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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.

  • Probabilistic Analysis and Related Topics

    Volume 2
    • 1st Edition
    • A. T. Bharucha-Reid
    • English
    Probabilistic Analysis and Related Topics, Volume 2 focuses on the integrability, continuity, and differentiability of random functions, as well as functional analysis, measure theory, operator theory, and numerical analysis. The selection first offers information on the optimal control of stochastic systems and Gleason measures. Discussions focus on convergence of Gleason measures, random Gleason measures, orthogonally scattered Gleason measures, existence of optimal controls without feedback, random necessary conditions, and Gleason measures in tensor products. The text then elaborates on an introduction to nonstandard analysis and hyperfinite probability theory, including applications to stochastic processes, conversion from nonstandard to standard measure spaces, and an introduction to nonstandard analysis. The text examines stochastic matrices, ergodic Markov chains, and measures on semigroups, as well as limit theorems for convolution products of probability measures on completely simple semigroups; ergodicity of Markov chains and probability measures on semigroups; and limits of convolutions in groups and semigroups. The selection is a dependable source of data for mathematicians and researchers interested in the general theory of random functions.

  • Pascal-SC

    A Computer Language for Scientific Computation
    • 1st Edition
    • Gerd Bohlender + 2 more
    • Werner Rheinboldt + 1 more
    • English
    Perspectives in Computing, Vol. 17: Pascal-SC: A Computer Language for Scientific Computation focuses on the application of Pascal-SC, a programming language developed as an extension of standard Pascal, in scientific computation. The publication first elaborates on the introduction to Pascal-SC, a review of standard Pascal, and real floating-point arithmetic. Discussions focus on optimal scalar product, standard functions, real expressions, program structure, simple extensions, real floating-point arithmetic, vector and matrix arithmetic, and dynamic arrays. The text then examines functions and operators with arbitrary result types and solving problems with Pascal-SC. The book ponders on strings and text processing, dynamic arrays, and modules. Topics include declaration and use of modules, compatibility of static and dynamic arrays, dynamic result types of functions and operators, strings in procedures, functions, and operators, and declaration of string variables. The publication is a dependable reference for computer science experts and researchers interested in the application of Pascal-SC in scientific computation.

  • 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.

  • Handbook of VLSI Chip Design and Expert Systems

    • 1st Edition
    • A. F. Schwarz
    • English
    Handbook of VLSI Chip Design and Expert Systems provides information pertinent to the fundamental aspects of expert systems, which provides a knowledge-based approach to problem solving. This book discusses the use of expert systems in every possible subtask of VLSI chip design as well as in the interrelations between the subtasks. Organized into nine chapters, this book begins with an overview of design automation, which can be identified as Computer-Aided Design of Circuits and Systems (CADCAS). This text then presents the progress in artificial intelligence, with emphasis on expert systems. Other chapters consider the impact of design automation, which exploits the basic capabilities of computers to perform complex calculations and to handle huge amounts of data with a high speed and accuracy. This book discusses as well the characterization of microprocessors. The final chapter deals with interactive I/O devices. This book is a valuable resource for system design experts, circuit analysts and designers, logic designers, device engineers, technologists, and application-specific designers.

  • Measure, Integration, and Functional Analysis

    • 1st Edition
    • Robert B. Ash
    • English
    Measure, Integration, and Functional Analysis deals with the mathematical concepts of measure, integration, and functional analysis. The fundamentals of measure and integration theory are discussed, along with the interplay between measure theory and topology. Comprised of four chapters, this book begins with an overview of the basic concepts of the theory of measure and integration as a prelude to the study of probability, harmonic analysis, linear space theory, and other areas of mathematics. The reader is then introduced to a variety of applications of the basic integration theory developed in the previous chapter, with particular reference to the Radon-Nikodym theorem. The third chapter is devoted to functional analysis, with emphasis on various structures that can be defined on vector spaces. The final chapter considers the connection between measure theory and topology and looks at a result that is a companion to the monotone class theorem, together with the Daniell integral and measures on topological spaces. The book concludes with an assessment of measures on uncountably infinite product spaces and the weak convergence of measures. This book is intended for mathematics majors, most likely seniors or beginning graduate students, and students of engineering and physics who use measure theory or functional analysis in their work.

