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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.

  • Mathematical Methods in Computer Aided Geometric Design

    • 1st Edition
    • Tom Lyche + 1 more
    • English
    Mathematical Methods in Computer Aided Geometric Design covers the proceedings of the 1988 International Conference by the same title, held at the University of Oslo, Norway. This text contains papers based on the survey lectures, along with 33 full-length research papers. This book is composed of 39 chapters and begins with surveys of scattered data interpolation, spline elastic manifolds, geometry processing, the properties of Bézier curves, and Gröbner basis methods for multivariate splines. The next chapters deal with the principles of box splines, smooth piecewise quadric surfaces, some applications of hierarchical segmentations of algebraic curves, nonlinear parameters of splines, and algebraic aspects of geometric continuity. These topics are followed by discussions of shape preserving representations, box-spline surfaces, subdivision algorithm parallelization, interpolation systems, and the finite element method. Other chapters explore the concept and applications of uniform bivariate hermite interpolation, an algorithm for smooth interpolation, and the three B-spline constructions. The concluding chapters consider the three B-spline constructions, design tools for shaping spline models, approximation of surfaces constrained by a differential equation, and a general subdivision theorem for Bézier triangles. This book will prove useful to mathematicians and advance mathematics students.

  • Cluster Analysis for Applications

    Probability and Mathematical Statistics: A Series of Monographs and Textbooks
    • 1st Edition
    • Michael R. Anderberg
    • English
    Cluster Analysis for Applications deals with methods and various applications of cluster analysis. Topics covered range from variables and scales to measures of association among variables and among data units. Conceptual problems in cluster analysis are discussed, along with hierarchical and non-hierarchical clustering methods. The necessary elements of data analysis, statistics, cluster analysis, and computer implementation are integrated vertically to cover the complete path from raw data to a finished analysis. Comprised of 10 chapters, this book begins with an introduction to the subject of cluster analysis and its uses as well as category sorting problems and the need for cluster analysis algorithms. The next three chapters give a detailed account of variables and association measures, with emphasis on strategies for dealing with problems containing variables of mixed types. Subsequent chapters focus on the central techniques of cluster analysis with particular reference to computational considerations; interpretation of clustering results; and techniques and strategies for making the most effective use of cluster analysis. The final chapter suggests an approach for the evaluation of alternative clustering methods. The presentation is capped with a complete set of implementing computer programs listed in the Appendices to make the use of cluster analysis as painless and free of mechanical error as is possible. This monograph is intended for students and workers who have encountered the notion of cluster analysis.

  • Transformations

    Mathematical Approaches to Culture Change
    • 1st Edition
    • Colin Renfrew + 1 more
    • English
    Transformations: Mathematical Approaches to Culture Change focuses on the application of contemporary mathematical techniques to the study of culture change and formulates problems in archaeology, anthropology, and historiography in such a way that they are susceptible to treatment of a mathematical kind. Mathematical models, extending from the almost purely quantitative methods of physics to the purely verbal conceptual explanations, are described. Emphasis is placed on catastrophe theoretic models that exemplify the use of soft mathematics in situations in which the use of hard quantitative models is not possible. Comprised of 21 chapters, this book begins with an overview of the role of mathematics in theoretical archaeology, followed by a discussion on two general categories of mathematical methods that seem to be suitable for modeling cultural transformations: methods of dynamical systems theory and methods that give greater emphasis on discrete entities and the structural relations or patterns among them. Subsequent chapters deal with the use of mathematics in history; morphogenesis in biological and social systems; simulation of the growth of hierarchies; and logistic trends in Southwest population growth. A reconstruction of political units in the Valley of Mexico during the Toltec period is also presented. This monograph will be of interest to archaeologists, anthropologists, historians, biologists, sociologists, and mathematicians.

  • Business Mathematics

    • 3rd Edition
    • Burton S. Kaliski
    • English
    Business Mathematics, Third Edition provides the step-by-step explanation of principles, practical aspects, and importance of business mathematics. This edition is organized into six sections encompassing 14 chapters that cover related topics of the metric system, no-fault insurance, individual retirement plans, charge account plans, home mortgages, and NOW accounts. Section 1 gives a thorough review of the fundamental processes, while Section 2 deals with buying and selling, the first factors considered in calculating a firm's profit or loss. Section 3 discusses the operating expenses that reduce the profit or increase the loss from buying and selling activities, and the actual calculation of net profit or loss. Sections 4 and 5 consider the principles of interest as a form of additional income or expense, as well as the investment in stocks, bonds, mutual funds, and other areas as still another source of income or expense. Section 6 describes the procedures for summarizing and analyzing data. The review part at the end of each section lists the important terms and reinforces the major principles learned in the unit. The summary problems in the Unit Review are intended as self-tests and should serve as effective review for examinations. This book will be of great value to business mathematicians, economists, and the general public who are interested in investments.

