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Elsevier

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.

  • Vector and Operator Valued Measures and Applications

    • 1st Edition
    • Don H. Tucker + 1 more
    • English
    Vector and Operator Valued Measures and Applications is a collection of papers presented at the Symposium on Vector and Operator Valued Measures and Applications held in Alta, Utah, on August 7-12, 1972. The symposium provided a forum for discussing vector and operator valued measures and their applications to various areas such as stochastic integration, electrical engineering, control theory, and scattering theory. Comprised of 37 chapters, this volume begins by presenting two remarks related to the result due to Kolmogorov: the first is a theorem holding for nonnegative definite functions from T X T to C (where T is an arbitrary index set), and the second applies to separable Hausdorff spaces T, continuous nonnegative definite functions ? from T X T to C, and separable Hilbert spaces H. The reader is then introduced to the extremal structure of the range of a controlled vector measure ? with values in a Hausdorff locally convex space X over the field of reals; how the theory of vector measures is connected with the theory of compact and weakly compact mappings on certain function spaces; and Daniell and Daniell-Bochner type integrals. Subsequent chapters focus on the disintegration of measures and lifting; products of spectral measures; and mean convergence of martingales of Pettis integrable functions. This book should be of considerable use to workers in the field of mathematics.

  • 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.

  • Handbook of Neural Computing Applications

    • 1st Edition
    • Alianna J. Maren + 2 more
    • English
    Handbook of Neural Computing Applications is a collection of articles that deals with neural networks. Some papers review the biology of neural networks, their type and function (structure, dynamics, and learning) and compare a back-propagating perceptron with a Boltzmann machine, or a Hopfield network with a Brain-State-in-a-Box network. Other papers deal with specific neural network types, and also on selecting, configuring, and implementing neural networks. Other papers address specific applications including neurocontrol for the benefit of control engineers and for neural networks researchers. Other applications involve signal processing, spatio-temporal pattern recognition, medical diagnoses, fault diagnoses, robotics, business, data communications, data compression, and adaptive man-machine systems. One paper describes data compression and dimensionality reduction methods that have characteristics, such as high compression ratios to facilitate data storage, strong discrimination of novel data from baseline, rapid operation for software and hardware, as well as the ability to recognized loss of data during compression or reconstruction. The collection can prove helpful for programmers, computer engineers, computer technicians, and computer instructors dealing with many aspects of computers related to programming, hardware interface, networking, engineering or design.

  • Mathematical Models of Attitude Change

    Change in Single Attitudes and Cognitive Structure
    • 1st Edition
    • John E. Hunter + 2 more
    • Peter R. Monge
    • English
    Mathematical Models of Attitude Change, Volume 1: Change in Single Attitudes and Cognitive Structure presents the mathematical models that address the existing verbal attitude change theories, which are translated into families of mathematical models. This book discusses the two types of attitude change, namely, the attitude toward the object of the message and the attitude toward the source of the message. Organized into three parts encompassing 17 chapters, this volume begins with an overview of the mathematical models of attitude change that are derived from several theories. This text then explains the empirical work designed to test selected mathematical models of attitude change. Other chapters consider the predictions made by different models, including reinforcement, information processing, social judgment, balance, dissonance, and congruity. This book discusses as well the attitude-related variable, namely, belief and belief change. The final chapter deals with models of change in hierarchical organized attitudes using alternative theories of attitude change. This book is a valuable resource for psychologists.

  • Neural Networks for Perception

    Human and Machine Perception
    • 1st Edition
    • Harry Wechsler
    • English
    Neural Networks for Perception, Volume 1: Human and Machine Perception focuses on models for understanding human perception in terms of distributed computation and examples of PDP models for machine perception. This book addresses both theoretical and practical issues related to the feasibility of both explaining human perception and implementing machine perception in terms of neural network models. The book is organized into two parts. The first part focuses on human perception. Topics on network model of object recognition in human vision, the self-organization of functional architecture in the cerebral cortex, and the structure and interpretation of neuronal codes in the visual system are detailed under this part. Part two covers the relevance of neural networks for machine perception. Subjects considered under this section include the multi-dimensional linear lattice for Fourier and Gabor transforms, multiple- scale Gaussian filtering, and edge detection; aspects of invariant pattern and object recognition; and neural network for motion processing. Neuroscientists, computer scientists, engineers, and researchers in artificial intelligence will find the book useful.

  • Numerical Solution of Systems of Nonlinear Algebraic Equations

    • 1st Edition
    • George D. Byrne + 1 more
    • English
    Numerical Solution of Systems of Nonlinear Algebraic Equations contains invited lectures of the NSF-CBMS Regional Conference on the Numerical Solution of Nonlinear Algebraic Systems with Applications to Problems in Physics, Engineering and Economics, held on July 10-14, 1972. This book is composed of 10 chapters and begins with the concepts of nonlinear algebraic equations in continuum mechanics. The succeeding chapters deal with the numerical solution of quasilinear elliptic equations, the nonlinear systems in semi-infinite programming, and the solution of large systems of linear algebraic equations. These topics are followed by a survey of some computational techniques for the nonlinear least squares problem. The remaining chapters explore the problem of nonlinear functional minimization, the modification methods, and the computer-oriented algorithms for solving system. These chapters also examine the principles of contractor theory of solving equations. This book will prove useful to undergraduate and graduate students.

