Skip to main content
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.

  • The IEA Study of Mathematics III

    Student Growth and Classroom Processes
    • 1st Edition
    • Rami Burstein
    • English
    The Second International Mathematics Study was conducted in the schools of 20 education systems under the sponsorship of the International Association for the Evaluation of Educational Achievement (IEA). This is the third of three international reports, each of which focus on a major component of the study. This volume describes the main findings from analyses of classroom processes and mathematic growth by posing such questions as: how successful have the national education systems been in providing the opportunity to learn mathematics by the end of the lower secondary school; what do students at the lower secondary level know across educational systems and what have they learned during their most recent schooling experiences; and what teaching practices are utilized in the mathematics classroom of the various systems and to what extent can these classroom processes explain differences in student achievements?

  • Developments in Statistics

    • 1st Edition
    • Volume 1
    • Paruchuri R. Krishnaiah
    • English
    Development in Statistics, Volume 1 is a collection of papers that deals with theory and application of parameter estimation in stochastic differential systems, the comparative aspects of the study of ordinary time series, and real multivariate distributions. Some papers discuss covariance analysis of nonstationary time series, nonparametric repeated significance tests, as well as discrete optimal factorial designs for statisticians and investigators of experiments. One paper cites an application of parameter estimation in stochastic differential systems in approximates of stability and control derivatives from flight test data. Another paper cites cases where procedures of ordinary time series (or point processes) have direct analogs in the study of point processes (or ordinary time series). One paper explains the applications of multivariate distributions in simultaneous tests on the equality of eigenvalues toward the covariance matrix, canonical correlation matrix, and a matrix associated with the multivariate analysis of variance. Another paper reviews two types of repeated significance tests, namely, the genuinely distribution-free tests based on a broad class of nonparametric statistics; and the asymptotically distribution-free tests based on a broad class of parametric statistics but having asymptotically nonparametric behavior. Both types can provide a unified solution to a broad class of problems. The collection can be valuable for mathematicians, students, and professors of calculus, statistics, or advanced mathematics.

  • Prehistoric Hunter-Gatherers

    The Emergence of Cultural Complexity
    • 1st Edition
    • RABIGER
    • English
    Prehistoric Hunters–Gatherers: The Emergence of Cultural Complexity focuses on the emergence of cultural complexity among hunter–gatherers. This book presents the demographic, ecological, and social perspectives that add to the understanding of the emergence of more elaborate organization. Organized into four parts encompassing 17 chapters, this book begins with an overview of previous perspectives on cultural complexity and suggests directions in the study of change. This text then proposes a synthesis of both ecological and social approaches as a more powerful interpretative framework for the study of complexity. Other chapters consider the relationship between population and social complexity in an elaboration of major argument regarding demographic pressure and cultural change. This book provides as well an intriguing look at the regional consequences of their focus on whaling. The final chapter characterizes approaches to hunter–gatherer complexity and reiterates the significance of change in human society prior to the adoption of domesticated animals and plants. This book is a valuable resource for archeologists and anthropologists.

  • Regiomontanus: His Life and Work

    • 1st Edition
    • Volume 1
    • E. Zinner + 1 more
    • English
    The 500th anniversary of Regiomontanus's birth has occasioned this depiction of his life and work. It is the first English translation of Ernst Zinner's monumental biography, plus a number of specially-written supplementary articles which help paint a more comprehensive picture of the current state of knowledge about Regiomontanus. The articles show the high regard in which the biography is still held by the community of scholars doing work on the mathematics of the Renaissance.Zinner's biography is a mine of information about early printing, astrolabes, tables of eclipses and the world of Henry of Langenstein, Johann of Gmunden, Georg Peuerbach, Cardinal Bessarion, Nicholas of Cusa and the extraordinary itinerant scholar, Johannes Müller of Königsberg — Regiomontanus. His contributions to mathematics are discussed (for example, he may have discovered the fifth and sixth perfect numbers) as well as the mysteries surrounding his life and death.

  • The Econometric Analysis of Non-Uniqueness in Rational Expectations Models

    • 1st Edition
    • Volume 201
    • L. Broze + 1 more
    • English
    This book is devoted to the econometric analysis of linear multivariate rational expectation models. It shows that the interpretation of multiplicity in terms of "new degrees of freedom" is consistent with a rigorous econometric reasoning. Non-uniqueness is the central theme of this book. Each chapter is concerned with a specific econometric aspect of rational expectations equilibria. The most constructive result lies in the possibility of an empirical determination of the equilibrium followed by the economy.

