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Books in Mathematics and applied mathematics

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    • Interval Mathematics 1980

      • 1st Edition
      • May 10, 2014
      • Karl L. E. Nickel
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 4 1 3 6
      • eBook
        9 7 8 1 4 8 3 2 7 3 8 4 6
      Interval Mathematics 1980 contains the proceedings of an International Symposium on Interval Mathematics held in Germany on May 27-31, 1980. The book introduces the reader to some of the most important work done in the field of interval mathematics and its application to computing. Topics covered range from purely theoretical to computational methods and computer architecture. Comprised of 41 chapters, this book begins with an overview of set functions and their applications, followed by a discussion on global constrained optimization using interval analysis. A model for the propagation of rounding error in floating arithmetic is then presented, and the importance of 3-valued notions for interval mathematics is highlighted. Subsequent chapters focus on the transformation of interval programs into convergent interval programs; specifications for interval programming languages; interval contractions for the solution of integral equations; and mean convergence enclosing of solutions of operator equations with convex and inverse monotonic operators. This monograph will be of value to both students and specialists in the fields of mathematics and computer science.

    • The Mathematical Structure of Raster Graphics

      • 1st Edition
      • May 10, 2014
      • Eugene L. Fiume
      • English
      • Paperback
        9 7 8 1 4 8 3 2 3 8 8 7 6
      • eBook
        9 7 8 1 4 8 3 2 6 0 8 2 2
      The Mathematical Structure of Raster Graphics presents a mathematical characterization of the structure of raster graphics, a popular and diverse form of computer graphics. The semantics and theory of the mathematical structure of raster graphics are discussed. Notations that help to clarify some of the concepts generally considered to be fundamental to computer graphics are included. Comprised of seven chapters, this book begins with a description of a general framework for specifying and manipulating scenes. Basic graphic entities, called primitive graphic objects, are defined using a simple notation over a Euclidean space. The reader is then introduced to a semantics of visibility; a mathematical semantics of rendering, developed using the very basic notion of measure; and a mathematical formalization of bit-mapped graphics. A framework for specifying illumination models is also described, along with the complexity of abstract ray tracing. This monograph will be a useful resource for undergraduate and graduate students, researchers, and practitioners in the fields of mathematics and computer graphics, and to those with some basic computer graphics background.

    • Contributions to Algebra

      • 1st Edition
      • May 10, 2014
      • Hyman Bass + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 3 5 9 2 9
      • eBook
        9 7 8 1 4 8 3 2 6 8 0 6 4
      Contributions to Algebra: A Collection of Papers Dedicated to Ellis Kolchin provides information pertinent to commutative algebra, linear algebraic group theory, and differential algebra. This book covers a variety of topics, including complex analysis, logic, K-theory, stochastic matrices, and differential geometry. Organized into 29 chapters, this book begins with an overview of the influence that Ellis Kolchin's work on the Galois theory of differential fields has had on the development of differential equations. This text then discusses the background model theoretic work in differential algebra and discusses the notion of model completions. Other chapters consider some properties of differential closures and some immediate consequences and include extensive notes with proofs. This book discusses as well the problems in finite group theory in finding the complex finite projective groups of a given degree. The final chapter deals with the finite forms of quasi-simple algebraic groups. This book is a valuable resource for students.

    • Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations

      • 1st Edition
      • May 10, 2014
      • A.K. Aziz
      • English
      • Paperback
        9 7 8 1 4 8 3 2 3 5 7 5 2
      • eBook
        9 7 8 1 4 8 3 2 6 7 9 9 9
      Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.

    • Programming Language Structures

      • 1st Edition
      • May 10, 2014
      • Elliott I. Organick + 2 more
      • English
      • eBook
        9 7 8 1 4 8 3 2 6 4 8 7 5
      Programming Language Structures deals with the structures of programming languages and introduces the reader to five important programming languages: Algol, Fortran, Lisp, Snobol, and Pascal. The fundamental similarities and differences among these languages are discussed. A unifying framework is constructed that can be used to study the structure of other languages, such as Cobol, PL/I, and APL. Several of the tools and methodologies needed to construct large programs are also considered. Comprised of 10 chapters, this book begins with a summary of the relevant concepts and principles about algorithms, flowcharts, and computation that a student is expected to know from the first course. The discussion then turns to the semantics of procedure and function call as well as argument-parameter matching with various kinds of parameters; recursion and its relation to tree traversal; syntax formalism for context-free languages; and ALGOL 60 and block structuring. Case study programs are presented to reinforce the reader's understanding of ALGOL 60 and Fortran semantics. The remaining chapters deal with Lisp, Snobol, and Pascal. This monograph is intended for working programmers and students in computer science who have an interest in the subject of programming.