  • Methods of Numerical Integration

    • 2nd Edition
    • Philip J. Davis + 1 more
    • Werner Rheinbolt
    • English
    Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.

  • International Conference on Differential Equations

    • 1st Edition
    • H.A. Antosiewicz
    • English
    International Conference on Differential Equations contains the proceedings of an International Conference on Differential Equations held at the University of Southern California, on September 3-7, 1974. The papers review advances in the qualitative-analytic theory of differential equations and highlight three broad areas: analytic theory (singular perturbations), qualitative theory (boundary value problems), and mathematical control theory (variational methods). Comprised of 82 chapters, this book begins with a discussion on continuous extensions, their construction, and their application in the theory of differential equations. The reader is then introduced to an approach to boundary control of partial differential equations based on the theory of semigroups of operators; lower closure and existence theorems in optimal control; and a nonlinear oscillation theorem. Subsequent chapters focus on matrices of rational functions; asymptotic integration of linear differential systems; solutions near bifurcated steady states; and geometric views in existence theory. This monograph will be of interest to students and instructors of mathematics.

  • Rational Politics

    Decisions, Games, and Strategy
    • 1st Edition
    • Steven J. Brams
    • English
    Rational Politics: Decisions, Games, and Strategy focuses on the unified presentation of politics as a rational human activity, including the paradox of voting and proportional representation. The publication first offers information on the study of rational politics, political intrigue in the Bible, and candidate strategies. Topics include the factor of timing in presidential primaries, rational positions in a multicandidate race, primacy of issues and their spatial representation, and politics in the story of Esther. The text then elaborates on voting paradoxes and the problems of representation, voting power, and threats and deterrence. Discussions focus on a sequential view of the Cuban missile crisis, use of threat power in Poland, power anomalies in the European Community Council of Ministers, probability of the paradox of voting, empirical examples of the paradox of voting, and problems in achieving proportional representation. The book is a valuable reference for researchers interested in rational politics.

  • 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.

  • Introductory Statistics for the Behavioral Sciences

    Workbook
    • 1st Edition
    • Robert B. Ewen
    • English
    Introductory Statistics for the Behavioral Sciences is a workbook on statistical procedures and formulas that are relevant to research and field work. The book explains frequency distributions, graphs, and measures of central tendency. The workbook uses as example hypothetical scores of a test given to students in four universities. The book then has sections on reminders and problems to guide the reader. Other topics the book discusses include measures of variability, transformed scores, probability, and general strategy of inferential statistics. Other subjects the book also covers include inferences about the mean of a single population and testing hypotheses about the differences between the means of two populations. The workbook also includes practice problems on linear correlation, prediction, and other correlational techniques such as the Spearmen rank-order correlation coefficient or the point biserial correlation coefficient. The book also includes review chapters on normal curves, standard error procedures, and inferential statistics. The workbook can be a great aid for students of behavioral and physical sciences where statistics is applied in research and analysis.

  • Projective Geometry and Algebraic Structures

    • 1st Edition
    • R. J. Mihalek
    • English
    Projective Geometry and Algebraic Structures focuses on the relationship of geometry and algebra, including affine and projective planes, isomorphism, and system of real numbers. The book first elaborates on euclidean, projective, and affine planes, including axioms for a projective plane, algebraic incidence bases, and self-dual axioms. The text then ponders on affine and projective planes, theorems of Desargues and Pappus, and coordination. Topics include algebraic systems and incidence bases, coordinatization theorem, finite projective planes, coordinates, deletion subgeometries, imbedding theorem, and isomorphism. The publication examines projectivities, harmonic quadruples, real projective plane, and projective spaces. Discussions focus on subspaces and dimension, intervals and complements, dual spaces, axioms for a projective space, ordered fields, completeness and the real numbers, real projective plane, and harmonic quadruples. The manuscript is a dependable reference for students and researchers interested in projective planes, system of real numbers, isomorphism, and subspaces and dimensions.

  • Probability, Statistics, and Mathematics

    Papers in Honor of Samuel Karlin
    • 1st Edition
    • T. W. Anderson + 2 more
    • English
    Probability, Statistics, and Mathematics: Papers in Honor of Samuel Karlin is a collection of papers dealing with probability, statistics, and mathematics. Conceived in honor of Polish-born mathematician Samuel Karlin, the book covers a wide array of topics, from the second-order moments of a stationary Markov chain to the exponentiality of the local time at hitting times for reflecting diffusions. Smoothed limit theorems for equilibrium processes are also discussed. Comprised of 24 chapters, this book begins with an introduction to the second-order moments of a stationary Markov chain, paying particular attention to the consequences of the autoregressive structure of the vector-valued process and how to estimate the stationary probabilities from a finite sequence of observations. Subsequent chapters focus on A. Selberg's second beta integral and an integral of mehta; a normal approximation for the number of local maxima of a random function on a graph; nonnegative polynomials on polyhedra; and the fundamental period of the queue with Markov-modulated arrivals. The rate of escape problem for a class of random walks is also considered. This monograph is intended for students and practitioners in the fields of statistics, mathematics, and economics.