  • Scientific Computing

    An Introduction with Parallel Computing
    • 1st Edition
    • Gene H. Golub + 1 more
    • English
    This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case.

  • An Introduction to the Statistical Theory of Classical Simple Dense Fluids

    • 1st Edition
    • G.H.A. Cole
    • English
    An Introduction to the Statistical Theory of Classical Simple Dense Fluids covers certain aspects of the study of dense fluids, based on the analysis of the correlation effects between representative small groupings of molecules. The book starts by discussing empirical considerations including the physical characteristics of fluids; measured molecular spatial distribution; scattering by a continuous medium; the radial distribution function; the mean potential; and the molecular motion in liquids. The text describes the application of the theories to the description of dense fluids (i.e. interparticle force, classical particle trajectories, and the Liouville Theorem) and the deduction of expressions for the fluid thermodynamic functions. The theory of equilibrium short-range order by using the concept of closure approximation or total correlation; some numerical consequences of the equilibrium theory; and irreversibility are also looked into. The book further tackles the kinetic derivation of the Maxwell-Boltzmann (MB) equation; the statistical derivation of the MB equation; the movement to equilibrium; gas in a steady state; and viscosity and thermal conductivity. The text also discusses non-equilibrium liquids. Physicists, chemists, and engineers will find the book invaluable.

  • Hilbertian Kernels and Spline Functions

    • 1st Edition
    • Volume 4
    • M. Atteia
    • English
    In this monograph, which is an extensive study of Hilbertian approximation, the emphasis is placed on spline functions theory. The origin of the book was an effort to show that spline theory parallels Hilbertian Kernel theory, not only for splines derived from minimization of a quadratic functional but more generally for splines considered as piecewise functions type.Being as far as possible self-contained, the book may be used as a reference, with information about developments in linear approximation, convex optimization, mechanics and partial differential equations.

  • Developments in Statistics

    • 1st Edition
    • Volume 3
    • Paruchuri R. Krishnaiah
    • English
    Development in Statistics, Volume 3 is a collection of papers that deals with asymptotic expansions in parametric statistical theory, orthogonal models for contingency tables, statistical concepts in economic analysis, and an exposition of path analysis. One paper presents an inference model based on a sample of independent identically distributed observations to arrive at a general statistical theory founded on asymptotic methods. Another paper discusses the applicability of statistical concepts to economics and related areas, with emphasis on not-so-obvious applications (known as utility and expected loss). The paper explains information theory concepts for the measurement of income inequality, intergenerational occupational mobility, as well as to first- and second-order moments of univariate and bivariate distributions (such as measurements applied to the cost of living and of real income). One paper notes that the starting point in path analysis is a linear predictor (in the least-squares sense) for one random variable in terms of a number of others. The paper adds that the work of Koopmans and Hood (1953) on econometrics is part of the starting point. Statisticians, economists, mathematicians, students, and professors of calculus or advanced mathematics will surely appreciate the collection.

  • Topics in Geometry

    • 1st Edition
    • Robert Bix
    • English
    This volume presents an accessible, self-contained survey of topics in Euclidean and non-Euclidean geometry. It includes plentiful illustrations and exercises in support of the thoroughly worked-out proofs. The author's emphasis on the connections between Euclidean and non-Euclidean geometry unifies the range of topics covered.The text opens with a brief review of elementary geometry before proceeding to advanced material. Topics covered include advanced Euclidean and non-Euclidean geometry, division ratios and triangles, transformation geometry, projective geometry, conic sections, and hyperbolic and absolute geometry. Topics in Geometry includes over 800 illustrations and extensive exercises of varying difficulty.

  • Numerical Mathematics and Applications

    • 1st Edition
    • Volume 1
    • J. Vignes + 1 more
    • English
    IMACS Transactions on Scientific Computation – 85, Volume I: Numerical Mathematics and Applications contains papers on theoretical and applied aspects of numerical mathematics presented at the 11th IMACS World Congress on Scientific Computation, held in Oslo, Norway on August 5-9, 1985. The book focuses on the processes, methodologies, and approaches involved in computer arithmetic. The selection first highlights the use of CESTAC method in the parallel computation of roots of polynomials, CESTAC, and reducing abbreviation errors in iterative resolution of linear systems. Discussions focus on notations and theoretical processes, sequence of iterates in floating-point arithmetic, perturbation method, and CESTAC tested on algorithm and numerical results. The book then takes a look at optimal termination criterion and accuracy tests in mathematical programming; use of the normed residue to check the quality of the solution of a linear system; and computable bounds for solutions of integral equations. The manuscript examines arbitrarily accurate boundaries for solutions of ODEs with initial values using variable precision arithmetic and remarks on some modified Romberg algorithms for numerical integration. Topics include speed of convergence and a priori truncation error estimates, acceleration of convergence, extrapolation schemes, and the initial boundary value problem. The selection is a dependable source of data for mathematicians and researchers interested in numerical mathematics and applications.

