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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.

  • Probability, Statistics, and Mathematics

    Papers in Honor of Samuel Karlin
    • 1st Edition
    • T. W. Anderson + 2 more
    • English
    Probability, Statistics, and Mathematics: Papers in Honor of Samuel Karlin is a collection of papers dealing with probability, statistics, and mathematics. Conceived in honor of Polish-born mathematician Samuel Karlin, the book covers a wide array of topics, from the second-order moments of a stationary Markov chain to the exponentiality of the local time at hitting times for reflecting diffusions. Smoothed limit theorems for equilibrium processes are also discussed. Comprised of 24 chapters, this book begins with an introduction to the second-order moments of a stationary Markov chain, paying particular attention to the consequences of the autoregressive structure of the vector-valued process and how to estimate the stationary probabilities from a finite sequence of observations. Subsequent chapters focus on A. Selberg's second beta integral and an integral of mehta; a normal approximation for the number of local maxima of a random function on a graph; nonnegative polynomials on polyhedra; and the fundamental period of the queue with Markov-modulated arrivals. The rate of escape problem for a class of random walks is also considered. This monograph is intended for students and practitioners in the fields of statistics, mathematics, and economics.

  • Proceedings of the Conference on Finite Groups

    • 1st Edition
    • William R. Scott + 1 more
    • English
    Proceedings of the Conference on Finite Groups provides information pertinent to the fundamental aspects of finite group theory. This book presents the problem of characterizing simple groups in terms of the local structure of a group. Organized into five parts encompassing 43 chapters, this book begins with an overview of the characterization of the Chevalley groups over fields of odd order and indicates the role of this characterization in the theory of component type groups. This text then examines the structure as well as the representations of specific simple groups. Other chapters consider the general theory of representations and characters of finite groups. This book discusses as well permutation groups and the connection between group theory and geometry. The final chapter deals with finite solvable groups as well as the theory of formations. This book is a valuable resource for mathematicians, graduate students, and research workers.

  • Numerical Methods for Partial Differential Equations

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin-Madison, October 23-25, 1978
    • 1st Edition
    • Seymour V. Parter
    • English
    Numerical Methods for Partial Differential Equations is a collection of papers dealing with techniques and practical solutions to problems concerning continuum mechanics, fluid dynamics, and plasma physics. One paper discusses the important considerations that lead to an efficient nonlinear dynamic finite element analysis using improved analysis techniques. Another paper describes the results obtained from fully discrete methods of higher order in time (order 3 and 4) for second order parabolic initial boundary value problems in which the equations have time dependent (or nonlinear) coefficients. Another paper reviews concepts of ellipticity of finite-difference approximations to general elliptic partial differential systems, with examples utilizing Cauchy-Riemann equations or Navier-Stokes equations. One paper describes fluid-dynamic computing using basic equations, boundary conditions, time dependent gas dynamics, shock waves, stream-function-vort... methods, and an example on the formation of a spherical vortex. Another paper evaluates a specific problem arising in the study of the equilibrium of plasma confined in a machine of the Tokomak type. The collection is suitable for mathematicians, physicists, and investigators in the field of continuum mechanics, fluid dynamics, plasma physics.

  • Nonlinear Evolution Equations

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 17–19, 1977
    • 1st Edition
    • Michael G. Crandall
    • English
    Nonlinear Evolution Equation covers the proceedings of the Symposium by the same title, conducted by the Mathematics Research Center at the University of Wisconsin, Madison on October 17-19, 1977. This book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and the computational aspects of Glimm’s method. The next chapters examine the theoretical and practical aspects of Boltzmann, Navier-Stokes, and evolution equations. These topics are followed by discussions of the practical applications of Trotter’s product formula for some nonlinear semigroups and the finite time blow-up in nonlinear problems. The closing chapters deal with a Hamiltonian approach to the K-dV and other equations, along with a variational method for finding periodic solutions of differential equations. This book will prove useful to mathematicians and engineers.

  • Numerical Solution of Systems of Nonlinear Algebraic Equations

    • 1st Edition
    • George D. Byrne + 1 more
    • English
    Numerical Solution of Systems of Nonlinear Algebraic Equations contains invited lectures of the NSF-CBMS Regional Conference on the Numerical Solution of Nonlinear Algebraic Systems with Applications to Problems in Physics, Engineering and Economics, held on July 10-14, 1972. This book is composed of 10 chapters and begins with the concepts of nonlinear algebraic equations in continuum mechanics. The succeeding chapters deal with the numerical solution of quasilinear elliptic equations, the nonlinear systems in semi-infinite programming, and the solution of large systems of linear algebraic equations. These topics are followed by a survey of some computational techniques for the nonlinear least squares problem. The remaining chapters explore the problem of nonlinear functional minimization, the modification methods, and the computer-oriented algorithms for solving system. These chapters also examine the principles of contractor theory of solving equations. This book will prove useful to undergraduate and graduate students.