  • Pattern-Directed Inference Systems

    • 1st Edition
    • D. A. Waterman + 1 more
    • English
    Pattern-Directed Inference Systems provides a description of the design and implementation of pattern-directed inference systems (PDIS) for various applications. The book also addresses the theoretical significance of PDIS for artificial intelligence and cognitive psychology. The book is divided into eight sections. The introduction provides a brief overview of pattern-directed inference systems, including a historical perspective, a review of basic concepts, and a survey of work in this area. Subsequent chapters address topics on architecture and design, methods for accessing and controlling rule based systems, methods for obtaining adaptive behavior via rule-based systems and cognitive modeling. Constructing models of human information processing, natural language understanding and multilevel systems and complexity are described as well. The last section discusses the earlier chapters in the book and provides a unifying set of principles for the PDIS formalism. Computer scientists, psychologists, engineers, and researchers in artificial intelligence will find the book very informative.

  • Introductory College Mathematics

    with Linear Algebra and Finite Mathematics
    • 1st Edition
    • Harley Flanders + 1 more
    • English
    Introductory College Mathematics: With Linear Algebra and Finite Mathematics is an introduction to college mathematics, with emphasis on linear algebra and finite mathematics. It aims to provide a working knowledge of basic functions (polynomial, rational, exponential, logarithmic, and trigonometric); graphing techniques and the numerical aspects and applications of functions; two- and three-dimensional vector methods; the fundamental ideas of linear algebra; and complex numbers, elementary combinatorics, the binomial theorem, and mathematical induction. Comprised of 15 chapters, this book begins with a discussion on functions and graphs, paying particular attention to quantities measured in the real number system. The next chapter deals with linear and quadratic functions as well as some of their applications. Tips on graphing are offered. Subsequent chapters focus on polynomial functions, along with graphs of factored polynomials; rational functions; exponential and logarithm functions; and trigonometric functions. Identities and inverse functions, vectors and matrices, and trigonometry are also explored, together with complex numbers, linear transformations, and the geometry of space. The book concludes by considering finite mathematics, with particular reference to mathematical induction and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

  • Generative Modeling for Computer Graphics and Cad

    Symbolic Shape Design Using Interval Analysis
    • 1st Edition
    • John M. Snyder
    • English
    Generative Modeling for Computer Graphics and Cad: Symbolic Shape Design Using Interval Analysis presents a symbolic approach to shape representation that is useful to the CAD/CAM and computer graphics communities. This book discusses the kinds of operators useful in a geometric modeling system, including arithmetic operators, vector and matrix operators, integration, differentiation, constraint solution, and constrained minimization. Associated with each operator are several methods that compute properties about the parametric functions represented with the operators. This text also elaborates how numerous rendering and analytical operations can be supported with only three methods—evaluation of the parametric function at a point, symbolic differentiation of the parametric function, and evaluation of an inclusion function for the parametric function. This publication is intended for people working in the area of computational geometry who are interested in a robust class of algorithms for manipulating shapes and those who want to know how human beings can specify and manipulate shape.

  • Advanced Calculus of Several Variables

    • 1st Edition
    • C. H. Edwards
    • English
    Advanced Calculus of Several Variables provides a conceptual treatment of multivariable calculus. This book emphasizes the interplay of geometry, analysis through linear algebra, and approximation of nonlinear mappings by linear ones. The classical applications and computational methods that are responsible for much of the interest and importance of calculus are also considered. This text is organized into six chapters. Chapter I deals with linear algebra and geometry of Euclidean n-space Rn. The multivariable differential calculus is treated in Chapters II and III, while multivariable integral calculus is covered in Chapters IV and V. The last chapter is devoted to venerable problems of the calculus of variations. This publication is intended for students who have completed a standard introductory calculus sequence.

  • Mathematical Methods in Computer Aided Geometric Design II

    • 1st Edition
    • Tom Lyche + 1 more
    • English
    Mathematical Methods in Computer Aided Geometric Design II covers the proceedings of the 1991 International Conference on Curves, Surfaces, CAGD, and Image Processing, held at Biri, Norway. This book contains 48 chapters that include the topics of blossoming, cyclides, data fitting and interpolation, and finding intersections of curves and surfaces. Considerable chapters explore the geometric continuity, geometrical optics, image and signal processing, and modeling of geological structures. The remaining chapters discuss the principles of multiresolution analysis, NURBS, offsets, radial basis functions, rational splines, robotics, spline and Bézier methods for curve and surface modeling, subdivision, terrain modeling, and wavelets. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.

  • The Mathematics of Finite Elements and Applications

    Proceedings of the Brunel University Conference of the Institute of Mathematics and Its Applications Held in April 1972
    • 1st Edition
    • J. R. Whiteman
    • English
    The Mathematics of Finite Elements and Applications provides information pertinent to the mathematics of finite elements, applications, algorithms, and computational techniques. This book discusses the developments in the mathematics of finite elements. Organized into 32 chapters, this book begins with an overview of the basis of the finite element process as a general approximation tool. This text then examines the methods for obtaining bounds on the errors in finite element solutions to two-dimensional elliptic boundary value problems defined on simply connected polygonal regions. Other chapters consider the practical implementation of the Galerkin and the Rayleigh–Ritz methods to equations of importance to physics and engineering. This book discusses as well a fundamental investigation into the problem of convergence in the finite element method. The final chapter deals with an algorithm that is applicable to the analysis of arbitrary plane stress or plane strain configurations. This book is a valuable resource for numerical analysts, mathematical physicist, applied mathematicians, computer scientists, and engineers.

