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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.

  • Annual Review in Automatic Programming

    International Tracts in Computer Science and Technology and Their Application, Vol. 4
    • 1st Edition
    • Richard Goodman
    • English
    Annual Review in Automatic Programming, Volume 4 is a collection of papers that deals with the GIER ALGOL compiler, a parameterized compiler based on mechanical linguistics, and the JOVIAL language. A couple of papers describes a commercial use of stacks, an IBM system, and what an ideal computer program support system should be. One paper reviews the system of compilation, the development of a more advanced language, programming techniques, machine independence, and program transfer to other machines. Another paper describes the ALGOL 60 system for the GIER machine including running ALGOL programs, storage allocation, addressing of variables, program references, procedure calls, storage problem of the translator, and writing the translator. Another paper investigates the internal operation of the ALGOL translator, the source and target languages, the parts of the translator, Polish postfix notation, symbol table in the translator, and the realization of the stack concept. One paper examines the components for a large digital computer, specific features, and compares these to IBM's IBSYS. The collection will prove valuable for programmers, computer engineers, computer instructors, and students of computer science.

  • Stochastic Differential Equations and Diffusion Processes

    • 2nd Edition
    • Volume 24
    • N. Ikeda + 1 more
    • English
    Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sections discussing complex (conformal) martingales and Kahler diffusions have been added.

  • Wavelets

    Theory, Algorithms, and Applications
    • 1st Edition
    • Volume 5
    • Laura Montefusco + 1 more
    • English
    Wavelets: Theory, Algorithms, and Applications is the fifth volume in the highly respected series, WAVELET ANALYSIS AND ITS APPLICATIONS. This volume shows why wavelet analysis has become a tool of choice infields ranging from image compression, to signal detection and analysis in electrical engineering and geophysics, to analysis of turbulent or intermittent processes. The 28 papers comprising this volume are organized into seven subject areas: multiresolution analysis, wavelet transforms, tools for time-frequency analysis, wavelets and fractals, numerical methods and algorithms, and applications. More than 135 figures supplement the text.

  • The Fix-Point Approach to Interdependent Systems

    • 1st Edition
    • Volume 132
    • H. Wold
    • English
    Contributions to Economic Analysis, 132: The Fix-Point Approach to Interdependent Systems focuses on the Fix-Point method for the estimation of interdependent systems, including the Algebraic Fix-Point, Parametric Fix-Point, and Parametric Fractional Fix-Point methods. The selection first ponders on the fix-point approach to interdependent systems, iterative algorithms for fix-point estimation, and GEID specification. Discussions focus on the GEID estimator, convergence to multiple parameter sets, design of iterative algorithms, and challenges of simultaneous equations systems. The text then takes a look at the Parametric Fix-Point (PFP) and the Algebraic Fix-Point (AFP) methods; estimation of real-world models by fix-point and other methods; and a search for asymptotically efficient estimators. Topics include autoregressive errors, estimation of the Klein-Goldberger model, estimation of a model of the Czechoslovak economy, and the Parametric Fractional Fix-Point (PFFP) and Parametric Recursive Fix-Point (PRFP) methods. The text elaborates on fix-point estimates of the structure of a model using different Y proxy starts; analysis of the nonlinear Klein-Goldberger model using fix-point estimation and other methods; and fix-point estimation in interdependent systems with specification errors. The selection is a vital reference for researchers interested in the Fix-Point method for the estimation of interdependent systems.

  • Statistical Inferences for Stochastic Processes

    Theory and Methods
    • 1st Edition
    • Ishwar V. Basawa + 1 more
    • English
    Statistical Inference Stochastic Processes provides information pertinent to the theory of stochastic processes. This book discusses stochastic models that are increasingly used in scientific research and describes some of their applications. Organized into three parts encompassing 12 chapters, this book begins with an overview of the basic concepts and procedures of statistical inference. This text then explains the inference problems for Galton–Watson process for discrete time and Markov-branching processes for continuous time. Other chapters consider problems of prediction, filtering, and parameter estimation for some simple discrete-time linear stochastic processes. This book discusses as well the ergodic type chains with finite and countable state-spaces and describes some results on birth and death processes that are of a non-ergodic type. The final chapter deals with inference procedures for stochastic processes through sequential procedures. This book is a valuable resource for graduate students.

