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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.

  • Real Analysis and Probability

    Solutions to Problems
    • 1st Edition
    • Robert P. Ash
    • English
    Real Analysis and Probability: Solutions to Problems presents solutions to problems in real analysis and probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability; the interplay between measure theory and topology; conditional probability and expectation; the central limit theorem; and strong laws of large numbers in terms of martingale theory. Comprised of eight chapters, this volume begins with problems and solutions for the theory of measure and integration, followed by various applications of the basic integration theory. Subsequent chapters deal with functional analysis, paying particular attention to structures that can be defined on vector spaces; the connection between measure theory and topology; basic concepts of probability; and conditional probability and expectation. Strong laws of large numbers are also taken into account, first from the classical viewpoint, and then via martingale theory. The final chapter is devoted to the one-dimensional central limit problem, with emphasis on the fundamental role of Prokhorov's weak compactness theorem. This book is intended primarily for students taking a graduate course in probability.

  • Robustness of Statistical Tests

    • 1st Edition
    • Takeaki Kariya + 1 more
    • Gerald L. Lieberman + 1 more
    • English
    Robustness of Statistical Tests provides a general, systematic finite sample theory of the robustness of tests and covers the application of this theory to some important testing problems commonly considered under normality. This eight-chapter text focuses on the robustness that is concerned with the exact robustness in which the distributional or optimal property that a test carries under a normal distribution holds exactly under a nonnormal distribution. Chapter 1 reviews the elliptically symmetric distributions and their properties, while Chapter 2 describes the representation theorem for the probability ration of a maximal invariant. Chapter 3 explores the basic concepts of three aspects of the robustness of tests, namely, null, nonnull, and optimality, as well as a theory providing methods to establish them. Chapter 4 discusses the applications of the general theory with the study of the robustness of the familiar Student’s r-test and tests for serial correlation. This chapter also deals with robustness without invariance. Chapter 5 looks into the most useful and widely applied problems in multivariate testing, including the GMANOVA (General Multivariate Analysis of Variance). Chapters 6 and 7 tackle the robust tests for covariance structures, such as sphericity and independence and provide a detailed description of univariate and multivariate outlier problems. Chapter 8 presents some new robustness results, which deal with inference in two population problems. This book will prove useful to advance graduate mathematical statistics students.

  • Large Problems, Small Machines

    Transforming Your Programs with Advanced Algorithms
    • 1st Edition
    • Steve Heller
    • English
    Large Problems, Small Machines: Transforming Your Programs with Advanced Algorithms describes a practical, real-world approach to program optimization based on advanced algorithms. Topics covered range from how to save storage using a restricted character set and how to speed up access to records by employing hash coding (or "scatter storage") and caching. A selective mailing list system is used to illustrate rapid access to and rearrangement of information selected by criteria specified at run-time. Comprised of six chapters, this book begins by discussing factors to consider when deciding whether a program needs optimization. In the next chapter, a supermarket price lookup system is used to illustrate how to save storage by using a restricted character set and how to speed up access to records with the aid of hash coding and caching. Attention is paid to rapid retrieval of prices. A selective mailing list system is then used to illustrate rapid access to and rearrangement of information selected by criteria specified at run-time. The book also considers the Huffman coding and arithmetic coding methods of data compression before concluding with a review of the characteristics of the algorithms encountered in previous chapters, as well as the future of the art of optimization. This monograph will be a useful resource for practicing computer programmers and those who intend to be working programmers.

  • Semigroups

    Proceedings of the Monash University Conference on Semigroups Held at the Monash University, Clayton, Victoria, Australia, October, 1979
    • 1st Edition
    • T. E. Hall + 2 more
    • English
    Semigroups is a collection of papers dealing with models of classical statistics, sequential computing machine, inverse semi-groups. One paper explains the structure of inverse semigroups that leads to P-semigroups or E-unitary inverse semigroups by utilizing the P-theorem of W.D. Nunn. Other papers explain the characterization of divisibility in the category of sets in terms of images and relations, as well as the universal aspects of completely simple semigroups, including amalgamation, the lattice of varieties, and the Hopf property. Another paper explains finite semigroups which are extensions of congruence-free semigroups, where their set of congruences forms a chain. The paper then shows how to construct such semigroups. A finite semigroup (which is decomposable into a direct product of cyclic semigroups which are not groups) is actually uniquely decomposable. One paper points out when a finite semigroup has such a decomposition, and how its non-group cyclic direct factors, if any, can be found. The collection can prove useful for mathematicians, statisticians, students, and professors of higher mathematics or computer science.

