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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.

  • Thinking Computers and Virtual Persons

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

  • Foundations of Constraint Satisfaction

    Computation in Cognitive Science
    • 1st Edition
    • Edward Tsang
    • English
    Foundations of Constraint Satisfaction discusses the foundations of constraint satisfaction and presents algorithms for solving constraint satisfaction problems (CSPs). Most of the algorithms described in this book are explained in pseudo code, and sometimes illustrated with Prolog codes (to illustrate how the algorithms could be implemented). Comprised of 10 chapters, this volume begins by defining the standard CSP and the important concepts around it and presenting examples and applications of CSPs. The reader is then introduced to the main features of CSPs and CSP solving techniques (problem reduction, searching, and solution synthesis); some of the most important concepts related to CSP solving; and problem reduction algorithms. Subsequent chapters deal with basic control strategies of searching which are relevant to CSP solving; the significance of ordering the variables, values and compatibility checking in searching; specialized search techniques which gain their efficiency by exploiting problem-specific features; and stochastic search approaches (including hill climbing and connectionist approaches) for CSP solving. The book also considers how solutions can be synthesized rather than searched for before concluding with an analysis of optimization in CSPs. This monograph can be used as a reference by artificial intelligence (AI) researchers or as a textbook by students on advanced AI courses, and should also help knowledge engineers apply existing techniques to solve CSPs or problems which embed CSPs.

  • 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.

  • 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.

  • Directions in Partial Differential Equations

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 28—30, 1985
    • 1st Edition
    • Michael G. Crandall + 2 more
    • English
    Directions in Partial Differential Equations covers the proceedings of the 1985 Symposium by the same title, conducted by the Mathematics Research Center, held at the University of Wisconsin, Madison. This book is composed of 13 chapters and begins with reviews of the calculus of variations and differential geometry. The subsequent chapters deal with the study of development of singularities, regularity theory, hydrodynamics, mathematical physics, asymptotic behavior, and critical point theory. Other chapters discuss the use of probabilistic methods, the modern theory of Hamilton-Jacobi equations, the interaction between theory and numerical methods for partial differential equations. The remaining chapters explore attempts to understand oscillatory phenomena in solutions of nonlinear equations. This book will be of great value to mathematicians and engineers.

  • 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.

  • Generatingfunctionology

    • 1st Edition
    • Herbert S. Wilf
    • English
    Generatingfunctionol... provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.

  • Introduction to Combinatorics

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

  • Data Structures

    Theory and Practice
    • 1st Edition
    • A. T. Berztiss
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Data Structures: Theory and Practice focuses on the processes, methodologies, principles, and approaches involved in data structures, including algorithms, decision trees, Boolean functions, lattices, and matrices. The book first offers information on set theory, functions, and relations, and graph theory. Discussions focus on linear formulas of digraphs, isomorphism of digraphs, basic definitions in the theory of digraphs, Boolean functions and forms, lattices, indexed sets, algebra of sets, and order pair and related concepts. The text then examines strings, trees, and paths and cycles in digraphs. Topics include algebra of strings, Markov algorithms, algebraic structures, languages and grammars, decision trees and decision tables, trees as grammatic markers, shortest path problems, and representation of prefix formulas. The publication ponders on digraphs of programs, arrays, pushdown stores, lists, and list structures, and organization of files. Concerns include scatter storage techniques, files and secondary storage, representation of digraphs as list structures, storage of arrays, and sparse matrices. The text is a valuable reference for computer science experts, mathematicians, and researchers interested in data structures.

  • Inverse and Ill-Posed Problems

    • 1st Edition
    • Heinz W. Engl + 1 more
    • English
    Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June 1986. The papers discuss inverse problems in various disciplines; mathematical solutions of integral equations of the first kind; general considerations for ill-posed problems; and the various regularization methods for integral and operator equations of the first kind. Other papers deal with applications in tomography, inverse scattering, detection of radiation sources, optics, partial differential equations, and parameter estimation problems. One paper discusses three topics on ill-posed problems, namely, the imposition of specified types of discontinuities on solutions of ill-posed problems, the use of generalized cross validation as a data based termination rule for iterative methods, and also a parameter estimation problem in reservoir modeling. Another paper investigates a statistical method to determine the truncation level in Eigen function expansions and for Fredholm equations of the first kind where the data contains some errors. Another paper examines the use of singular function expansions in the inversion of severely ill-posed problems arising in confocal scanning microscopy, particle sizing, and velocimetry. The collection can benefit many mathematicians, students, and professor of calculus, statistics, and advanced mathematics.

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