    • Parallel Computations

      • 1st Edition
      • May 10, 2014
      • Garry Rodrigue
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 5 5 5 3
      • eBook
        9 7 8 1 4 8 3 2 7 6 6 4 9
      Parallel Computations focuses on parallel computation, with emphasis on algorithms used in a variety of numerical and physical applications and for many different types of parallel computers. Topics covered range from vectorization of fast Fourier transforms (FFTs) and of the incomplete Cholesky conjugate gradient (ICCG) algorithm on the Cray-1 to calculation of table lookups and piecewise functions. Single tridiagonal linear systems and vectorized computation of reactive flow are also discussed. Comprised of 13 chapters, this volume begins by classifying parallel computers and describing techniques for performing matrix operations on them. The reader is then introduced to FFTs and the tridiagonal linear system as well as the ICCG method. Different versions of the conjugate gradient method for solving the time-dependent diffusion equation are considered. Subsequent chapters deal with two- and three-dimensional fluid flow calculations, paying particular attention to the principal issues in designing efficient numerical methods for hydrodynamic calculations; the decisions that a numerical modeler must make to optimize chemically reactive flow simulations; and how to handle disk-to-core data transfer and storage allocation for the solution of the implicit equations for three-dimensional flows. The book also describes the time-split finite difference scheme for solving the two-dimensional Navier-Stokes equation for flows through slotted nozzles. Finally, the large-scale stimulation of plasmas, as carried out on a small computer with an array processor, is discussed. This monograph should be of interest to specialists in computer science.

    • Metric Affine Geometry

      • 1st Edition
      • May 10, 2014
      • Ernst Snapper + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 6 6 8 0
      • eBook
        9 7 8 1 4 8 3 2 6 9 3 3 7
      Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector spaces. The metric affine geometry is treated in Chapter 3. This text specifically discusses the concrete model for affine space, dilations in terms of coordinates, parallelograms, and theorem of Desargues. The inner products in terms of coordinates and similarities of affine spaces are also elaborated. The prerequisites for this publication are a course in linear algebra and an elementary course in modern algebra that includes the concepts of group, normal subgroup, and quotient group. This monograph is suitable for students and aspiring geometry high school teachers.

    • Mathematical Models of Attitude Change

      • 1st Edition
      • May 10, 2014
      • John E. Hunter + 2 more
      • Peter R. Monge
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 0 7 9 4
      • eBook
        9 7 8 1 4 8 3 2 6 3 0 3 8
      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.

    • Multiple Time Scales

      • 1st Edition
      • May 10, 2014
      • Jeremiah U. Brackbill + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 3 6 5 7 5
      • eBook
        9 7 8 1 4 8 3 2 5 7 5 6 3
      Multiple Time Scales presents various numerical methods for solving multiple-time-scale problems. The selection first elaborates on considerations on solving problems with multiple scales; problems with different time scales; and nonlinear normal-mode initialization of numerical weather prediction models. Discussions focus on analysis of observations, nonlinear analysis, systems of ordinary differential equations, and numerical methods for problems with multiple scales. The text then examines the diffusion-synthetic acceleration of transport iterations, with application to a radiation hydrodynamics problem and implicit methods in combustion and chemical kinetics modeling. The publication ponders on molecular dynamics and Monte Carlo simulations of rare events; direct implicit plasma simulation; orbit averaging and subcycling in particle simulation of plasmas; and hybrid and collisional implicit plasma simulation models. Topics include basic moment method, electron subcycling, gyroaveraged particle simulation, and the electromagnetic direct implicit method. The selection is a valuable reference for researchers interested in pursuing further research on the use of numerical methods in solving multiple-time-scale problems.

    • Elementary Functions and Analytic Geometry

      • 1st Edition
      • May 10, 2014
      • Harley Flanders
      • English
      • Paperback
        9 7 8 1 4 8 3 2 3 8 8 8 3
      • eBook
        9 7 8 1 4 8 3 2 7 1 9 6 5
      Elementary Functions and Analytic Geometry is an introduction to college mathematics, with emphasis on elementary functions and analytic geometry. It aims to provide a working knowledge of basic functions (polynomial, rational, exponential, logarithmic, and trigonometric); graphing techniques and the numerical aspects and applications of functions; two- and three-dimensional vector methods; and complex numbers, mathematical induction, and the binomial theorem. Comprised of 13 chapters, this book begins with a discussion on functions and graphs, paying particular attention to quantities measured in the real number system. The next chapter deals with linear and quadratic functions as well as some of their applications. Tips on graphing are offered. Subsequent chapters focus on polynomial functions, along with graphs of factored polynomials; rational functions; exponential and logarithm functions; and trigonometric functions. Identities and inverse functions, vectors, and trigonometry are also explored, together with complex numbers and solid analytic geometry. The book concludes by considering mathematical induction, binomial coefficients, and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

Related subjects

Abstract harmonic analysis

Algebra and number theory

Algebraic geometry

Algebraic topology

Analysis

Applied mathematics

Approximations and expansions

Associative rings and algebras

Biomathematics

Calculus of variations and optimal control optimization

Category theory homological algebra

Commutative rings and algebras

Computer science

Convex sets and related geometric topics

Differential geometry

Discrete mathematics combinatorics

Field theory and polynomials

Finite differences and functional equations

Fourier analysis

Functional analysis

Functions of a complex variable

General mathematical systems

General topology

Geometry

Global analysis analysis of manifolds

Group theory and generalizations

Integral equations

Integral transforms operational calculus

K theory

Linear and multilinear algebra matrix theory

Logic

Manifolds and cell complexes

Mathematical economics and game theory

Mathematical logic and foundations

Mathematical programming

Mathematics general

Mathematics history and biography

Measure and integration

Nonassociative rings and algebras

Number theory

Numerical analysis

Operator theory

Order lattices ordered algebraic structures

Ordinary differential equations

Partial differential equations

Real functions

Relativity

Sequences series summability

Set theory

Several complex variables and analytic spaces

Special functions

Systems theory control

Topological groups lie groups