  • An Introduction to Stochastic Modeling

    • 1st Edition
    • Howard M. Taylor + 1 more
    • English
    An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

  • Mathematical Algorithms for Linear Regression

    • 1st Edition
    • Helmuth Späth
    • Werner Rheinboldt
    • English
    Mathematical Algorithms for Linear Regression discusses numerous fitting principles related to discrete linear approximations, corresponding numerical methods, and FORTRAN 77 subroutines. The book explains linear Lp regression, method of the lease squares, the Gaussian elimination method, the modified Gram-Schmidt method, the method of least absolute deviations, and the method of least maximum absolute deviation. The investigator can determine which observations can be classified as outliers (those with large errors) and which are not by using the fitting principle. The text describes the elimination of outliers and the selection of variables if too many or all of them are given by values. The clusterwise linear regression accounts if only a few of the relevant variables have been collected or are collectible, assuming that their number is small in relation to the number of observations. The book also examines linear Lp regression with nonnegative parameters, the Kuhn-Tucker conditions, the Householder transformations, and the branch-and-bound method. The text points out the method of least squares is mainly used for models with nonlinear parameters or for orthogonal distances. The book can serve and benefit mathematicians, students, and professor of calculus, statistics, or advanced mathematics.

  • Multivariable Calculus with Linear Algebra and Series

    • 1st Edition
    • William F. Trench + 1 more
    • English
    Multivariable Calculus with Linear Algebra and Series presents a modern, but not extreme, treatment of 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. Comprised of seven chapters, this book begins with an introduction to linear equations and matrices, including determinants. The next chapter deals with vector spaces and linear transformations, along with eigenvalues and eigenvectors. The discussion then turns to 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 considered, 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.

  • Algorithmically Specialized Parallel Computers

    • 1st Edition
    • Lawrence Snyder + 2 more
    • English
    Algorithmically Specialized Parallel Computers focuses on the concept and characteristics of an algorithmically specialized computer. This book discusses the algorithmically specialized computers, algorithmic specialization using VLSI, and innovative architectures. The architectures and algorithms for digital signal, speech, and image processing and specialized architectures for numerical computations are also elaborated. Other topics include the model for analyzing generalized inter-processor, pipelined architecture for search tree maintenance, and specialized computer organization for raster graphics display. The data base applications of the FETCH-AND-ADD instruction, distributed parallel architecture for speech understanding, and two parallel formulations of particle-in-cell models are likewise covered in this text. This publication is suitable for students, researchers and professionals concerned with algorithmically specialized computers.

  • Fourier Expansions

    A Collection of Formulas
    • 1st Edition
    • Fritz Oberhettinger
    • English
    Fourier Expansions: A Collection of Formulas provides a collection of Fourier series. Its limited scope made a number of compromises necessary. The question regarding the choice and organization of the material to be included posed certain problems. In order to preserve some consistency it seemed best to stay within the framework of what one could call the ""classical"" Fourier series, i.e., those of the trigonometric and their simplest generalization the Fourier-Bessel series. The book is organized into five sections: Section I presents Fourier series with elementary coefficients representing elementary functions. Section II presents Fourier series with elementary coefficients representing higher functions. Section III presents Fourier series with higher function coefficients representing elementary functions. Section IV presents Fourier series with higher function coefficients representing higher functions. Section V presents exponential Fourier and Fourier-Bessel series. This arrangement should be helpful in equally balancing the task of either establishing the sum function of a given Fourier series or finding the Fourier expansion of a given function. It is hoped that this book will meet the requirements so often needed in applied mathematics, physics, and engineering.

  • Applied Statistical Methods

    • 1st Edition
    • Irving W. Burr
    • J. William Schmidt
    • English
    Applied Statistical Methods covers the fundamental understanding of statistical methods necessary to deal with a wide variety of practical problems. This 14-chapter text presents the topics covered in a manner that stresses clarity of understanding, interpretation, and method of application. The introductory chapter illustrates the importance of statistical analysis. The next chapters introduce the methods of data summarization, including frequency distributions, cumulative frequency distributions, and measures of central tendency and variability. These topics are followed by discussions of the fundamental principles of probability, the concepts of sample spaces, outcomes, events, probability, independence of events, and the characterization of discrete and continuous random variables. Other chapters explore the distribution of several important statistics; statistical tests of hypotheses; point and interval estimation; and simple linear regression. The concluding chapters review the elements of single- and two-factor analysis of variance and the design of analysis of variance experiments. This book is intended primarily for advanced undergraduate and graduate students in the mathematical, physical, and engineering sciences, as well as in economics, business, and related areas. Researchers and line personnel in industry and government will find this book useful in self-study.

