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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.

  • Frontiers of Pattern Recognition

    The Proceedings of the International Conference on Frontiers of Pattern Recognition
    • 1st Edition
    • Satosi Watanabe
    • English
    Frontiers of Pattern Recognition contains the proceedings of the International Conference on Frontiers of Pattern Recognition which took place on January 18-20, 1971, at the University of Hawaii, Honolulu. The compendium consists of 30 papers from authorities from eleven different countries, which describe the frontiers of pattern recognition as viewed from diverse viewpoints. Topics discussed include some techniques for recognizing structures in pictures, grammatical inference, syntactic pattern recognition and stochastic languages, and pattern cognition and the organization of information. Also covered are subjects on human face recognition, cluster analysis, and learning algorithms of pattern recognition in non-stationary conditions. Computer scientists, mathematicians, statisticians, linguists, and psychologists will find the book informative.

  • Contributions to Analysis

    A Collection of Papers Dedicated to Lipman Bers
    • 1st Edition
    • Lars V. Ahlfors + 2 more
    • English
    Contributions to Analysis: A Collection of Papers Dedicated to Lipman Bers is a compendium of papers provided by Bers, friends, students, colleagues, and professors. These papers deal with Teichmuller spaces, Kleinian groups, theta functions, algebraic geometry. Other papers discuss quasiconformal mappings, function theory, differential equations, and differential topology. One paper discusses the results of the rigidity theorem of Mostow and its generalization by Marden in relation to geometric properties of Kleinian groups of the first kind. These results, obtained by planar methods, are presented in terms of the hyperbolic 3-space language, which is a natural pedestal in approaching the action of the Kleinian groups. Another paper reviews Riemann's vanishing theorem which solves the Jacobi inversion problem, by relating the vanishing properties of the theta function (particularly at half periods) to properties of certain linear series on the Riemann surface. One paper examines the problem of obtaining relations among the periods of the differentials of first kind on a compact Riemann surface. An application of a computer program involves supersonic transport. The program is based on the hodograph transformation and a method of complex characteristics to calculate profiles that are shock-less at a specified angle of attack, or at a specified subsonic free-stream Mach number. The collection can prove useful for engineers, statisticians, students, and professors in advance mathematics or courses related to aeronautics.

  • Mathematical Functions and Their Approximations

    • 1st Edition
    • Yudell L. Luke
    • English
    Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the 1954 Conference on Mathematical Tables, held at Cambridge, Massachusetts. The aim of the conference is to determine the need for mathematical tables in view of the availability of high speed computing machinery. This work is composed of 14 chapters that cover the machinery for the expansion of the generalized hypergeometric function and other functions in infinite series of Jacobi and Chebyshev polynomials of the first kind. Numerical coefficients for Chebyshev expansions of the more common functions are tabulated. Other chapters contain polynomial and rational approximations for certain class of G-functions, the coefficients in the early polynomials of these rational approximations, and the Padé approximations for many of the elementary functions and the incomplete gamma functions. The remaining chapters describe the development of analytic approximations and expansions. This book will prove useful to mathematicians, advance mathematics students, and researchers.

  • Probabilistic Analysis and Related Topics

    Volume 2
    • 1st Edition
    • A. T. Bharucha-Reid
    • English
    Probabilistic Analysis and Related Topics, Volume 2 focuses on the integrability, continuity, and differentiability of random functions, as well as functional analysis, measure theory, operator theory, and numerical analysis. The selection first offers information on the optimal control of stochastic systems and Gleason measures. Discussions focus on convergence of Gleason measures, random Gleason measures, orthogonally scattered Gleason measures, existence of optimal controls without feedback, random necessary conditions, and Gleason measures in tensor products. The text then elaborates on an introduction to nonstandard analysis and hyperfinite probability theory, including applications to stochastic processes, conversion from nonstandard to standard measure spaces, and an introduction to nonstandard analysis. The text examines stochastic matrices, ergodic Markov chains, and measures on semigroups, as well as limit theorems for convolution products of probability measures on completely simple semigroups; ergodicity of Markov chains and probability measures on semigroups; and limits of convolutions in groups and semigroups. The selection is a dependable source of data for mathematicians and researchers interested in the general theory of random functions.