  • Order Statistics & Inference

    Estimation Methods
    • 1st Edition
    • Narayanaswamy Balakrishnan + 1 more
    • English
    The literature on order statistics and inferenc eis quite extensive and covers a large number of fields ,but most of it is dispersed throughout numerous publications. This volume is the consolidtion of the most important results and places an emphasis on estimation. Both theoretical and computational procedures are presented to meet the needs of researchers, professionals, and students. The methods of estimation discussed are well-illustrated with numerous practical examples from both the physical and life sciences, including sociology,psychology... nd electrical and chemical engineering. A complete, comprehensive bibliography is included so the book can be used both aas a text and reference.

  • Handbook of Set-Theoretic Topology

    • 1st Edition
    • K. Kunen + 1 more
    • English
    This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest.In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.

  • Mathematical Problem Solving

    • 1st Edition
    • ALAN H. SCHOENFELD
    • English
    Mathematical Problem Solving provides information pertinent to the nature of mathematical thinking at any level. This book provides a framework for the analysis of complex problem-solving behavior. Organized into two parts encompassing 10 chapters, this book begins with an overview of the four qualitatively different aspects of complex intellectual activity, namely, cognitive resources, heuristics, control, and belief systems. This text then presents a series of empirical investigations that flesh out the analytical framework. Other chapters consider the ways that competent problem solvers make the most of the knowledge at their disposal. This book discusses as well the kind s of learning that can result from carefully designed instruction. The final chapter deals with observations made in typical high school classrooms, which serve to indicate some of the sources of students' mathematical behavior. This book is a valuable resource for mathematicians and mathematics teachers. Readers who are interested in higher-order thinking skills in any domain will also find this book useful.

  • Inequalities

    Theory of Majorization and Its Applications
    • 1st Edition
    • Volume 143
    • Ingram Olkin + 1 more
    • English
    Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of inequalities." For certain kinds of inequalities, the notion of majorization leads to such a theory that is sometimes extremely useful and powerful for deriving inequalities. Moreover, the derivation of an inequality by methods of majorization is often very helpful both for providing a deeper understanding and for suggesting natural generalizations.Anyo... wishing to employ majorization as a tool in applications can make use of the theorems; for the most part, their statements are easily understood.

  • Introduction to Structural Equation Models

    • 1st Edition
    • Otis Dudley Duncan
    • English
    Introduction to Structural Equation Models prepares the reader to understand the recent sociological literature on the use of structural equation models in research, and discusses methodological questions pertaining to such models. The material in first seven chapters is almost entirely standard, with the remaining four introducing progressively more open-ended issues, seducing the reader into beginning to think for himself about the properties of models or even to suggest problems that may intrigue the advanced student.

  • Developments in Statistics

    • 1st Edition
    • Volume 4
    • Paruchuri R. Krishnaiah
    • English
    Developments in Statistics, Volume 4 reviews developments in the theory and applications of statistics, covering topics such as time series, identifiability and model selection, and missing data. The application of structured exploratory data analysis to human genetics, specifically, the mode of inheritance, is also considered. Comprised of four chapters, this volume begins with an introduction to spectrum parameter estimation in time series analysis, restricting the discussion to the simplest univariate (that is, scalar) real-valued time series X(t). An accurate formulation of the general problem is presented. The accuracy of different consistent estimates obtained for large but fixed values of T (maximum likelihood estimates, Whittle's estimates, and simplified asymptotically efficient estimates) is also compared. The next chapter deals with identifiability and modeling in econometrics, focusing on the theoretical framework relating realization theory, identification, and parametrization. The realization theory is illustrated on various levels of generality by means of examples related to econometrics, along with some advanced applications of system theory. The book also examines inference on parameters of multivariate normal populations when some data are missing before concluding with an evaluation of structured exploratory data as applied to the study of the mode of inheritance. This monograph will be of interest to students and practitioners of statistics.

