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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.

  • Current Issues in Computer Simulation

    • 1st Edition
    • Nabil R. Adam + 1 more
    • English
    Current Issues in Computer Simulation is a collection of papers dealing with computer simulation languages, statistical aspects of simulation, linkage with optimization and analytical models, as well as theory and application of simulation methodology. Some papers explain the General Purpose Simulation System (GPSS), a programming package incorporating a language to simulate discrete systems; and the SIMSCRIPT, a general-purpose simulation language using English commands, for example, FORTRAN. Another simulation language is the General Activity Simulation Program (GASP), providing for an organizational structure to build models to simulate the dynamic performance of systems on a digital computer. Other papers discuss simulation models of real systems, including corporate simulation models, multistage consumer choice process, determination of maximum occupancy for hospital facilities, and the juvenile court system. Many computer simulations are statistical sampling experiments performed on a model of the system under investigation. Other papers discuss some of the variables involved in the statistical design and analysis of simulation experiments such as variance reduction techniques, generation of random variates, and experimental layout. For example, one application simulates inventory systems when many items are stocked in various locations. The collection is suitable for programmers, computer engineers, businessmen, hospital administrators, schools officials, and depositories of huge volumes of information or data.

  • Mathematical Tables

    Tables of in G [z] for Complex Argument
    • 1st Edition
    • A. A. Abramov
    • English
    Mathematical Tables of In ? (z) for Complex Argument is a compilation of tables of In ? (z), z = x + iy, calculated for steps in x and y of 0.01 and with an accuracy of one unit in the last (the sixth) decimal place. Interpolation is used to calculate In ? (z) for intermediate values and is carried out separately for the real and imaginary parts of In ? (z). Six places are retained in interpolation. This book first explains how the values of In ? (z) are calculated using the asymptotic formula in a wide lattice with step h = 0.16, and how the tables and the nomograph are used. The values in the lattice are interpolated successively at the centers of various symmetric figures. The calculation of In ? (z) outside the quadrangle is also considered. Formulas for the calculation of In ? (z) outside the given rectangle are listed. The nomograph is intended to facilitate the interpolation procedure. Some of the calculations (including the rounding off of the results to the sixth place and the calculation of second differences) are carried out with the aid of analytical computers. This monograph will be of interest to mathematicians and mathematics students.

  • Homotopy Theory

    The Mathematical Works of J. H. C. Whitehead
    • 1st Edition
    • I. M. James
    • English
    Homotopy Theory contains all the published mathematical work of J. H. C. Whitehead, written between 1947 and 1955. This volume considers the study of simple homotopy types, particularly the realization of problem for homotopy types. It describes Whitehead's version of homotopy theory in terms of CW-complexes. This book is composed of 21 chapters and begins with an overview of a theorem to Borsuk and the homotopy type of ANR. The subsequent chapters deal with four-dimensional polyhedral, the homotopy type of a special kind of polyhedron, and the combinatorial homotopy I and II. These topics are followed by reviews of other homotopy types, such as group extensions with homotopy operators, cohomology systems, secondary boundary operator, algebraic homotopy, and the G-dual of a semi-exact couple. The last chapters examine the connected complex homotopy types and the second non-vanishing homotopy groups. This book will be of great value to mathematicians.

  • Issues of Organizational Design

    A Mathematical Programming View of Organizations
    • 1st Edition
    • Børge Obel
    • English
    Issues of Organizational Design: A Mathematical Programming View of Organizations analyzes the view that organizations can be represented satisfactorily by a mathematical programming model and relates it to other theories of organizational behavior. The potential of this approach to organizational analysis is evaluated. Comprised of seven chapters, this book begins with an overview of the three major schools of organizational theory: the classical/structural school, the human relations school, and the contingency school. It then defines what an organization is and outlines the relationship between organizational elements. The example of the two-product firm is used to illustrate the basic model framework, and how coordination, diversification, and incentives can be treated in this framework.Subsequent chapters explore the relationship between the contingency approach and the mathematical programming approach to organizational design; the coordination problem and the process of decision making in a decentralized organization; the decomposition of the organization into a number of smaller units; and types of evaluation and incentive schemes for addressing cheating in a multi-level organization. The book also presents a series of empirical studies where a mathematical programming view of organizations has been assumed before concluding with a discussion on the process of designing organizations. This monograph will be useful for students of organizational design and for practitioners who use models in connection with decision making.

  • Mathematics with Understanding

    • 1st Edition
    • Harold Fletcher + 1 more
    • C. Plumpton
    • English
    Mathematics with Understanding, Book 1 provides a guide for teaching primary mathematics. This book consists of nine main topics–aims of a modern approach; language of sets; relations and sorting; recording of number and use of different bases; open sentences, number facts and pictorial representation; natural numbers and addition; subtraction; multiplication; and division. In these topics, this text specifically discusses the union and intersection of two sets, Cardinal number of a set, and recording by means of a mapping. The collection of data, fundamental operations for natural numbers, and subtraction algorithm are also deliberated. This compilation likewise covers the Cartesian product of two sets and properties of division. This publication is recommended for math teachers intending to acquire a deeper understanding of the structure behind many mathematical ideas and processes.