  • High Performance Computing Demystified

    • 1st Edition
    • David Loshin
    • English
    High Performance Computing Demystified provides an overview of high performance resources and their applications across many disciplines. This book is organized into five parts encompassing 16 chapters that cover the principles, mode of operation, and practical aspects of supercomputers. The first and second parts provide a brief history of high performance computing and describe the “basic” parts needed to build high performance computers, including high performance microprocessors and network topologies. The third part examines the features of multiprocessor architectures of high performance, such as the large number crunchers, massively parallel processing machines, and networks of workstations. The fourth part deals with the software paradigms for high performance, while the fifth part looks into the high performance computing resources that are available to the public, with some guide to accessing those resources. This book is intended primarily for engineers and business managers who have a basic understanding of computers and would like to learn about high performance computing.

  • Mastering Mathematica®

    Programming Methods and Applications
    • 1st Edition
    • John W. Gray
    • English
    Mastering Mathematica®: Programming Methods and Applications presents the mathematical results and turn them into precise algorithmic procedures that can be executed by a computer. This book provides insight into more complex situations that can be investigated by hand. Organized into four parts, this book begins with an overview of the use of a pocket calculator. This text then looks in more detail at numerical calculations and solving equations, both algebraic and differential equations. Other parts consider the built-in graphics and show how to make pictures without programming. This book discusses as well the four styles of programming, namely, functional programming, imperative programming, rewrite programing, and object oriented programming. The reader is also introduced to differentiable mapping to show the analysis of critical points of functions and the developments in differential geometry that are required to study minimal surfaces. This book is a valuable resource for graduate students in mathematics, mathematics education, engineering, and the sciences.

  • Algebra

    • 1st Edition
    • Harley Flanders + 1 more
    • English
    Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms. Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of algebraic notation and practical manipulative skills such as factoring, using exponents and radicals, and simplifying rational expressions is highlighted, along with the most common mistakes in algebra. The reader is then introduced to the solution of linear, quadratic, and other types of equations and systems of equations, as well as the solution of inequalities. Subsequent chapters deal with the most basic functions of algebra: polynomial, rational, exponential, and logarithm. The book concludes with a review of sequences, permutations and combinations, and the binomial theorem, as well as summation and mathematical induction. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

  • Introduction to Parallel Programming

    • 1st Edition
    • Steven Brawer
    • English
    Introduction to Parallel Programming focuses on the techniques, processes, methodologies, and approaches involved in parallel programming. The book first offers information on Fortran, hardware and operating system models, and processes, shared memory, and simple parallel programs. Discussions focus on processes and processors, joining processes, shared memory, time-sharing with multiple processors, hardware, loops, passing arguments in function/subroutine calls, program structure, and arithmetic expressions. The text then elaborates on basic parallel programming techniques, barriers and race conditions, and nested loops. The manuscript takes a look at overcoming data dependencies, scheduling summary, linear recurrence relations, and performance tuning. Topics include parallel programming and the structure of programs, effect of the number of processes on overhead, loop splitting, indirect scheduling, block scheduling and forward dependency, and induction variable. The publication is a valuable reference for researchers interested in parallel programming.

  • Workbook for Introductory Statistics for the Behavioral Sciences

    • 2nd Edition
    • Robert B. Ewen
    • English
    Workbook for Introductory Statistics for the Behavioral Sciences, Second Edition provides an introduction to the concepts of statistics. This book aims to help students obtain the necessary practice in a first course in statistics, which is essential to learning and understanding the material. This edition begins with an overview of summation notation exercises with additional computational practices. This text then provides computational exercises for regular frequency distributions, grouped frequency distributions, cumulative frequency distribution, graphic representations, measures of central tendency, measures of variability, and general transformations. This book discusses as well the probability and the general strategy of inferential statistics as well as the differences between the means of two populations. The reader is also introduced to the main advantage of nonparametric and distribution-free statistical tests in which they do not require the population being sampled to the normally distributed. This book is a valuable resource for students of behavioral and social sciences.

  • Discriminant Analysis and Applications

    • 1st Edition
    • T. Cacoullos
    • English
    Discriminant Analysis and Applications comprises the proceedings of the NATO Advanced Study Institute on Discriminant Analysis and Applications held in Kifissia, Athens, Greece in June 1972. The book presents the theory and applications of Discriminant analysis, one of the most important areas of multivariate statistical analysis. This volume contains chapters that cover the historical development of discriminant analysis methods; logistic and quasi-linear discrimination; and distance functions. Medical and biological applications, and computer graphical analysis and graphical techniques for multidimensional data are likewise discussed. Statisticians, mathematicians, and biomathematicians will find the book very interesting.

  • Practical Parallel Computing

    • 1st Edition
    • H. Stephen Morse
    • English
    Practical Parallel Computing provides information pertinent to the fundamental aspects of high-performance parallel processing. This book discusses the development of parallel applications on a variety of equipment. Organized into three parts encompassing 12 chapters, this book begins with an overview of the technology trends that converge to favor massively parallel hardware over traditional mainframes and vector machines. This text then gives a tutorial introduction to parallel hardware architectures. Other chapters provide worked-out examples of programs using several parallel languages. This book deals as well with benchmarking and performance estimation on parallel machines. The final chapter provides a structured, flexible methodology for selecting a parallel machine and for integrating it into operations. This book is a valuable resource for readers who are confronted with the practical realities of parallel computing for the first time. Mid-level technical managers, algorithm designers, computer scientists, and doctorate-level mathematicians will also find this book extremely useful.