  • Topoi

    The Categorial Analysis of Logic
    • 2nd Edition
    • Volume 98
    • R. Goldblatt
    • English
    The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-varia... classical real number''.The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.

  • Linear Panel Analysis

    Models of Quantitative Change
    • 1st Edition
    • Ronald C. Kessler
    • English
    Linear Panel Analysis: Models of Quantitative Change focuses on the use of linear models in the analysis of change data measured on a sample of individuals over multiple time points. This book is organized into 12 chapters. After a general introduction to change analysis in Chapter 1, some basic algebraic results on change scores are presented in Chapter 2. Chapter 3 constructs and analyzes structural equation models for studying the causes of change, while Chapter 4 outlines several ways of simply describing change in groups. The uses and abuses of cross-lagged panel correlations are discussed in Chapter 5. Chapters 6 to 10 deal with a variety of special topics that arise in panel analysis. The alternatives to the analysis of over-time data for a set of individuals are described in Chapter 11. The last chapter is devoted to the practical aspects of designing and carrying out the data collection phase of a panel study. This publication is intended for social scientists who work with change data.

  • Convexity Theory and its Applications in Functional Analysis

    • 1st Edition
    • L. Asimow
    • English
    Convexity Theory and its Applications in Functional Analysis is a five-chapter text that provides a geometric perspective of the convexity theory and its practical applications. Chapter 1 reviews the functional analytic preliminaries, including the Krein-Smulyan Theorem, the basic Choquet Theory, and the Bishop-Phelps Theorem. Chapter 2 gives the basic duality results, lattice theory and concrete representation theorems for order unit spaces and Banach lattices of type Mand L. Chapters 3 and 4 deal with the real affine function spaces through examining the Choquet simplex and the application of the study of real A(K) spaces to complex-values function spaces by means of a complex state space. Chapter 5 highlights the application of the theory to the study of non-commutative Banach algebras. This book will prove useful to mathematicians, engineers, and physicists.

  • Subharmonic Functions

    Volume 2
    • 1st Edition
    • Volume 2
    • W. K. Hayman
    • P. M. Cohn + 1 more
    • English
    Building on the foundation laid in the first volume of Subharmonic Functions, which has become a classic, this second volume deals extensively with applications to functions of a complex variable. The material also has applications in differential equations and differential equations and differential geometry. It reflects the increasingly important role that subharmonic functions play in these areas of mathematics. The presentation goes back to the pioneering work of Ahlfors, Heins, and Kjellberg, leading to and including the more recent results of Baernstein, Weitsman, and many others. The volume also includes some previously unpublished material. It addresses mathematicians from graduate students to researchers in the field and will also appeal to physicists and electrical engineers who use these tools in their research work. The extensive preface and introductions to each chapter give readers an overview. A series of examples helps readers test their understatnding of the theory and the master the applications.

  • 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.

  • Computer Chess

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

  • 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.

  • 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.

  • Self-Validating Numerics for Function Space Problems

    Computation with Guarantees for Differential and Integral Equations
    • 1st Edition
    • Edgar W. Kaucher + 1 more
    • Werner Rheinboldt
    • English
    Self-Validating Numerics for Function Space Problems describes the development of computational methods for solving function space problems, including differential, integral, and function equations. This seven-chapter text highlights three approaches, namely, the E-methods, ultra-arithmetic, and computer arithmetic. After a brief overview of the different self-validating approaches, this book goes on introducing the mathematical preliminaries consisting principally of fixed-point theorems and the computational context for the development of validating methods in function spaces. The subsequent chapters deals with the development and application of point of view of ultra-arithmetic and the constructs of function-space arithmetic spaces, such as spaces, bases, rounding, and approximate operations. These topics are followed by discussion of the iterative residual correction methods for function problems and the requirements of a programming language needed to make the tools and constructs of the methodology available in actual practice on a computer. The last chapter describes the techniques for adapting the methodologies to a computer, including the self-validating results for specific problems. This book will prove useful to mathematicians and advance mathematics students.