  • Mathematical Methods in Computer Aided Geometric Design II

    • 1st Edition
    • Tom Lyche + 1 more
    • English
    Mathematical Methods in Computer Aided Geometric Design II covers the proceedings of the 1991 International Conference on Curves, Surfaces, CAGD, and Image Processing, held at Biri, Norway. This book contains 48 chapters that include the topics of blossoming, cyclides, data fitting and interpolation, and finding intersections of curves and surfaces. Considerable chapters explore the geometric continuity, geometrical optics, image and signal processing, and modeling of geological structures. The remaining chapters discuss the principles of multiresolution analysis, NURBS, offsets, radial basis functions, rational splines, robotics, spline and Bézier methods for curve and surface modeling, subdivision, terrain modeling, and wavelets. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.

  • Special Purpose Computers

    • 1st Edition
    • Berni J. Alder
    • English
    Special Purpose Computers describes special-purpose computers and compares them to general-purpose computers in terms of speed and cost. Examples of computers that were designed for the efficient solution of long established algorithms are given, including Navier-Stokes hydrodynamic solvers, classical molecular dynamic machines, and Ising model computers. Comprised of seven chapters, this volume begins by documenting the progress of the CalTech Concurrent Computation Program and its evolution from computational high-energy physics to a supercomputer initiative, with emphasis on the lessons learned including computer architecture issues and the trade-offs between in-house and commercial development. The reader is then introduced to the QCD Machine, a special-purpose parallel supercomputer that was designed and built to solve the lattice quantum chromodynamics problem. Subsequent chapters focus on the Geometry-Defining Processors and their application to the solution of partial differential equations; the Navier-Stokes computer; parallel processing using the Loosely Coupled Array of Processors (LCAP) system; and the Delft Ising system processor. The design and implementation of the Delft molecular-dynamics processor are also described. This book will be of interest to computer engineers and designers.

  • Dynamics and Modelling of Reactive Systems

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin—Madison, October 22–24, 1979
    • 1st Edition
    • Warren E. Stewart + 2 more
    • English
    Dynamics and Modelling of Reactive Systems contains the proceedings of the Advanced Seminar on Dynamics and Modeling of Reactive Systems, held at the University of Wisconsin on October 1979. The book presents papers that assess the level of understanding of the dynamics of chemically reacting systems. The topics discussed include the hierarchies of models in reactive systems; model reduction of chemically reacting systems; and some consequences of nonlinearity in the diffusion process. Time-periodic and spatially irregular patterns; important aspects in simulating the dynamics of aerosols; and the diffusion and reaction in carbon burning are covered as well. Engineers and applied mathematicians will find the book highly insightful.

  • Applied Finite Mathematics

    • 2nd Edition
    • Howard Anton + 1 more
    • English
    Applied Finite Mathematics, 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. Some applications of probability, game theory, and Markov chains are given. Comprised of 10 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 and algebraic point of view; 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. The final chapter is devoted to computers and programming languages such as BASIC. This monograph is intended for students and instructors of applied mathematics.

  • Mathematical Models of Attitude Change

    Change in Single Attitudes and Cognitive Structure
    • 1st Edition
    • John E. Hunter + 2 more
    • Peter R. Monge
    • English
    Mathematical Models of Attitude Change, Volume 1: Change in Single Attitudes and Cognitive Structure presents the mathematical models that address the existing verbal attitude change theories, which are translated into families of mathematical models. This book discusses the two types of attitude change, namely, the attitude toward the object of the message and the attitude toward the source of the message. Organized into three parts encompassing 17 chapters, this volume begins with an overview of the mathematical models of attitude change that are derived from several theories. This text then explains the empirical work designed to test selected mathematical models of attitude change. Other chapters consider the predictions made by different models, including reinforcement, information processing, social judgment, balance, dissonance, and congruity. This book discusses as well the attitude-related variable, namely, belief and belief change. The final chapter deals with models of change in hierarchical organized attitudes using alternative theories of attitude change. This book is a valuable resource for psychologists.

  • Aphids as Virus Vectors

    • 1st Edition
    • Kerry F. Harris + 1 more
    • English
    Aphids as Virus Vectors focuses on aphids as vectors of plant viruses and the fundamentals of their relationship with virus and host. The mouthparts and feeding mechanism of aphids are discussed, along with aphid penetration of plant tissues and the transmission mechanisms of aphids as virus vectors. The intrinsic properties and taxonomy of aphid-borne viruses are also examined. Comprised of 22 chapters, this book begins with an overview of the importance of aphids as vectors, their biology, and the properties of the viruses they transmit. These introductory chapters prepare the reader for later ones on aphid-virus-plant interactions. The next section deals with transmission mechanisms, with emphasis on several novel alternatives to many of the traditionally held concepts of how aphids transmit viruses. Accessory factors in non-persistent virus transmission are considered. Subsequent chapters focus on technological advances in aphid-virus research, including the use of aphid cell culturing, radioisotope methodology, membrane feeding, and electrical measurement systems. The most promising frontiers in epidemiological and control-oriented research are discussed in the last two sections. This monograph will be a useful resource for researchers from such varied sciences as entomology, plant science, and virology, as well as for graduate students taking entomology and plant pathology courses on insects in relation to plant diseases.

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