  • Numerical Computation Using C

    • 1st Edition
    • Robert Glassey
    • Werner Rheinboldt
    • English
    Numerical Computation Using C is a four-chapter text guide for learning C language from the numerical analysis viewpoint. C is a general-purpose language that has been used in systems programming. The first chapter discusses the basic principles, logic, operators, functions, arrays, and structures of C language. The next two chapters deal with the uses of the so-called pointers in the C language, which is a variable that contains the address of some object in memory. These chapters also elaborate on several constructs to show how the use of C language can be fine-tuned. The last chapter highlights the practical aspects of C language. This book will be of value to computer scientists and mathematicians.

  • Contributions to Correlational Analysis

    • 1st Edition
    • Robert J. Wherry
    • English
    Contributions to Correlational Analysis provides information pertinent to the fundamental aspects of correlational analysis that can be used to replace and enhance many of the parametric and nonparametric inferential statistical tests. This book discusses the basic concern of correctional analysis, which is the relationship between two sets of measure. Organized into 18 chapters, this book begins with an overview of the nature of correction analysis. This text then explains the simple linear relationships in which explains the simple linear relationships in which Y and X each consists of some single measurement per person and the relationship is assumed to be linear. Other chapters consider basic ways of expanding the process to include more or different measurements of either X or Y but with no attempt to find the best functions. This book discusses as well the topic of factor analysis. The final chapter deals with canonical correlation. This book is a valuable resource for psychologists.

  • Numerical Analysis

    A Second Course
    • 1st Edition
    • James M. Ortega
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Numerical Analysis: A Second Course presents some of the basic theoretical results pertaining to the three major problem areas of numerical analysis—rounding error, discretization error, and convergence error. This book is organized into four main topics: mathematical stability and ill conditioning, discretization error, convergence of iterative methods, and rounding error. In these topics, this text specifically discusses the systems of linear algebraic equations, eigenvalues and eigenvectors, and differential and difference equations. The discretization error for initial and boundary value problems, systems of linear and nonlinear equations, and rounding error for Gaussian elimination are also elaborated. This publication is recommended for undergraduate level students and students taking a one-semester first-year graduate course for computer science and mathematics majors.

  • Elementary Topology

    A Combinatorial and Algebraic Approach
    • 1st Edition
    • Donald W. Blackett
    • English
    Elementary Topology: A Combinatorial and Algebraic Approach focuses on the application of algebraic methods to topological concepts and theorems. The publication first elaborates on some examples of surfaces and their classifications. Discussions focus on combinatorial invariants of a surface, combinatorial equivalence, surfaces and their equations, topological surfaces, coordinates on a sphere and torus, and properties of the sphere and torus. The text then examines complex conics and covering surfaces and mappings into the sphere, including applications of the winding number in complex analysis, mappings into the plane, winding number of a plane curve, covering surfaces, and complex conies. The book examines vector fields, network topology, and three-dimensional topology. Topics include topological products and fiber bundles, manifolds of configurations, paths, circuits, and trees, vector fields and hydrodynamics, vector fields on a sphere, and vector fields and differential equations. The publication is highly recommended for sophomores, juniors, and seniors who have completed a year of calculus.

  • Dynamic Programming and Its Applications

    Proceedings of the International Conference on Dynamic Programming and Its Applications, University of British Columbia, Vancouver, British Columbia, Canada, April 14-16, 1977
    • 1st Edition
    • Martin L. Puterman
    • English
    Dynamic Programming and Its Applications provides information pertinent to the theory and application of dynamic programming. This book presents the development and future directions for dynamic programming. Organized into four parts encompassing 23 chapters, this book begins with an overview of recurrence conditions for countable state Markov decision problems, which ensure that the optimal average reward exists and satisfies the functional equation of dynamic programming. This text then provides an extensive analysis of the theory of successive approximation for Markov decision problems. Other chapters consider the computational methods for deterministic, finite horizon problems, and present a unified and insightful presentation of several foundational questions. This book discusses as well the relationship between policy iteration and Newton's method. The final chapter deals with the main factors severely limiting the application of dynamic programming in practice. This book is a valuable resource for growth theorists, economists, biologists, mathematicians, and applied management scientists.

  • Combinatorics

    • 1st Edition
    • N. Ya. Vilenkin
    • English
    Combinatorics deals with simple combinatorial problems, recurrence relations, and generating functions, particularly the binomial expansions. The book expounds on the general rules of combinatorics, the rule of sum, the rule of product, samples, permutations, combinations, and arrangements of subjects with various restrictions. The text also explains ordered or unordered partitions of numbers, geometric methods, random walk problems, and variants of the arithmetical triangle. One example of the use of combinatorics is the choice of the number 3 in the genetic code. Another example involves the choice of crew for a spaceship where it is necessary to consider the psychological conditions of the applicants for space travel. The text also investigates the sieve of Erastothenes whose problem concerns finding all the primes in the sequence of natural numbers from 1 to N. The book also tackles the application of power series to proof of identities, the binomial series expansion, decomposition into elementary fractions, and nonlinear recurrence relation. The book can be highly educational and interesting to students or academicians involved in mathematics, algebra, and statistics.