  • University Education in Computing Science

    Proceedings of a Conference on Graduate Academic and Related Research Programs in Computing Science, Held at the State University of New York at Stony Brook, June 1967
    • 1st Edition
    • Aaron Finerman
    • English
    University Education in Computing Science documents the proceedings of a conference on graduate academic and related research programs in computing science, held at the State University of New York at Stony Brook on June 8, 1967. This book provides a comprehensive study of the role of the computing sciences as an academic program, including its organizational structure and relationship to the computing center. The undergraduate education in computing science and operational policies of university computing centers are also elaborated. Other topics include the graduate computer science program at American universities, dilemma of computer sciences, and science and engineering of information. The industry's view of computing science and doctoral program in computing science are likewise covered. This publication is suitable for educational, industrial, and governmental organizations concerned with education related to computing science.

  • Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equation

    Mathematical Tables Series
    • 1st Edition
    • L. N. Nosova + 1 more
    • English
    Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations contains tables of the special functions, namely, the generalized Airy functions, and their first derivatives, for real and pure imaginary values. The tables are useful for calculations on toroidal shells, laminae, rode, and for the solution of certain other problems of mathematical physics. The values of the functions were computed on the "Strela" highspeed electronic computer. This book will be of great value to mathematicians, researchers, and students.

  • Computer Security

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

  • Stochastic Differential Equations and Applications

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

  • The Laws of Large Numbers

    • 1st Edition
    • Pál Révész
    • Z. W. Birnbaum + 1 more
    • English
    The Law of Large Numbers deals with three types of law of large numbers according to the following convergences: stochastic, mean, and convergence with probability 1. The book also investigates the rate of convergence and the laws of the iterated logarithm. It reviews measure theory, probability theory, stochastic processes, ergodic theory, orthogonal series, Huber spaces, Banach spaces, as well as the special concepts and general theorems of the laws of large numbers. The text discusses the laws of large numbers of different classes of stochastic processes, such as independent random variables, orthogonal random variables, stationary sequences, symmetrically dependent random variables and their generalizations, and also Markov chains. It presents other laws of large numbers for subsequences of sequences of random variables, including some general laws of large numbers which are not related to any concrete class of stochastic processes. The text cites applications of the theorems, as in numbers theory, statistics, and information theory. The text is suitable for mathematicians, economists, scientists, statisticians, or researchers involved with the probability and relative frequency of large numbers.

  • Parallel Sorting Algorithms

    • 1st Edition
    • Selim G. Akl
    • Werner Rheinboldt
    • English
    Parallel Sorting Algorithms explains how to use parallel algorithms to sort a sequence of items on a variety of parallel computers. The book reviews the sorting problem, the parallel models of computation, parallel algorithms, and the lower bounds on the parallel sorting problems. The text also presents twenty different algorithms, such as linear arrays, mesh-connected computers, cube-connected computers. Another example where algorithm can be applied is on the shared-memory SIMD (single instruction stream multiple data stream) computers in which the whole sequence to be sorted can fit in the respective primary memories of the computers (random access memory), or in a single shared memory. SIMD processors communicate through an interconnection network or the processors communicate through a common and shared memory. The text also investigates the case of external sorting in which the sequence to be sorted is bigger than the available primary memory. In this case, the algorithms used in external sorting is very similar to those used to describe internal sorting, that is, when the sequence can fit in the primary memory, The book explains that an algorithm can reach its optimum possible operating time for sorting when it is running on a particular set of architecture, depending on a constant multiplicative factor. The text is suitable for computer engineers and scientists interested in parallel algorithms.

  • Tables of Laguerre Polynomials and Functions

    Mathematical Tables Series, Vol. 39
    • 1st Edition
    • V.S. Aizenshtadt + 2 more
    • English
    Tables of Laguerre Polynomials and Functions contains the values of Laguerre polynomials and Laguerre functions for n = 2 , 3 , . . . , 7 ; s = 0(0.1) 1; x = 0(0.1) 10(0.2) 30, and the zeroes and coefficients of the polynomials for n = 2 (1) 10 and s = 0(0.05) 1. The book also explains the Laguerre polynomials, their properties, Laguerre functions, and the tabulation of the Laguerre polynomials and functions. The book contains three tables: tables of values of Laguerre polynomials and functions, tables of the coefficients of the polynomials, and tables of their roots. The first table consists of six parts arranged successively in the ascending order of the degree n. Researchers have calculated the tables for a wider range of values of the parameters n, s and x (n = 2(1) 10, s = 0(0.05) 1, x = 0(0.1) 10(0.2) 30(0.5) 80) using computers at the Institute of Mathematics and Computer Technology of the Byelorussian Academy of Sciences and the Computer Centre of the Academy of Sciences of the U.S.S.R. Scientists and investigators at computer centers, research institutes, and engineering organizations will find the book highly valuable.