  • Algebraical and Topological Foundations of Geometry

    Proceedings of a Colloquium Held in Utrecht, August 1959
    • 1st Edition
    • Hans Freudenthal
    • English
    Algebraical and Topological Foundations of Geometry contains the proceedings of the Colloquium on Algebraic and Topological Foundations of Geometry, held in Utrecht, the Netherlands in August 1959. The papers review the algebraical and topological foundations of geometry and cover topics ranging from the geometric algebra of the Möbius plane to the theory of parallels with applications to closed geodesies. Groups of homeomorphisms and topological descriptive planes are also discussed. Comprised of 26 chapters, this book introduces the reader to the theory of parallels with applications to closed geodesies; groups of homeomorphisms; complemented modular lattices; and topological descriptive planes. Subsequent chapters focus on collineation groups; exceptional algebras and exceptional groups; the connection between algebra and constructions with ruler and compasses; and the use of differential geometry and analytic group theory methods in foundations of geometry. Von Staudt projectivities of Moufang planes are also considered, and an axiomatic treatment of polar geometry is presented. This monograph will be of interest to students of mathematics.

  • Differential Equations with Maple V®

    • 1st Edition
    • Martha L Abell + 1 more
    • English
    Differential Equations with Maple V provides an introduction and discussion of topics typically covered in an undergraduate course in ordinary differential equations as well as some supplementary topics such as Laplace transforms, Fourier series, and partial differential equations. It also illustrates how Maple V is used to enhance the study of differential equations not only by eliminating the computational difficulties, but also by overcoming the visual limitations associated with the solutions of differential equations. The book contains chapters that present differential equations and illustrate how Maple V can be used to solve some typical problems. The text covers topics on differential equations such as first-order ordinary differential equations, higher order differential equations, power series solutions of ordinary differential equations, the Laplace Transform, systems of ordinary differential equations, and Fourier Series and applications to partial differential equations. Applications of these topics are also provided. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

  • Problems and Methods in Analysis

    • 1st Edition
    • W. Krysicki + 2 more
    • W. J. Langford + 1 more
    • English
    Problems and Methods in Analysis, Volume 2 provides information pertinent to the methods of calculus. This book provides solutions to problems in analytical calculus. Organized into five chapters, this volume begins with an overview of the integration of functions that are not defined or are not bounded at a finite number of points, and with integrals in which the interval of integration is infinitely large. This text then defines the radius of curvature and provides the formula for curvature and radius of curvature. Other chapters consider the equation of tangent and normal. This book discusses as well the amplitudes of the harmonic components of a set of oscilloscope time base potentials. The final chapter deals with the Euler–Fourier formula, the Fourier series, and Dirichlet's conditions. This book is intended to be suitable for sixth form students, particularly scholarship students. First year university students who need a systematic course in calculus will also find this book useful.

  • An Introduction to Digital Computing

    Pergamon Programmed Texts
    • 1st Edition
    • F. H. George
    • English
    An Introduction to Digital Computing provides information pertinent to the fundamental aspects of digital computing. This book represents a major step towards the universal availability of programmed material. Organized into four chapters, this book begins with an overview of the fundamental workings of the computer, including the way it handles simple arithmetic problems. This text then provides a brief survey of the basic features of a typical computer that is divided into three sections, namely, the input and output system, the memory system for data storage, and a processing system. Other chapters focus on programming and on the workings of the computer control unit. This book discusses as well the various arithmetic codes such as binary, decimal, octal, duodecimal, and hexadecimal codes. The final chapter deals with some of the more detailed workings of the control unit. This book is a valuable resource for university students and computer specialists.

  • Elements of Combinatorial Computing

    • 1st Edition
    • Mark B. Wells
    • English
    Elements of Combinatorial Computing focuses on the processes, principles, methodologies, and approaches involved in combinatorial computing. The publication first takes a look at a language for combinatorial computing, language implementation and program efficiency, and computer representation of mathematical objects. Discussions focus on geometric configurations, elementary combinatorial configurations, sets and vectors, natural numbers, program optimization, data representation, set manipulation, notation for iteration and recursion, and nested iteration and recursive programming. The text then takes a look at backtrack programming, generation of elementary configurations, and additional basic techniques and manipulations. Topics include isomorph rejection, transformations, finite set covering, sorting techniques, permutations with repeated objects, compositions, partitions, subsets and combinations, and basic backtracking and impasse detection. The book examines additional basic techniques and manipulations and applications of advanced algorithms. The publication is highly recommended for computer science experts and researchers interested in the elements in combinatorial computing.

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