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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.

  • Vector Analysis and Cartesian Tensors

    • 2nd Edition
    • D. E. Bourne + 1 more
    • English
    Vector Analysis and Cartesian Tensors, Second Edition focuses on the processes, methodologies, and approaches involved in vector analysis and Cartesian tensors, including volume integrals, coordinates, curves, and vector functions. The publication first elaborates on rectangular Cartesian coordinates and rotation of axes, scalar and vector algebra, and differential geometry of curves. Discussions focus on differentiation rules, vector functions and their geometrical representation, scalar and vector products, multiplication of a vector by a scalar, and angles between lines through the origin. The text then elaborates on scalar and vector fields and line, surface, and volume integrals, including surface, volume, and repeated integrals, general orthogonal curvilinear coordinates, and vector components in orthogonal curvilinear coordinates. The manuscript ponders on representation theorems for isotropic tensor functions, Cartesian tensors, applications in potential theory, and integral theorems. Topics include geometrical and physical significance of divergence and curl, Poisson's equation in vector form, isotropic scalar functions of symmetrical second order tensors, and diagonalization of second-order symmetrical tensors. The publication is a valuable reference for mathematicians and researchers interested in vector analysis and Cartesian tensors.

  • Discriminant Analysis and Applications

    • 1st Edition
    • T. Cacoullos
    • English
    Discriminant Analysis and Applications comprises the proceedings of the NATO Advanced Study Institute on Discriminant Analysis and Applications held in Kifissia, Athens, Greece in June 1972. The book presents the theory and applications of Discriminant analysis, one of the most important areas of multivariate statistical analysis. This volume contains chapters that cover the historical development of discriminant analysis methods; logistic and quasi-linear discrimination; and distance functions. Medical and biological applications, and computer graphical analysis and graphical techniques for multidimensional data are likewise discussed. Statisticians, mathematicians, and biomathematicians will find the book very interesting.

  • Computer Science and Scientific Computing

    Proceedings of the Third ICASE Conference on Scientific Computing, Williamsburg, Virginia, April 1 and 2, 1976
    • 1st Edition
    • James M. Ortega
    • English
    Computer Science and Scientific Computing contains the proceedings of the Third ICASE Conference on Scientific Computing held in Williamsburg, Virginia, on April l and 2, 1976, under the auspices of the Institute for Computer Applications in Systems Engineering at the NASA Langley Research Center. The conference provided a forum for reviewing all the aspects of scientific computing and covered topics ranging from computer-aided design (CAD) and computer science technology to the design of large hydrodynamics codes. Case studies in reliable computing are also presented. Comprised of 13 chapters, this book begins with an introduction to the use of the hierarchical family concept in the development of scientific programming systems. The discussion then turns to the data structures of scientific computing and their representation and management; some important CAD capabilities required to support aerospace design in the areas of interactive support, information management, and computer hardware advances as well as some computer science developments which may contribute significantly to making such capabilities possible; and the use of symbolic computation systems for problem solving in scientific research. Subsequent chapters deal with computer applications in astrophysics; the possibility of computing turbulence and numerical wind tunnels; and the basis for a general-purpose program for finite element analysis. Software tools for computer graphics are also considered. This monograph will be of value to scientists, systems designers and engineers, and students in computer science who have an interest in the subject of scientific computing.

  • The Desktop Fractal Design Handbook

    • 1st Edition
    • Michael F. Barnsley
    • English
    The Desktop Fractal Design Handbook is a four-chapter introductory text to fractal geometry. The underlying algorithms are derived from mathematics, which is reflected in the images they produce. Chapter 1 provides an overview of the products of the desktop fractal design system. Chapter 2 describes the installation and operation of hardware and operating system of the design system, along with its maintenance. Chapter 3 outlines the use of the desktop fractal design system, specifically on hot to design fractals on the fractal design screen, maps, paintings, and help screens. Chapter 4 focuses on the many practical applications of fractals. This book will be of value to mathematicians, engineers, graphic artists, teachers, and students.

  • Combinatorial Algorithms

    For Computers and Calculators
    • 2nd Edition
    • Albert Nijenhuis + 1 more
    • Werner Rheinboldt
    • English
    Combinatorial Algorithms for Computers and Calculators, Second Edition deals with combinatorial algorithms for computers and calculators. Topics covered range from combinatorial families such as the random subset and k-subset of an n-set and Young tableaux, to combinatorial structures including the cycle structure of a permutation and the spanning forest of a graph. Newton forms of a polynomial and the composition of power series are also discussed. Comprised of 30 chapters, this volume begins with an introduction to combinatorial algorithms by considering the generation of all of the 2n subsets of the set {1, 2,...,n}. The discussion then turns to the random subset and k-subset of an n-set; next composition of n into k parts; and random composition of n into k parts. Subsequent chapters focus on sequencing, ranking, and selection algorithms in general combinatorial families; renumbering rows and columns of an array; the cycle structure of a permutation; and the permanent function. Sorting and network flows are also examined, along with the backtrack method and triangular numbering in partially ordered sets. This book will be of value to both students and specialists in the fields of applied mathematics and computer science.

