language. The succeeding chapters deal with psychological and linguistic modeling, discourse processing analysis, text and content analysis, and natural language understanding, as well as knowledge organization, memory models, and learning. Other chapters describe the programming systems and considerations for computation linguistics. The last chapters look into the nature of natural language front-end processes to database systems. These chapters also examine the human factors interface. This book will prove useful to computing scientists, philosophers, psychologists, and linguists.

  • Computer Security

    • 1st Edition
    • David K. Hsiao + 2 more
    • Robert L. Ashenhurst
    • English
    Computer Security provides information pertinent to the growing concern with computer security and privacy, extending beyond the conventional military requirement to cover the entire civilian and business community. This book discusses the approaches to ensure the integrity of stored data. Organized into eight chapters, this book begins with an overview of the relationships between privacy issues and security measures. This text then provides a discussion on privacy issues, legislative measures, and their implications on security. Other chapters consider the technical implications of the enactment of privacy legislation and explain the control of access required by the privacy legislation. This book discusses as well the internal policies and procedures of operational security, which is adopted by management to ensure the security of their data and computer installation. The final chapter deals with optimizing database management system to facilitate the use of data effectively and efficiently. This book is a valuable resource for technical managers.

  • Mathematical Methods of Reliability Theory

    • 1st Edition
    • B. V. Gnedenko + 2 more
    • Z. W. Birnbaum + 1 more
    • English
    Mathematical Methods of Reliability Theory discusses fundamental concepts of probability theory, mathematical statistics, and an exposition of the relationships among the fundamental quantitative characteristics encountered in the theory. The book deals with the set-theoretic approach to reliability theory and the central concepts of set theory to the phenomena. It also presents methods of finding estimates for reliability parameters based on observations and methods of testing reliability hypotheses. Based on mathematical statistics, the book also explains formulation of some selected results. It presents a method that increases the reliability of manufactured articles—redundancy. An important part of product quality control is the standards of acceptance-sampling plans which require simplicity, wide content for flexibility, comprehensive characteristics, and variability. The book also tackles economical and rational methods of sampling inspections, highlighting the need for a correct evaluation of environmental conditions—the factors which predetermine the choice of the inspection method. The book then explains how to estimate the efficiency of the operation of the sampling plan after its selection. The book can be helpful for engineers, mathematicians, economists, or industrial managers, as well as for other professionals who work in the technological, political, research, structural, and physico-chemical areas.

  • Stochastic Differential Equations and Applications

    Volume 1
    • 1st Edition
    • Avner Friedman
    • Z. W. Birnbaum + 1 more
    • English
    Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume is divided into nine chapters. Chapters 1 to 5 deal with the basic theory of stochastic differential equations, including discussions of the Markov processes, Brownian motion, and the stochastic integral. Chapter 6 examines the connections between solutions of partial differential equations and stochastic differential equations, while Chapter 7 describes the Girsanov’s formula that is useful in the stochastic control theory. Chapters 8 and 9 evaluate the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity. This book is intended primarily for undergraduate and graduate mathematics students.

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