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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.

  • High-Level Language Computer Architecture

    • 1st Edition
    • Yaohan Chu
    • English
    High-Level Language Computer Architecture offers a tutorial on high-level language computer architecture, including von Neumann architecture and syntax-oriented architecture as well as direct and indirect execution architecture. Design concepts of Japanese-language data processing systems are discussed, along with the architecture of stack machines and the SYMBOL computer system. The conceptual design of a direct high-level language processor is also described. Comprised of seven chapters, this book first presents a classification of high-level language computer architecture according to the proximity of the machine language and the programming language. This classification gives four types: von Neumann architecture, syntax-oriented architecture, indirect execution architecture, and direct execution architecture. In order to illustrate the possible evolution of computer architecture, design concepts of Japanese-language data processing systems are chosen as an example. Subsequent chapters focus on the syntax-oriented architecture; the historical SYMBOL computer system which makes use of an indirect execution architecture; and design concepts of direct-execution architecture for the ALGOL 60 language. The final chapter describes the architecture for the processor for an APL subset. This monograph will be of interest to specialists in electronics and computer science.

  • Advanced Calculus of Several Variables

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

  • Science, Computers, and the Information Onslaught

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

  • Differential Equations

    • 1st Edition
    • Shair Ahmad + 2 more
    • English
    Differential Equations is a collection of papers from the "Eight Fall Conference on Differential Equations" held at Oklahoma State University in October 1979. The papers discuss hyperbolic problems, bifurcation function, boundary value problems for Lipschitz equations, and the periodic solutions of systems of ordinary differential equations. Some papers deal with the existence of periodic solutions for nonlinearly perturbed conservative systems, the saddle-point theorem, the periodic solutions of the forced pendulum equation, as well as the structural identification (inverse) problem for illness-death processes. One paper presents an elementary proof of the work of deOliveira and Hale, and applies the stability for autonomous systems in the critical case of one zero root. Another paper explains the necessary and sufficient conditions for structural identification prior to application in states of illness-death processes. An illness-death process is a continuous Markov model with n illness (transient) states each having one (and only one) transfer into a death state. The paper examines two theorems whether these apply to an illness-death process under certain given elements. The collection is an ideal source of reference for mathematicians, students, and professor of calculus and advanced mathematics.

  • Operating Systems

    • 1st Edition
    • Dionysios C. Tsichritzis + 1 more
    • Werner Rheinboldt
    • English
    Operating Systems deals with the fundamental concepts and principles that govern the behavior of operating systems. Many issues regarding the structure of operating systems, including the problems of managing processes, processors, and memory, are examined. Various aspects of operating systems are also discussed, from input-output and files to security, protection, reliability, design methods, performance evaluation, and implementation methods. Comprised of 10 chapters, this volume begins with an overview of what constitutes an operating system, followed by a discussion on the definition and properties of the basic unit of computation within an operating system, the process. The reader is then introduced to processor allocation schemes as well as various classes of scheduling disciplines and their implementations; memory management functions; and virtual memory. Subsequent chapters focus on input-output and files; protection in an operating system; and design and implementation of an operating system. The book concludes by describing two operating systems to help the reader visualize how the major components of a system interact in a complete system: the Venus Operating System developed by MITRE Corp. and the SUE nucleus, designed at the University of Toronto. This monograph is intended for fourth-year undergraduates and first-year graduate students, as well as lecturers who plans to institute a course on operating systems.

  • Applied Statistical Methods

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

  • Scientific Inference, Data Analysis, and Robustness

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

  • Vector and Operator Valued Measures and Applications

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

  • Precalculus

    Functions & Graphs
    • 1st Edition
    • Bernard Kolman + 1 more
    • English
    Precalculus: Functions & Graphs provides a complete and self-contained presentation of the basic mathematical techniques and ideas required for the successful completion of a calculus course. The book emphasizes the learning and understanding of the concept of a function, using function notation, and being able to sketch graphs of functions with ease. The text employs a number of pedagogic devices that have been proven effective in teaching college mathematics. The mathematical concepts are presented in a style that is informal, supportive, and "user-friendly". Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appr This textbook is intended for college students.

  • Study Guide for Applied Finite Mathematics

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

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