  • Computational Linguistics

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

  • Topics in Stochastic Processes

    Probability and Mathematical Statistics: A Series of Monographs and Textbooks
    • 1st Edition
    • Robert B. Ash + 1 more
    • Z. W. Birnbaum + 1 more
    • English
    Topics in Stochastic Processes covers specific processes that have a definite physical interpretation and that explicit numerical results can be obtained. This book contains five chapters and begins with the L2 stochastic processes and the concept of prediction theory. The next chapter discusses the principles of ergodic theorem to real analysis, Markov chains, and information theory. Another chapter deals with the sample function behavior of continuous parameter processes. This chapter also explores the general properties of Martingales and Markov processes, as well as the one-dimensional Brownian motion. The aim of this chapter is to illustrate those concepts and constructions that are basic in any discussion of continuous parameter processes, and to provide insights to more advanced material on Markov processes and potential theory. The final chapter demonstrates the use of theory of continuous parameter processes to develop the Itô stochastic integral. This chapter also provides the solution of stochastic differential equations. This book will be of great value to mathematicians, engineers, and physicists.

  • Decomposability

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

  • Decomposition of Multivariate Probabilities

    • 1st Edition
    • Roger Cuppens
    • Z. W. Birnbaum + 1 more
    • English
    Decomposition of Multivariate Probability is a nine-chapter text that focuses on the problem of multivariate characteristic functions. After a brief introduction to some useful results on measures and integrals, this book goes on dealing with the classical theory and the Fourier-Stieltjes transforms of signed measures. The succeeding chapters explore the multivariate extension of the well-known Paley-Wiener theorem on functions that are entire of exponential type and square-integrable; the theory of infinitely divisible probabilities and the classical results of Hin?in; and the decompositions of analytic characteristic functions. Other chapters are devoted to the important problem of the description of a specific class on n-variate probabilities without indecomposable factors. The final chapter studies the problem of ?-decomposition of multivariate characteristic functions. This book will prove useful to mathematicians and advance undergraduate and graduate students.

  • Computability Theory

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

  • Sequential Statistical Procedures

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

  • Stochastic Differential Equations and Applications

    Volume 2
    • 1st Edition
    • Avner Friedman
    • Z. W. Birnbaum + 1 more
    • English
    Stochastic Differential Equations and Applications, Volume 2 is an eight-chapter text that focuses on the practical aspects of stochastic differential equations. This volume begins with a presentation of the auxiliary results in partial differential equations that are needed in the sequel. The succeeding chapters describe the behavior of the sample paths of solutions of stochastic differential equations. These topics are followed by a consideration of an issue whether the paths can hit a given set with positive probability, as well as the stability of paths about a given manifold and with spiraling of paths about this manifold. Other chapters deal with the applications to partial equations, specifically with the Dirichlet problem for degenerate elliptic equations. These chapters also explore the questions of singular perturbations and the existence of fundamental solutions for degenerate parabolic equations. The final chapters discuss stopping time problems, stochastic games, and stochastic differential games. This book is intended primarily to undergraduate and graduate mathematics students.

  • Stochastic Integrals

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

  • Mathematical Methods of Reliability Theory

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

  • Human and Machine Vision

    • 1st Edition
    • Jacob Beck + 2 more
    • English
    Human and Machine Vision provides information pertinent to an interdisciplinary program of research in visual perception. This book presents a psychophysical study of the human visual system, which provides insights on how to model the flexibility required by a general-purpose visual system. Organized into 17 chapters, this book begins with an overview of how a visual display is segmented into components on the basis of textual differences. This text then proposes three criteria for judging representations of shape. Other chapters consider an increased use of machine vision programs as models of human vision and of data from human vision in developing programs for machine vision. This book discusses as well the diversity and flexibility of systems for representing visual information. The final chapter deals with dot patterns and discusses the process of interring orientation information from collections of them. This book is a valuable resource for psychologists, neurophysiologists, and computer scientists.

