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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.

  • Analytic Computational Complexity

    • 1st Edition
    • J.F. Traub
    • English
    Analytic Computational Complexity contains the proceedings of the Symposium on Analytic Computational Complexity held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7-8, 1975. The symposium provided a forum for assessing progress made in analytic computational complexity and covered topics ranging from strict lower and upper bounds on iterative computational complexity to numerical stability of iterations for solution of nonlinear equations and large linear systems. Comprised of 14 chapters, this book begins with an introduction to analytic computational complexity before turning to proof techniques used in analytic complexity. Subsequent chapters focus on the complexity of obtaining starting points for solving operator equations by Newton's method; maximal order of multipoint iterations using n evaluations; the use of integrals in the solution of nonlinear equations in N dimensions; and the complexity of differential equations. Algebraic constructions in an analytic setting are also discussed, along with the computational complexity of approximation operators. This monograph will be of interest to students and practitioners in the fields of applied mathematics and computer science.

  • Calculus Using Mathematica

    • 1st Edition
    • K.D. Stroyan
    • English
    Calculus Using Mathematica is intended for college students taking a course in calculus. It teaches the basic skills of differentiation and integration and how to use Mathematica, a scientific software language, to perform very elaborate symbolic and numerical computations. This is a set composed of the core text, science and math projects, and computing software for symbolic manipulation and graphics generation. Topics covered in the core text include an introduction on how to get started with the program, the ideas of independent and dependent variables and parameters in the context of some down-to-earth applications, formulation of the main approximation of differential calculus, and discrete dynamical systems. The fundamental theory of integration, analytical vector geometry, and two dimensional linear dynamical systems are elaborated as well. This publication is intended for beginning college students.

  • Calculus

    • 2nd Edition
    • Stanley I. Grossman
    • English
    Calculus, Second Edition discusses the techniques and theorems of calculus. This edition introduces the sine and cosine functions, distributes ?-? material over several chapters, and includes a detailed account of analytic geometry and vector analysis. This book also discusses the equation of a straight line, trigonometric limit, derivative of a power function, mean value theorem, and fundamental theorems of calculus. The exponential and logarithmic functions, inverse trigonometric functions, linear and quadratic denominators, and centroid of a plane region are likewise elaborated. Other topics include the sequences of real numbers, dot product, arc length as a parameter, quadric surfaces, higher-order partial derivatives, and Green's theorem in the plane. This publication is a good source for students learning calculus.

  • Analysis, et Cetera

    Research Papers Published in Honor of Jürgen Moser's 60th Birthday
    • 1st Edition
    • Paul H. Rabinowitz + 1 more
    • English
    Analysis, et cetera: Research Papers Published in Honor of Jürgen Moser's 60th Birthday provides a collection of papers dedicated to Jürgen Moser on the occasion of his 60th birthday. This book covers a variety of topics, including Helmholtz equation, algebraic complex integrability, theory of Lie groups, and trigonometric polynomials. Organized into 31 chapters, this book begins with an overview of some basic consequences of the definition of algebraic complete integrability. This text then derives a representation theorem for solutions of the Helmholtz equation. Other chapters consider the integrable generalizations of the Volterra system and explain the dynamical system in the finite-dimensional case. This book discusses as well the global periodic solutions for the planar triple pendulum. The final chapter deals with the problem of deriving the macroscopic conservation laws, or the Euler equations, in accurate fashion from the microscopic equations of classical mechanics. This book is a valuable resource for mathematicians.

  • Mathematics with Applications for the Management, Life, and Social Sciences

    • 2nd Edition
    • Howard Anton + 1 more
    • English
    Mathematics with Applications for the Management, Life, and Social Sciences, 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 in management, life sciences, and social sciences. Some applications of probability, game theory, and Markov chains are given. Comprised of 16 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 point of view; matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and permutations, combinations, and counting methods. Probability for finite sample spaces and basic concepts in statistics are also considered, along with the mathematics of finance and applications of calculus. This monograph is intended for students and instructors of applied mathematics.