  • Contributions to Correlational Analysis

    • 1st Edition
    • Robert J. Wherry
    • English
    Contributions to Correlational Analysis provides information pertinent to the fundamental aspects of correlational analysis that can be used to replace and enhance many of the parametric and nonparametric inferential statistical tests. This book discusses the basic concern of correctional analysis, which is the relationship between two sets of measure. Organized into 18 chapters, this book begins with an overview of the nature of correction analysis. This text then explains the simple linear relationships in which explains the simple linear relationships in which Y and X each consists of some single measurement per person and the relationship is assumed to be linear. Other chapters consider basic ways of expanding the process to include more or different measurements of either X or Y but with no attempt to find the best functions. This book discusses as well the topic of factor analysis. The final chapter deals with canonical correlation. This book is a valuable resource for psychologists.

  • Studies in Topology

    • 1st Edition
    • Nick M. Stavrakas + 1 more
    • English
    Studies in Topology is a compendium of papers dealing with a broad portion of the topological spectrum, such as in shape theory and in infinite dimensional topology. One paper discusses an approach to proper shape theory modeled on the "ANR-systems" of Mardesic-Segal, on the "mutations" of Fox, or on the "shapings" of Mardesic. Some papers discuss homotopy and cohomology groups in shape theory, the structure of superspace, on o-semimetrizable spaces, as well as connected sets that have one or more disconnection properties. One paper examines "weak" compactness, considered as either a strengthening of absolute closure or a weakening of relative compactness (subject to entire topological spaces or to subspaces of larger spaces). To construct spaces that have only weak properties, the investigator can use the various productivity theorems of Scarborough and Stone, Saks and Stephenson, Frolik, Booth, and Hechler. Another paper analyzes the relationship between "normal Moore space conjecture" and productivity of normality in Moore spaces. The compendium is suitable for mathematicians, physicists, engineers, and other professionals involved in topology, set theory, linear spaces, or cartography.

  • Applied Finite Mathematics

    • 1st Edition
    • Howard Anton + 1 more
    • English
    Applied Finite Mathematics 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. Applications in fields such as business, biology, behavioral sciences, and social sciences are included. Comprised of nine chapters, this book begins with an introduction to set theory, explaining concepts such as sets and union and intersection of sets as well as counting elements in sets. The next chapter deals with coordinate systems and graphs, along with applications of linear equations and graphs of linear inequalities. The discussion then turns to linear programming; matrices and linear systems; probability; and statistics. Examples of applications are given, including those of game theory, Markov chains, and probability. The final chapter is devoted to computers and programming languages such as FORTRAN. This monograph is intended for students and instructors of applied mathematics.

  • Chaotic Dynamics and Fractals

    • 1st Edition
    • Michael F. Barnsley + 1 more
    • English
    Chaotic Dynamics and Fractals covers the proceedings of the 1985 Conference on Chaotic Dynamics, held at the Georgia Institute of Technology. This conference deals with the research area of chaos, dynamical systems, and fractal geometry. This text is organized into three parts encompassing 16 chapters. The first part describes the nature of chaos and fractals, the geometric tool for some strange attractors, and other complicated sets of data associated with chaotic systems. This part also considers the Henon-Hiles Hamiltonian with complex time, a Henon family of maps from C2 into itself, and the idea of turbulent maps in the course of presenting results on iteration of continuous maps from the unit interval to itself. The second part discusses complex analytic dynamics and associated fractal geometry, specifically the bursts into chaos, algorithms for obtaining geometrical and combinatorial information, and the parameter space for iterated cubic polynomials. This part also examines the differentiation of Julia sets with respects to a parameter in the associated rational map, permitting the formulation of Taylor series expansion for the sets. The third part highlights the applications of chaotic dynamics and fractals. This book will prove useful to mathematicians, physicists, and other scientists working in, or introducing themselves to, the field.

  • Algorithmically Specialized Parallel Computers

    • 1st Edition
    • Lawrence Snyder + 2 more
    • English
    Algorithmically Specialized Parallel Computers focuses on the concept and characteristics of an algorithmically specialized computer. This book discusses the algorithmically specialized computers, algorithmic specialization using VLSI, and innovative architectures. The architectures and algorithms for digital signal, speech, and image processing and specialized architectures for numerical computations are also elaborated. Other topics include the model for analyzing generalized inter-processor, pipelined architecture for search tree maintenance, and specialized computer organization for raster graphics display. The data base applications of the FETCH-AND-ADD instruction, distributed parallel architecture for speech understanding, and two parallel formulations of particle-in-cell models are likewise covered in this text. This publication is suitable for students, researchers and professionals concerned with algorithmically specialized computers.

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