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

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

  • Perspectives on Computer Science

    From the 10th Anniversary Symposium at the Computer Science Department, Carnegie-Mellon University
    • 1st Edition
    • Anita K. Jones
    • English
    Perspectives on Computer Science provides information pertinent to the fundamental aspects of computer science. This book discusses the weaknesses frequently found in minicomputers. Organized into 12 chapters, this book begins with an overview of the technological, economic, and human aspects of the environment in which PDP–11 was designed and built. This text then examines the set of techniques for tree searching. Other chapters consider a tutorial on automatic planning systems, with emphasis given to knowledge representation issues. This book discusses as well the classical least-fixedpoint approach toward recursive programs and examines the interplay between time and space determined by a variety of machine models. The final chapter deals with some of the primary influences in contemporary programming language design, namely, programming methodology, program specification, verification, and formal semantic definition techniques. This book is a valuable resource for students and teachers. Computer science theoreticians and mathematicians will also find this book useful.

  • Fourier Analysis in Probability Theory

    • 1st Edition
    • Tatsuo Kawata
    • Z. W. Birnbaum + 1 more
    • English
    Fourier Analysis in Probability Theory provides useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related studies. This 14-chapter work highlights the clarification of the interactions and analogies among these theories. Chapters 1 to 8 present the elements of classical Fourier analysis, in the context of their applications to probability theory. Chapters 9 to 14 are devoted to basic results from the theory of characteristic functions of probability distributors, the convergence of distribution functions in terms of characteristic functions, and series of independent random variables. This book will be of value to mathematicians, engineers, teachers, and students.

  • Six-Figure Tables of Trigonometric Functions

    Mathematical Tables Series
    • 1st Edition
    • L. S. Khrenov
    • English
    THE PRESENT six-figure trigonometric tables complete the series of tables of the natural values of the trigonometric functions published by Fizmatgiz. Now that small computers have become very widely available, almost all computations are carried out by machine, and the majority of computational schemes arc suited to this purpose. The situation calls urgently for the availability of tables containing the natural values of all six trigonometric functions. The following special factor emerges here. In logarithmic computations the same relative accuracy is guaranteed more or less automatically for all values of the argument: the number of correct significant figures in the result is either equal to or (in rare cases) one less than, the number of significant figures in the mantissa of the logarithm. In computations with natural values of the functions the same relative accuracy is guaranteed in practice for all arguments only by having a constant nmber of significant figures throughout the tables. Until recently however, tables of the natural values of the trigonometric functions have been compiled both in Russia and abroad with the same number of places after the decimal point, which leads to a loss of accuracy when computing with functions of small angles. In view of this there is an urgent need for tables of the natural values of the trigonometric functions with a constant number of significant figures which substantially guarantees roughly the- same relative accuracy for all angles. The present tables, together with the following, already published by Fizmatgiz: Fil'e-figure Tables (L. S. Khrenov~ 1954), Five-.figure Tables l~,ith the Argument in Time (L. S. Khrenov, 1954), Seven-figure Tables(L. S. Khrenov, 1956) and Six-figure Tables with the Argunlent in Time (S. A. Angelov, 1957), form a complete series ~ith the same number of significant figures, satisfying the main requirements of a wide variety of computers. When compiling the present tables, use was made for purposes of collation of the following tables of the natural values of the trigonometric functions: The I)-figure Table..' of H. Andoyer, (Paris, 1915-1918), the Eight-figure Table of J. Peters (Berlin) J939), the Seven-figure Table of °L.S. Khrenov (2nd. ed., Gostekhizdat, 1956), the Seven-figure Table of H. C. Ives, and the Eight-figure Tables oj' the Logarith,l1.ft of NumberaV and oJ the Trigonometric functions of J. Bauschin.e;er and J. Peters (Geodezizdat, 1942 and 1944).

  • Mathematical Methods

    A Course of Mathematics for Engineers and Scientists
    • 2nd Edition
    • Brian H. Chirgwin + 1 more
    • English
    Mathematical Methods is an introductory course on mathematical methods for students aiming for a first degree in engineering or science. Topics covered include differentiation and integration and their applications; the geometry of two dimensions, and complex numbers. Statistics and probability are also discussed. Comprised of eight chapters, this volume begins with an introduction to fundamental concepts, including the roots of equations; elementary two-dimensional coordinate geometry; limits and continuity; inequalities and quadratic forms; mathematical induction; and convergence. The discussion then turns to the techniques of differentiation and integration and their applications; the geometry of two dimensions; and complex numbers and their roots, together with trigonometric expansions. The book concludes with a chapter on statistics and probability, paying particular attention to the properties of a frequency distribution; some special probability distributions; normal distribution and the error function; and some probability problems. This monograph is intended for students taking a course in engineering or science.

Related subjects