  • A Graduate Course in Probability

    • 1st Edition
    • Howard G. Tucker
    • Z. W. Birnbaum + 1 more
    • English
    Probability and Mathematical Statistics: A Series of Monographs and Textbooks: A Graduate Course in Probability presents some of the basic theorems of analytic probability theory in a cohesive manner. This book discusses the probability spaces and distributions, stochastic independence, basic limiting operations, and strong limit theorems for independent random variables. The central limit theorem, conditional expectation and martingale theory, and Brownian motion are also elaborated. The prerequisite for this text is knowledge of real analysis or measure theory, particularly the Lebesgue dominated convergence theorem, Fubini's theorem, Radon-Nikodym theorem, Egorov's theorem, monotone convergence theorem, and theorem on unique extension of a sigma-finite measure from an algebra to the sigma-algebra generated by it. This publication is suitable for a one-year graduate course in probability given in a mathematics program and preferably for students in their second year of graduate work.

  • A Computational Logic

    • 1st Edition
    • Robert S. Boyer + 1 more
    • Thomas A. Standish
    • English
    ACM Monograph Series: A Computational Logic focuses on the use of induction in proving theorems, including the use of lemmas and axioms, free variables, equalities, and generalization. The publication first elaborates on a sketch of the theory and two simple examples, a precise definition of the theory, and correctness of a tautology-checker. Topics include mechanical proofs, informal development, formal specification of the problem, well-founded relations, natural numbers, and literal atoms. The book then examines the use of type information to simplify formulas, use of axioms and lemmas as rewrite rules, and the use of definitions. Topics include nonrecursive functions, computing values, free variables in hypothesis, infinite backwards chaining, infinite looping, computing type sets, and type prescriptions. The manuscript takes a look at rewriting terms and simplifying clauses, eliminating destructors and irrelevance, using equalities, and generalization. Concerns include reasons for eliminating isolated hypotheses, precise statement of the generalization heuristic, restricting generalizations, precise use of equalities, and multiple destructors and infinite looping. The publication is a vital source of data for researchers interested in computational logic.

  • Differential Equations and Numerical Mathematics

    Selected Papers Presented to a National Conference Held in Novosibirsk, September 1978
    • 1st Edition
    • G. I. Marchuk
    • English
    Differential Equations and Numerical Mathematics contains selected papers presented in a national conference held in Novosibirsk on September 1978. This book, as the conference, is organized into three sections. Section A describes the modern theory of efficient cubature formulas; embedding theorems; and problems of spectral analysis. Section B considers the theoretical questions of partial differential equations, with emphasis on hyperbolic equations and systems, formulations, and methods for nonclassical problems of mathematical physics. Section C addresses the various problems of numerical mathematics, with focus on the optimum and asymptotically optimum algorithms for solving the problems of numerical mathematics.

  • Algebraic Theory of Automata

    • 1st Edition
    • Abraham Ginzburg
    • Robert L. Ashenhurst
    • English
    Algebraic Theory of Automata provides information pertinent to the methods and results of algebraic theory of automata. This book covers a variety of topics, including sets, semigroup, groupoids, isomorphism, semiautomata, proof of Kleene's theorem, and algebraic manipulations. Organized into seven chapters, this book begins with an overview of the fundamental properties of groups and semigroups. This text then examines the notion of semiautomaton, which serves as a basis for a rich and interesting theory. Other chapters consider algebraic notions and methods that are very useful in dealing with semiautomata. This book discusses as well some properties of the notion of covering of semiautomata. The final chapter deals with the theory of Krohn and Rhodes. This book is a valuable resource for graduate students.

  • Foundations of Microprogramming

    Architecture, Software, and Applications
    • 1st Edition
    • Ashok K. Agrawala + 1 more
    • Robert L. Ashenhurst
    • English
    Foundations of Microprogramming: Architecture, Software, and Applications discusses the foundations and trends in microprogramming, focusing on the architectural, software, and application aspects of microprogramming. The book reviews microprocessors, microprogramming concepts, and characteristics, as well as the architectural features in microprogrammed computers. The text explains support software and the different hierarchies or levels of languages. These include assembler languages which are mnemonic or symbolic representation of machine commands; the procedure oriented machine-dependent; and the procedure oriented machine independent. A simulator is used to interpret programs written in machine or micro-language before the instructions in the program can be run. A simulator and translator (which change some steps from one program written in another language to another program) should interface with the design language of the computer for these components to operate even when a new machine is developed. The book cites four existing computers which have "simple" diagonal microinstructions such as the Hewlett-Packard HP21MX and the Microdata 3200. Horizontal types of microinstructions allow parallel execution of many micro-operations, such as the Cal Data family of computers, the Varian 73, and the NANODATA QM-1. Microprogramming is applied in emulation, program enhancement, operating systems, signal processing, and graphics. The text can benefit programmers, computer engineers, computer technicians, and computer instructors dealing with many aspects of computers such as programming, hardware interface, networking, engineering or design.

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