  • Frontiers of Pattern Recognition

    The Proceedings of the International Conference on Frontiers of Pattern Recognition
    • 1st Edition
    • Satosi Watanabe
    • English
    Frontiers of Pattern Recognition contains the proceedings of the International Conference on Frontiers of Pattern Recognition which took place on January 18-20, 1971, at the University of Hawaii, Honolulu. The compendium consists of 30 papers from authorities from eleven different countries, which describe the frontiers of pattern recognition as viewed from diverse viewpoints. Topics discussed include some techniques for recognizing structures in pictures, grammatical inference, syntactic pattern recognition and stochastic languages, and pattern cognition and the organization of information. Also covered are subjects on human face recognition, cluster analysis, and learning algorithms of pattern recognition in non-stationary conditions. Computer scientists, mathematicians, statisticians, linguists, and psychologists will find the book informative.

  • Scientific Inference, Data Analysis, and Robustness

    Proceedings of a Conference Conducted by the Mathematics Research Center, the University of Wisconsin—Madison, November 4–6, 1981
    • 1st Edition
    • G. E. P. Box + 2 more
    • English
    Mathematics Research Center Symposium: Scientific Inference, Data Analysis, and Robustness focuses on the philosophy of statistical modeling, including model robust inference and analysis of data sets. The selection first elaborates on pivotal inference and the conditional view of robustness and some philosophies of inference and modeling, including ideas on modeling, significance testing, and scientific discovery. The book then ponders on parametric empirical Bayes confidence intervals, ecumenism in statistics, and frequency properties of Bayes rules. Discussions focus on consistency of Bayes rules, scientific method and the human brain, and statistical estimation and criticism. The book takes a look at the purposes and limitations of data analysis, likelihood, shape, and adaptive inference, statistical inference and measurement of entropy, and the robustness of a hierarchical model for multinomials and contingency tables. Topics include numerical results for contingency tables and robustness, multinomials, flattening constants, and mixed Dirichlet priors, entropy and likelihood, and test as measurement of entropy. The selection is a valuable reference for researchers interested in robust inference and analysis of data sets.

  • Science, Computers, and the Information Onslaught

    A Collection of Essays
    • 1st Edition
    • Donald M. Kerr + 2 more
    • English
    Science, Computers, and the Information Onslaught: A Collection of Essays covers the proceedings of the 1981 meeting on “Science and the Information Onslaught”, held at Los Alamos, New Mexico. This book is organized into five parts encompassing 19 chapters. The first part deals with the problems of measurement and the uses of information in decisions concerning national security. This part also emphasizes the dependence of survival on technological progress. The next part examines the foundations of information theory, the interaction between psychological concepts and the mathematical theories of automata, and the major problems in robotics. These topics are followed by discussions of the efforts to codify languages in formal grammatical systems and the past misuse of irrelevantly detailed information in decision making, specifically the use and misuse of information in government decisions about technological projects. The remaining parts consider the project of enhancing human abilities by the insertion of silicon chips in the body. These parts also assess the implications of a microelectronic technology capable of producing chips bearing millions of logically active circuit elements. Accounts of cryptanalytic successes in World War II are also included. This book will be of value to mathematicians, physicists, linguistics, and computer scientists.

  • Recent Advances in Differential Equations

    • 1st Edition
    • Roberto Conti
    • English
    Recent Advances in Differential Equations contains the proceedings of a meeting held at the International Center for Theoretical Physics in Trieste, Italy, on August 24-28, 1978 under the auspices of the U.S. Army Research Office. The papers review the status of research in the field of differential equations (ordinary, partial, and functional). Both theoretical aspects (differential operators, periodic solutions, stability and bifurcation, asymptotic behavior of solutions, etc.) and problems arising from applications (reaction-diffusion equations, control problems, heat flow, etc.) are discussed. Comprised of 33 chapters, this book first examines non-cooperative trajectories of n-person dynamical games and stable non-cooperative equilibria, followed by a discussion on the determination and application of Vekua resolvents. The reader is then introduced to generalized Hopf bifurcation; some Cauchy problems arising in computational methods; and boundary value problems for pairs of ordinary differential operators. Subsequent chapters focus on degenerate evolution equations and singular optimal control; stability of neutral functional differential equations; local exact controllability of nonlinear evolution equations; and turbulence and higher order bifurcations. This monograph will be of interest to students and practitioners in the field of mathematics.

  • Computational Geometry

    Curve and Surface Modeling
    • 1st Edition
    • Su Bu-qing + 1 more
    • English
    Computational Geometry: Curve and Surface Modeling provides information pertinent to the fundamental aspects of computational geometry. This book discusses the geometric properties of parametric polynomial curves by using the theory of affine invariants for algebraic curves. Organized into eight chapters, this book begins with an overview of the objects studies in computational geometry, namely surfaces and curves. This text then explores the developments in the theory and application of spline functions, which began with cubic spline functions. Other chapters consider the mechanical background of the cubic spline functions, which is the wooden spline with small deflection. This book discusses as well that in mathematical lofting the information of a geometric shape is given by a set of data points, while in geometric design other ways of representations are available. The final chapter deals with the concepts in the theory of algebraic curves. This book is a valuable resource for mathematicians.