  • Optimizing Methods in Statistics

    Proceedings of a Symposium Held at the Center for Tomorrow, the Ohio State University, June 14-16, 1971
    • 1st Edition
    • Jagdish S. Rustagi
    • English
    Optimizing Method in Statistics is a compendium of papers dealing with variational methods, regression analysis, mathematical programming, optimum seeking methods, stochastic control, optimum design of experiments, optimum spacings, and order statistics. One paper reviews three optimization problems encountered in parameter estimation, namely, 1) iterative procedures for maximum likelihood estimation, based on complete or censored samples, of the parameters of various populations; 2) optimum spacings of quantiles for linear estimation; and 3) optimum choice of order statistics for linear estimation. Another paper notes the possibility of posing various adaptive filter algorithms to make the filter learn the system model while the system is operating in real time. By reducing the time necessary for process modeling, the time required to implement the acceptable system design can also be reduced One paper evaluates the parallel structure between duality relationships for the linear functional version of the generalized Neyman-Pearson problem, as well as the duality relationships of linear programming as these apply to bounded-variable linear programming problems. The compendium can prove beneficial to mathematicians, students, and professor of calculus, statistics, or advanced mathematics.

  • Social Issues in Computing

    • 1st Edition
    • C. C. Gotlieb + 1 more
    • Werner Rheinboldt
    • English
    Social Issues in Computing provides information pertinent to the social implications of technology. This book presents the highly dynamic interaction between computers and society. Organized into 13 chapters, this book begins with an overview of the problems associated with computers and attempts to indicate some of the viewpoints, assumptions, and biases from which the discussion is undertaken. This text then examines in detail the effects of computers on society ad describes the extent of computer use. Other chapters consider the disparities in computer use between various countries, as well as the degree to which various countries are able to share in the market for computer products and services. This book discusses as well the factors that led to the rapid and widespread adoption of computers. The final chapter deals with the effects of automation, computers, and technology. This book is a valuable resource for computer science students and research workers.

  • A Second Course in Elementary Differential Equations

    • 1st Edition
    • Paul Waltman
    • English
    A Second Course in Elementary Differential Equations deals with norms, metric spaces, completeness, inner products, and an asymptotic behavior in a natural setting for solving problems in differential equations. The book reviews linear algebra, constant coefficient case, repeated eigenvalues, and the employment of the Putzer algorithm for nondiagonalizable coefficient matrix. The text describes, in geometrical and in an intuitive approach, Liapunov stability, qualitative behavior, the phase plane concepts, polar coordinate techniques, limit cycles, the Poincaré-Bendixson theorem. The book explores, in an analytical procedure, the existence and uniqueness theorems, metric spaces, operators, contraction mapping theorem, and initial value problems. The contraction mapping theorem concerns operators that map a given metric space into itself, in which, where an element of the metric space M, an operator merely associates with it a unique element of M. The text also tackles inner products, orthogonality, bifurcation, as well as linear boundary value problems, (particularly the Sturm-Liouville problem). The book is intended for mathematics or physics students engaged in ordinary differential equations, and for biologists, engineers, economists, or chemists who need to master the prerequisites for a graduate course in mathematics.

  • Combinatorics on Words

    Progress and Perspectives
    • 1st Edition
    • Larry J. Cummings
    • English
    Combinatorics on Words: Progress and Perspectives covers the proceedings of an international meeting by the same title, held at the University of Waterloo, Canada on August 16-22, 1982. This meeting highlights the diverse aspects of combinatorics on words, including the Thue systems, topological dynamics, combinatorial group theory, combinatorics, number theory, and computer science. This book is organized into four parts encompassing 19 chapters. The first part describes the Thue systems with the Church-Rosser property. A Thue system will be called “Church-Rosser” if two strings are congruent with respect to that system if and only if they have a common descendant, that is, a string that can be obtained applying only rewriting rules that reduce length. The next part deals with the problems related to the encoding of codes and the overlapping of words in rational languages. This part also explores the features of polynomially bounded DOL systems yield codes. These topics are followed by discussions of some combinatorial properties of metrics over the free monoid and the burnside problem of semigroups of matrices. The last part considers the ambiguity types of formal grammars, finite languages, computational complexity of algebraic structures, and the Bracket-context tree functions. This book will be of value to mathematicians and advance undergraduate and graduate students.

  • Solutions for Networked Databases

    How to Move from Heterogeneous Structures to Federated Concepts
    • 1st Edition
    • Dimitris N. Chorafas + 1 more
    • English
    Solutions for Networked Databases: How to Move from Heterogeneous Structures to Federated Concepts reviews developments in standards and ad hoc solutions aimed at providing cross-database connectivity for networked databases. The emphasis is on how to move from heterogeneous structures to federated concepts. The advent of the multidatabase is discussed, along with schemata, dictionaries, and protocols. Applications with federated databases are also considered. Comprised of 18 chapters, this book begins with an introduction to database and knowledge bank concepts; reliability and availability characteristics; and the synergy necessary to create and sustain federated databases. Centralized and distributed databases are then compared, and the different ways of managing distributed databases are outlined. Subsequent chapters focus on the importance of treating the networked database as a corporate resource; the use of schemata to solve cross-database problems; the Information Resource Dictionary System; and application programming interface and remote data access. A solution to heterogeneous distributed databases, the Data Access Integrated Services (DAIS), is described. This monograph is written for specialists in computers and communications.

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