  • Elementary Linear Algebra

    • 1st Edition
    • Richard O. Hill
    • English
    Elementary Linear Algebra reviews the elementary foundations of linear algebra in a student-oriented, highly readable way. The many examples and large number and variety of exercises in each section help the student learn and understand the material. The instructor is also given flexibility by allowing the presentation of a traditional introductory linear algebra course with varying emphasis on applications or numerical considerations. In addition, the instructor can tailor coverage of several topics. Comprised of six chapters, this book first discusses Gaussian elimination and the algebra of matrices. Applications are interspersed throughout, and the problem of solving AX = B, where A is square and invertible, is tackled. The reader is then introduced to vector spaces and subspaces, linear independences, and dimension, along with rank, determinants, and the concept of inner product spaces. The final chapter deals with various topics that highlight the interaction between linear algebra and all the other branches of mathematics, including function theory, analysis, and the singular value decomposition and generalized inverses. This monograph will be a useful resource for practitioners, instructors, and students taking elementary linear algebra.

  • Hyperbolic Equations and Related Topics

    Proceedings of the Taniguchi International Symposium, Katata and Kyoto, 1984
    • 1st Edition
    • Sigeru Mizohata
    • English
    Hyperbolic Equations and Related Topics covers the proceedings of the Taniguchi International Symposium, held in Katata, Japan on August 27-31, 1984 and in Kyoto, Japan on September 3-5, 1984. The book focuses on the mathematical analyses involved in hyperbolic equations. The selection first elaborates on complex vector fields; holomorphic extension of CR functions and related problems; second microlocalization and propagation of singularities for semi-linear hyperbolic equations; and scattering matrix for two convex obstacles. Discussions focus on the construction of asymptotic solutions, singular vector fields and Leibniz formula, second microlocalization along a Lagrangean submanifold, and hypo-analytic structures. The text then ponders on the Cauchy problem for effectively hyperbolic equations and for uniformly diagonalizable hyperbolic systems in Gevrey classes. The book takes a look at generalized Hamilton flows and singularities of solutions of the hyperbolic Cauchy problem and analytic and Gevrey well-posedness of the Cauchy problem for second order weakly hyperbolic equations with coefficients irregular in time. The selection is a dependable reference for researchers interested in hyperbolic equations.

  • An Introduction to Stochastic Modeling

    • 1st Edition
    • Howard M. Taylor + 1 more
    • English
    An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

  • Contributions to the Theory and Application of Statistics

    A Volume in Honor of Herbert Solomon
    • 1st Edition
    • Alan E. Gelfand
    • English
    Contributions to the Theory and Application of Statistics: A Volume in Honor of Herbert Solomon is a collection of 20 papers that cover the significant contributions of Herbert Solomon in the field of statistics. This text is organized into four sections encompassing 20 chapters. Each section defines an area in which Herb has made a contribution and the papers are ordered alphabetically. The first section consists of four papers in the area of operations research and applied probability, while the second section gathers six papers looking into problems in distribution theory and geometric probability. The third section contains five applied articles in the areas of law and justice, medicine, and psychology. The fourth section covers five papers that explore several inference issues. This book will be of value to statisticians and advance students.

  • Computer-Assisted Analysis and Model Simplification

    Proceedings of the First Symposium on Computer-Assisted Analysis and Model Simplification, University of Colorado, Boulder, Colorado, March 28, 1980
    • 1st Edition
    • Harvey J. Greenberg + 1 more
    • English
    Computer-Assisted Analysis and Model Simplification deals with problems associated with the implementation, understanding, and management of large-scale, computer-resident models. This book focuses on five general research areas—structural modeling, qualitative economics, mathematical programming systems, relational databases, and combinatorics. In these topics, this compilation discusses the scope of computer-assisted analysis and model, structural models and graph theory, and qualitative stability of matrices and economic theory. The strong sign-solvability and weak satisfiability, automatic identification of embedded structure in large-scale optimization models, and query systems for linear programming models are also deliberated. This publication is a good source for students, specialists, and researchers interested in computer-assisted analysis and model simplification.

  • 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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