  • Statistical Computer Performance Evaluation

    • 1st Edition
    • Walter Freiberger
    • English
    Statistical Computer Performance Evaluation contains the proceedings of a Conference on Statistical Computer Performance Evaluation held at Brown University in Providence, Rhode Island, on November 22-23, 1971, under the auspices of the Division of Applied Mathematics and the Center for Computer and Information Sciences. The papers review the application of quantitative, and particularly statistical, methods to the study of computer performance. Comprised of 19 chapters, this book begins with an overview of the state of the art of computer system evaluation and some quantitative methods (analytical, simulation, and empirical methods) that are applicable to the problem. A utility theoretic approach to evaluation of a time-sharing system is then described, followed by a discussion on the results of a multi-factor paging experiment. Subsequent chapters focus on statistical quantification of instruction and operand traces; measurement and improvement of program behavior under paging systems; free-storage algorithms; and probabilistic models for predicting software reliability. This monograph will be of interest to practitioners in the fields ofcomputer science and applied mathematics.

  • Recent Advances in Statistics

    Papers in Honor of Herman Chernoff on His Sixtieth Birthday
    • 1st Edition
    • M. Haseeb Rizvi + 2 more
    • English
    Recent Advances in Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday is a collection of papers on statistics in honor of Herman Chernoff on the occasion of his 60th birthday. Topics covered range from sequential analysis (including designs) to optimization (including control theory), nonparametrics (including large sample theory), and statistical graphics. Comprised of 27 chapters, this book begins with a discussion on optimal stopping of Brownian motion, followed by an analysis of sequential design of comparative clinical trials. A two-sample sequential test for shift with one sample size fixed in advance is then presented. Subsequent chapters focus on set-valued parameters and set-valued statistics; large deviations of the maximum likelihood estimate in the Markov chain case; the limiting behavior of multiple roots of the likelihood equation; and optimal uniform rate of convergence for nonparametric estimators of a density function and its derivatives. The book concludes by considering significance and confidence levels, closed regions and models, and discrete distributions. This monograph should be of interest to students, researchers, and specialists in the fields of mathematics and statistics.

  • Algebra, Topology, and Category Theory

    A Collection of Papers in Honor of Samuel Eilenberg
    • 1st Edition
    • Alex Heller + 1 more
    • English
    Algebra, Topology, and Category Theory: A Collection of Papers in Honor of Samuel Eilenberg is a collection of papers dealing with algebra, topology, and category theory in honor of Samuel Eilenberg. Topics covered range from large modules over artin algebras to two-dimensional Poincaré duality groups, along with the homology of certain H-spaces as group ring objects. Variable quantities and variable structures in topoi are also discussed. Comprised of 16 chapters, this book begins by looking at the relationship between the representation theories of finitely generated and large (not finitely generated) modules over an artin algebra. The reader is then introduced to reduced bar constructions on deRham complexes; some properties of two-dimensional Poincaré duality groups; and properties invariant within equivalence types of categories. Subsequent chapters explore the work of Samuel Eilenberg in topology; local complexity of finite semigroups; global dimension of ore extensions; and the spectrum of a ringed topos. This monograph will be a useful resource for students and practitioners of algebra and mathematics.

  • Fixed Points

    Algorithms and Applications
    • 1st Edition
    • Stepan Karamardian
    • English
    Fixed Points: Algorithms and Applications covers the proceedings of the First International Conference on Computing Fixed Points with Applications, held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina on June 26-28, 1974. This book is composed of 21 chapters and starts with reviews of finding roots of polynomials by pivoting procedures and the relations between convergence and labeling in approximation algorithm. The next chapters deal with the principles of complementary pivot theory and the Markovian decision chains; the method of continuation for Brouwer fixed point calculation; a fixed point approach to stability in cooperative games; and computation of fixed points in a nonconvex region. Other chapters discuss a computational comparison of fixed point algorithms, the fundamentals of union jack triangulations, and some aspects of Mann’s iterative method for approximating fixed points. The final chapters consider the application of fixed point algorithms to the analysis of tax policies and the pricing for congestion in telephone networks. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.

  • Probability, Statistics, and Queueing Theory

    With Computer Science Applications
    • 1st Edition
    • Arnold O. Allen
    • Werner Rheinboldt
    • English
    Probability, Statistics, and Queueing Theory: With Computer Science Applications focuses on the use of statistics and queueing theory for the design and analysis of data communication systems, emphasizing how the theorems and theory can be used to solve practical computer science problems. This book is divided into three parts. The first part discusses the basic concept of probability, probability distributions commonly used in applied probability, and important concept of a stochastic process. Part II covers the discipline of queueing theory, while Part III deals with statistical inference. This publication is designed as a junior-senior level textbook on applied probability and statistics with computer science applications, but is also a self-study book for practicing computer science (data processing) professionals.

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