  • Identification, Equivalent Models, and Computer Algebra

    Statistical Modeling and Decision Science
    • 1st Edition
    • Paul A. Bekker + 2 more
    • Gerald J. Lieberman + 1 more
    • English
    Identification, Equivalent Models, and Computer Algebra provides information pertinent to computer algebra. This book presents a brief discussion of the commutation matrix, an operator that plays a role when derivatives have to be evaluated involving symmetric matrices. Organized into eight chapters, this book begins with an overview of the link between identification of a parameter and the existence of a consistent estimator, and the link between identification of a model and the rank of a Jacobian matrix. This text then describes an algorithm for the determination of the exact rank of a parametrized matrix. Other chapters consider the identification in the simultaneous equation model. This book discusses as well the identification assessment in confirmatory factor analysis, a problem related to the simultaneous equations model. The final chapter deals with various computer programs that the enclosed diskette contains. This book is a valuable resource for readers who are interested in computer algebra.

  • Partial Differential Equations

    Theory and Technique
    • 1st Edition
    • George F. Carrier + 1 more
    • English
    Partial Differential Equations: Theory and Technique provides formal definitions, notational conventions, and a systematic discussion of partial differential equations. The text emphasizes the acquisition of practical technique in the use of partial differential equations. The book contains discussions on classical second-order equations of diffusion, wave motion, first-order linear and quasi-linear equations, and potential theory. Certain chapters elaborate Green's functions, eigenvalue problems, practical approximation techniques, perturbations (regular and singular), difference equations, and numerical methods. Students of mathematics will find the book very useful.

  • Analytic Geometry

    • 1st Edition
    • A. C. Burdette
    • English
    Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus. This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes. This book will prove useful to undergraduate trigonometric students.

  • Study Guide for Applied Finite Mathematics

    • 3rd Edition
    • Nicholas A. Macri
    • English
    Study Guide for Applied Finite Mathematics, Third Edition is a study guide that introduces beginners to the fundamentals of finite mathematics and its various realistic and relevant applications. Some applications of probability, game theory, and Markov chains are given. Each chapter includes exercises, and each set begins with basic computational "drill" problems and then progresses to problems with more substance. Comprised of 10 chapters, this book begins with exercises related to set theory and concepts such as the union and intersection of sets. Exercises on Cartesian coordinate systems and graphs as well as linear programming from a geometric and algebraic point of view are then given. Subsequent chapters deal with matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and probability and probability models for finite sample spaces as well as permutations, combinations, and counting methods. Basic concepts in statistics are also considered, along with the mathematics of finance. Some applications of probability, game theory, and Markov chains are also considered. This monograph is intended for students and instructors of applied mathematics.

  • Nonlinear Programming

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin, Madison, May 4-6, 1970
    • 1st Edition
    • J. B. Rosen + 2 more
    • English
    Nonlinear Programming contains the proceedings of a Symposium on Nonlinear Programming held in Madison, Wisconsin on May 4-6, 1970. This book emphasizes algorithms and related theories that lead to efficient computational methods for solving nonlinear programming problems. This compilation consists of 17 chapters. Chapters 1 to 9 are concerned primarily with computational algorithms, while Chapters 10 to 13 are devoted to theoretical aspects of nonlinear programming. Certain applications of nonlinear programming are considered in Chapters 14 to 17. The algorithms for nonlinear constraint problems, investigation of convergence rates, and use of nonlinear programming for approximation are also covered in this text. This publication is a good source for students and researchers concerned with nonlinear programming.

  • Iterative Solution of Nonlinear Equations in Several Variables

    • 1st Edition
    • J. M. Ortega + 1 more
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Iterative Solution of Nonlinear Equations in Several Variables presents a survey of the basic theoretical results about nonlinear equations in n dimensions and analysis of the major iterative methods for their numerical solution. This book discusses the gradient mappings and minimization, contractions and the continuation property, and degree of a mapping. The general iterative and minimization methods, rates of convergence, and one-step stationary and multistep methods are also elaborated. This text likewise covers the contractions and nonlinear majorants, convergence under partial ordering, and convergence of minimization methods. This publication is a good reference for specialists and readers with an extensive functional analysis background.

  • Introduction to Applied Probability

    • 1st Edition
    • Paul E. Pfeiffer + 1 more
    • English
    Introduction to Applied Probability provides a basis for an intelligent application of probability ideas to a wide variety of phenomena for which it is suitable. It is intended as a tool for learning and seeks to point out and emphasize significant facts and interpretations which are frequently overlooked or confused by the beginner. The book covers more than enough material for a one semester course, enhancing the value of the book as a reference for the student. Notable features of the book are: the systematic handling of combinations of events (Section 3-5); extensive use of the mass concept as an aid to visualization; an unusually careful treatment of conditional probability, independence, and conditional independence (Section 6-4); the resulting clarification facilitates the formulation of many applied problems; the emphasis on events determined by random variables, which gives unity and clarity to many topics important for interpretation; and the utilization of the indicator function, both as a tool for dealing with events and as a notational device in the handling of random variables. Students of mathematics, engineering, biological and physical sciences will find the text highly useful.

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