  • Elliptic Problem Solvers

    • 1st Edition
    • Martin H. Schultz
    • English
    Elliptic Problem Solvers provides information pertinent to some aspects of the numerical solution of elliptic partial differential equations. This book presents the advances in developing elliptic problem solvers and analyzes their performance. Organized into 40 chapters, this book begins with an overview of the approximate solution of using a standard Galerkin method employing piecewise linear triangular finite elements. This text then defines the types of vector architecture and discusses the variation in performance that can occur on a vector processor as a function of algorithm and implementation. Other chapters consider the implementation of techniques for elliptical problems. This book discusses as well the six techniques for the solution of nonsymmetric linear systems arising from finite difference discretization of the convection-diffusion equation. The final chapter deals with the basic semiconductor device equations. This book is a valuable resource for electrical and computer engineers, scientists, computer programmers, pure mathematicians, and research workers.

  • Neural Networks for Perception

    Computation, Learning, and Architectures
    • 1st Edition
    • Harry Wechsler
    • English
    Neural Networks for Perception, Volume 2: Computation, Learning, and Architectures explores the computational and adaptation problems related to the use of neuronal systems, and the corresponding hardware architectures capable of implementing neural networks for perception and of coping with the complexity inherent in massively distributed computation. This book addresses both theoretical and practical issues related to the feasibility of both explaining human perception and implementing machine perception in terms of neural network models. The text is organized into two sections. The first section, computation and learning, discusses topics on learning visual behaviors, some of the elementary theory of the basic backpropagation neural network architecture, and computation and learning in the context of neural network capacity. The second section is on hardware architecture. The chapters included in this part of the book describe the architectures and possible applications of recent neurocomputing models. The Cohen-Grossberg model of associative memory, hybrid optical/digital architectures for neorocomputing, and electronic circuits for adaptive synapses are some of the subjects elucidated. Neuroscientists, computer scientists, engineers, and researchers in artificial intelligence will find the book useful.

  • Rational Politics

    Decisions, Games, and Strategy
    • 1st Edition
    • Steven J. Brams
    • English
    Rational Politics: Decisions, Games, and Strategy focuses on the unified presentation of politics as a rational human activity, including the paradox of voting and proportional representation. The publication first offers information on the study of rational politics, political intrigue in the Bible, and candidate strategies. Topics include the factor of timing in presidential primaries, rational positions in a multicandidate race, primacy of issues and their spatial representation, and politics in the story of Esther. The text then elaborates on voting paradoxes and the problems of representation, voting power, and threats and deterrence. Discussions focus on a sequential view of the Cuban missile crisis, use of threat power in Poland, power anomalies in the European Community Council of Ministers, probability of the paradox of voting, empirical examples of the paradox of voting, and problems in achieving proportional representation. The book is a valuable reference for researchers interested in rational politics.

  • Probabilistic Analysis and Related Topics

    Volume 1
    • 1st Edition
    • A. T. Bharucha-Reid
    • English
    Probabilistic Analysis and Related Topics, Volume 1 focuses on the continuity, differentiability, and integrability of random functions, including functional analysis, operator theory, measure theory, and numerical analysis. The selection first offers information on stochastic partial differential equations in turbulence related problems and estimation and stochastic control for linear infinite-dimensional systems. Discussions focus on deterministic quadratic cost-control problem; partial differential equations in stochastic wave propagation; and theory of stochastic partial differential equations. The text then examines random integrodifferential equations, including small perturbations, existence and uniqueness of solutions, stochastic properties of solution processes, and vibration string. The manuscript ponders on equivalence and singularity of Gaussian measures and applications and stochastic Riemannian geometry. Concerns include semilocal properties, Brownian motion, reproducing kernel Hilbert spaces and Gaussian processes, equivalence and singularity of Gaussian processes, and general problem of equivalence and singularity. The selection is a vital source of information for mathematicians and researchers interested in the general theory of random functions.

  • Classification and Clustering

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin at Madison, May 3–5, 1976
    • 1st Edition
    • J. Van Ryzin
    • English
    Classification and Clustering documents the proceedings of the Advanced Seminar on Classification and Clustering held in Madison, Wisconsin on May 3-5, 1976. This compilation discusses the relationship between multidimensional scaling and clustering, distribution problems in clustering, and botryology of botryology. The graph theoretic techniques for cluster analysis algorithms, data dependent clustering techniques, and linguistic approach to pattern recognition are also elaborated. This text likewise covers the discriminant analysis when scale contamination is present in the initial sample and statistical basis of computerized diagnosis using the electrocardiogram. Other topics include the simple histogram method for nonparametric classification and optimal smoothing of density estimates. This book is intended for mathematicians, biological scientists, social scientists, computer scientists, statisticians, and engineers interested in classification and clustering.

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