  • Almost Everywhere Convergence II

    Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, Evanston, Illinois, October 16–20, 1989
    • 1st Edition
    • Alexandra Bellow + 1 more
    • English
    Almost Everywhere Convergence II presents the proceedings of the Second International Conference on Almost Everywhere Convergence in Probability and Ergodotic Theory, held in Evanston, Illinois on October 16–20, 1989. This book discusses the many remarkable developments in almost everywhere convergence. Organized into 19 chapters, this compilation of papers begins with an overview of a generalization of the almost sure central limit theorem as it relates to logarithmic density. This text then discusses Hopf's ergodic theorem for particles with different velocities. Other chapters consider the notion of a log–convex set of random variables, and proved a general almost sure convergence theorem for sequences of log–convex sets. This book discusses as well the maximal inequalities and rearrangements, showing the connections between harmonic analysis and ergodic theory. The final chapter deals with the similarities of the proofs of ergodic and martingale theorems. This book is a valuable resource for mathematicians.

  • 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.

  • Stochastic Economics

    Stochastic Processes, Control, and Programming
    • 1st Edition
    • Gerhard Tintner + 1 more
    • English
    Stochastic Economics: Stochastic Processes, Control, and Programming presents some aspects of economics from a stochastic or probabilistic point of view. The application of stochastic processes to the theory of economic development, stochastic control theory, and various aspects of stochastic programming is discussed. Comprised of four chapters, this book begins with a short survey of the stochastic view in economics, followed by a discussion on discrete and continuous stochastic models of economic development. The next chapter focuses on methods of stochastic control and their application to dynamic economic models, with emphasis on those aspects connected especially with the theory of quantitative economic policy. Some basic operational problems of applying stochastic control, particularly in economic systems and organizations for problems such as dynamic resource allocation, growth planning, and economic coordination are considered. The last chapter is devoted to stochastic programming, paying particular attention to the decision rule theory of operations research under the chance-constrained model and a method of incorporating reliability measures into a systems reliability model. This book will be of interest to economists, statisticians, applied mathematicians, operations researchers, and systems engineers.

  • A Computational Logic Handbook

    Formerly Notes and Reports in Computer Science and Applied Mathematics
    • 1st Edition
    • Robert S. Boyer + 1 more
    • Werner Rheinboldt + 1 more
    • English
    Perspectives in Computing: A Computational Logic Handbook contains a precise description of the logic and a detailed reference guide to the associated mechanical theorem proving system, including a primer for the logic as a functional programming language, an introduction to proofs in the logic, and a primer for the mechanical theorem. The publication first offers information on a primer for the logic, formalization within the logic, and a precise description of the logic. Discussions focus on induction and recursion, quantification, explicit value terms, dealing with features and omissions, elementary mathematical relationships, Boolean operators, and conventional data structures. The text then takes a look at proving theorems in the logic, mechanized proofs in the logic, and an introduction to the system. The text examines the processes involved in using the theorem prover, four classes of rules generated from lemmas, and aborting or interrupting commands. Topics include executable counterparts, toggle, elimination of irrelevancy, heuristic use of equalities, representation of formulas, type sets, and the crucial check points in a proof attempt. The publication is a vital reference for researchers interested in computational logic.

  • Combinatorial Algorithms

    For Computers and Calculators
    • 2nd Edition
    • Albert Nijenhuis + 1 more
    • Werner Rheinboldt
    • English
    Combinatorial Algorithms for Computers and Calculators, Second Edition deals with combinatorial algorithms for computers and calculators. Topics covered range from combinatorial families such as the random subset and k-subset of an n-set and Young tableaux, to combinatorial structures including the cycle structure of a permutation and the spanning forest of a graph. Newton forms of a polynomial and the composition of power series are also discussed. Comprised of 30 chapters, this volume begins with an introduction to combinatorial algorithms by considering the generation of all of the 2n subsets of the set {1, 2,...,n}. The discussion then turns to the random subset and k-subset of an n-set; next composition of n into k parts; and random composition of n into k parts. Subsequent chapters focus on sequencing, ranking, and selection algorithms in general combinatorial families; renumbering rows and columns of an array; the cycle structure of a permutation; and the permanent function. Sorting and network flows are also examined, along with the backtrack method and triangular numbering in partially ordered sets. This book will be of value to both students and specialists in the fields of applied mathematics and computer science.

  • Mathematics with Applications for the Management, Life, and Social Sciences

    • 2nd Edition
    • Howard Anton + 1 more
    • English
    Mathematics with Applications for the Management, Life, and Social Sciences, Second Edition presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so that the student can see a rich variety of realistic and relevant applications in management, life sciences, and social sciences. Some applications of probability, game theory, and Markov chains are given. Comprised of 16 chapters, this book begins with an introduction to set theory, followed by a discussion on Cartesian coordinate systems and graphs. Subsequent chapters focus on linear programming from a geometric point of view; matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and permutations, combinations, and counting methods. Probability for finite sample spaces and basic concepts in statistics are also considered, along with the mathematics of finance and applications of calculus. This monograph is intended for students and instructors of applied mathematics.

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