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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 Literacy

    Issues and Directions for 1985
    • 1st Edition
    • Robert J. Seidel + 2 more
    • English
    Computer Literacy: Issues and Directions for 1985 is based on a conference entitled "National Goals for Computer Literacy in 1985", held in Reston, Virginia, on December 18-20, 1980, under the auspices of the National Science Foundation. The conference provided a forum for discussing views on computer literacy, as well as methods for infusion of computer-related objectives and activities into existing curricula for different age levels. Issues and barriers to developing national goals for achieving a computer-literate society in the United States are also examined. Comprised of 31 chapters, this book begins by presenting four major approaches to a perspective on computer literacy: impact of computer literacy on the citizenry; major national components of a computer literacy program; development of an information handling curriculum for an evolving computer literacy concept; and a 30-year historical overview of "computer events in three strands" (research/developmen... education, and social/political institutional). The next section considers the definitions and requirements of computer literacy as they impact society, students, and teachers. The use of the computer in cognitive research and in problem solving is also discussed, together with curriculum development in computer literacy. This monograph will be of interest to students, teachers, school administrators, and educational policymakers.

  • Applied Time Series Analysis II

    Proceedings of the Second Applied Time Series Symposium Held in Tulsa, Oklahoma, March 3-5, 1980
    • 1st Edition
    • David F. Findley
    • English
    Applied Time Series Analysis II contains the proceedings of the Second Applied Time Series Symposium Held in Tulsa, Oklahoma, on March 3-5, 1980. The symposium provided a forum for discussing significant advances in time series analysis and signal processing. Effective alternatives to the familiar least-square and maximum likelihood procedures are described, along with maximum likelihood procedures for modeling irregularly sampled series and for classifying non-stationary series. Comprised of 22 chapters, this volume begins with an introduction to the multidimensional filtering theory and presents specific case histories related to the multidimensional recursive filter stability problem; the least squares inverse problem; realization of filters; and spectral estimation. The unique properties of the three-dimensional wave equation are also considered. Subsequent chapters focus on high-resolution spectral estimators; time series analysis of geophysical inverse scattering problems; minimum entropy deconvolution; and fitting of a continuous time autoregression to discrete data. This monograph will appeal to students and practitioners in the fields of mathematics and statistics, electrical and electronics engineering, and information and computer sciences.

  • Numerical Methods for Initial Value Problems in Ordinary Differential Equations

    • 1st Edition
    • Simeon Ola Fatunla
    • Werner Rheinboldt + 1 more
    • English
    Numerical Method for Initial Value Problems in Ordinary Differential Equations deals with numerical treatment of special differential equations: stiff, stiff oscillatory, singular, and discontinuous initial value problems, characterized by large Lipschitz constants. The book reviews the difference operators, the theory of interpolation, first integral mean value theorem, and numerical integration algorithms. The text explains the theory of one-step methods, the Euler scheme, the inverse Euler scheme, and also Richardson's extrapolation. The book discusses the general theory of Runge-Kutta processes, including the error estimation, and stepsize selection of the R-K process. The text evaluates the different linear multistep methods such as the explicit linear multistep methods (Adams-Bashforth, 1883), the implicit linear multistep methods (Adams-Moulton scheme, 1926), and the general theory of linear multistep methods. The book also reviews the existing stiff codes based on the implicit/semi-implic... singly/diagonally implicit Runge-Kutta schemes, the backward differentiation formulas, the second derivative formulas, as well as the related extrapolation processes. The text is intended for undergraduates in mathematics, computer science, or engineering courses, andfor postgraduate students or researchers in related disciplines.

  • Thinking Computers and Virtual Persons

    Essays on the Intentionality of Machines
    • 1st Edition
    • Eric Dietrich
    • English
    Thinking Computers and Virtual Persons: Essays on the Intentionality of Machines explains how computations are meaningful and how computers can be cognitive agents like humans. This book focuses on the concept that cognition is computation. Organized into four parts encompassing 13 chapters, this book begins with an overview of the analogy between intentionality and phlogiston, the 17th-century principle of burning. This text then examines the objection to computationalism that it cannot prevent arbitrary attributions of content to the various data structures and representations involved in a computational process. Other chapters consider that the notion of original intentionality is incoherent. This book argues as well that the only way to build an intelligent machine is to build a neural network. The final chapter claims that an entire theoretical framework in cognitive psychology is incompatible with the view that human brains are computers of some sort. This book is a valuable resource for cognitive scientists.

  • Geometry and Combinatorics

    • 1st Edition
    • J. J. Seidel
    • D. G. Corneil + 1 more
    • English
    Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.

  • Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series

    • 1st Edition
    • William F. Trench + 1 more
    • English
    Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series contains the answers to selected problems in linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples. The problems and corresponding solutions deal with linear equations and matrices, including determinants; vector spaces and linear transformations; eigenvalues and eigenvectors; vector analysis and analytic geometry in R3; curves and surfaces; the differential calculus of real-valued functions of n variables; and vector-valued functions as ordered m-tuples of real-valued functions. Integration (line, surface, and multiple integrals) is also covered, together with Green's and Stokes's theorems and the divergence theorem. The final chapter is devoted to infinite sequences, infinite series, and power series in one variable. This monograph is intended for students majoring in science, engineering, or mathematics.

  • Mathematical Aspects of Finite Elements in Partial Differential Equations

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, April 1 – 3, 1974
    • 1st Edition
    • Carl de Boor
    • English
    Mathematical Aspects of Finite Elements in Partial Differential Equations addresses the mathematical questions raised by the use of finite elements in the numerical solution of partial differential equations. This book covers a variety of topics, including finite element method, hyperbolic partial differential equation, and problems with interfaces. Organized into 13 chapters, this book begins with an overview of the class of finite element subspaces with numerical examples. This text then presents as models the Dirichlet problem for the potential and bipotential operator and discusses the question of non-conforming elements using the classical Ritz- and least-squares-method... Other chapters consider some error estimates for the Galerkin problem by such energy considerations. This book discusses as well the spatial discretization of problem and presents the Galerkin method for ordinary differential equations using polynomials of degree k. The final chapter deals with the continuous-time Galerkin method for the heat equation. This book is a valuable resource for mathematicians.

  • Optical Computing Hardware

    Optical Computing
    • 1st Edition
    • Jürgen Jahns + 1 more
    • Sing H. Lee
    • English
    Optical Computing Hardware provides information pertinent to the advances in the development of optical computing hardware. This book discusses the two application areas, namely, high-performance computing and high-throughput photonic switching. Organized into 11 chapters, this book begins with an overview of the requirements on hardware from s system perspective. This text then presents the self-electro-optic-e... devices (SPEED), the vertical-cavity-surf... emitting microlasers (VCSEL), and the vertical-to-surface transmission electrophotonic device (VSTEP). Other chapters consider the fundamental principles of the devices and their operation either as logic devices or for optical interconnection applications. This book discusses as well the planar optical microlens as an example of a refractive microlens of the gradient-index type and explains the diffractive optical elements. The final chapter describes a method for writing and reading optically in parallel from a three-dimensional matrix by means of two-photon interaction in photochromic organic materials. This book is a valuable resource for engineers, scientists, and researchers.

  • Introduction to Combinatorics

    • 1st Edition
    • Gerald Berman + 1 more
    • English
    Introduction to Combinatorics focuses on the applications, processes, methodologies, and approaches involved in combinatorics or discrete mathematics. The book first offers information on introductory examples, permutations and combinations, and the inclusion-exclusion principle. Discussions focus on some applications of the inclusion-exclusion principle, derangements, calculus of sets, permutations, combinations, Stirling's formula, binomial theorem, regions of a plane, chromatic polynomials, and a random walk. The text then examines linear equations with unit coefficients, recurrence relations, and generating functions. Topics include derivatives and differential equations, solution of difference equations by means of generating functions, recurrence relations, summation method, difference methods, combinations with repetitions, solutions bounded below, and solutions bounded above and below. The publication takes a look at generating functions and difference equations, ramifications of the binomial theorem, finite structures, coloring problems, maps on a sphere, and geometry of the plane. The manuscript is a valuable reference for researchers interested in combinatorics.

  • Contributions to Survey Sampling and Applied Statistics

    Papers in Honor of H.O Hartley
    • 1st Edition
    • H. O. Hartley
    • H. A. David
    • English
    Contributions to Survey Sampling and Applied Statistics: Papers in Honor of H. O. Hartley covers the significant advances in survey sampling, modeling, and applied statistics. This book is organized into five parts encompassing 20 chapters. The opening part looks into some aspects of statistics, sampling, randomization, predictive estimation, and internal congruency. This part also considers the properties of variance estimation for a specified multiple frame survey design and some sampling designs involving unequal probabilities of selection and robust estimation of a finite population total. The next parts present the analysis and the theoretical and practical aspects of linear models, as well as the applications of time series analysis. These topics are followed by discussions of the testing for outliers in linear regression; the robustness of location estimators; and completeness comparisons among sample sequences. The closing part deals with the properties of norm estimators in regression and geometric programming. This part also provides tables of the normal conditioned on t-distribution. This book will prove useful to mathematicians and statisticians.

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