Skip to main content
Elsevier

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.

  • Numerical Methods for Differential Systems

    Recent Developments in Algorithms, Software, and Applications
    • 1st Edition
    • L. Lapidus + 1 more
    • English
    Numerical Methods for Differential Systems: Recent Developments in Algorithms, Software, and Applications reviews developments in algorithms, software, and applications of numerical methods for differential systems. Topics covered include numerical algorithms for ordinary and partial differential equations (ODE/PDEs); theoretical approaches to the solution of nonlinear algebraic and boundary value problems via associated differential systems; integration algorithms for initial-value ODEs with particular emphasis on stiff systems; finite difference algorithms; and general- and special-purpose computer codes for ODE/PDEs. Comprised of 15 chapters, this book begins with an introduction to high-order A-stable averaging algorithms for stiff differential systems, followed by a discussion on second derivative multistep formulas based on g-splines; numerical integration of linearized stiff ODEs; and numerical solution of large systems of stiff ODEs in a modular simulation framework. Subsequent chapters focus on numerical methods for mass action kinetics; a systematized collection of codes for solving two-point boundary value problems; general software for PDEs; and the choice of algorithms in automated method of lines solution of PDEs. The final chapter is devoted to quality software for ODEs. This monograph should be of interest to mathematicians, chemists, and chemical engineers.

  • A Syntax-Oriented Translator

    • 1st Edition
    • Peter Zilahy Ingerman
    • English
    A Syntax-Oriented Translator focuses on the field of programming and the characteristics and functions of compilers and translators. The book first offers information on the metasyntactic language and the details of a parsing processor. Discussions focus on processing, recovery, and output sections, detailed flow-chart of the parsing processor, parsing form of a grammar, canonical ordering, and the metasyntactic language in general. The text then elaborates on some extensions to the metasyntactic language and metasemantic and metapragmatic language, including punctuation marks and format control, metasemantic and metapragmatic functions, basic form of the construct, and substitution MSF. The publication examines the details of an unparsing processor, as well as lists used in unparsing, subroutines, and the unparsing processor itself. The book is a dependable source of information for home compiler-writers who are interested in the use of a syntax-oriented translator.

  • Applications of Finite Groups

    • 1st Edition
    • J. S. Lomont
    • English
    Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.

  • Failure-Tolerant Computer Design

    • 1st Edition
    • William H. Pierce
    • English
    Failure-Tolerant Computer Design focuses on the use of redundancy theory in improving the reliability of computers. The book first offers information on redundancy theory and limit theorems. Discussions focus on applications in determining the optimum placement of restoring organs; time asymptotes for log failure probability for exponential survival probability; reliability of multiple-function system with paralleled individual units; and basic concepts for making reliable computers out of unreliable parts. The text then examines decision theory in redundant systems and adaptive decision elements. The publication examines the interconnection structure for redundant logic and redundant relay theory. Topics include Moore-Shannon limit theorem; systematic groupings of inputs in single-layer error-correcting interwoven redundant logic; interwoven logic with alternating-layer error correction; and interwoven logic with single-layer error correction. The book also elaborates on transition analyses in reliability theory, including Markov chain theory and probability bounds in Markov chains having many states or inexactly known transition matrices. The manuscript is a vital source of data for engineers and researchers interested in failure-tolerant computer design.

  • Axiomatic Projective Geometry

    • 2nd Edition
    • A. Heyting
    • N. G. De Bruijn + 2 more
    • English
    Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume V: Axiomatic Projective Geometry, Second Edition focuses on the principles, operations, and theorems in axiomatic projective geometry, including set theory, incidence propositions, collineations, axioms, and coordinates. The publication first elaborates on the axiomatic method, notions from set theory and algebra, analytic projective geometry, and incidence propositions and coordinates in the plane. Discussions focus on ternary fields attached to a given projective plane, homogeneous coordinates, ternary field and axiom system, projectivities between lines, Desargues' proposition, and collineations. The book takes a look at incidence propositions and coordinates in space. Topics include coordinates of a point, equation of a plane, geometry over a given division ring, trivial axioms and propositions, sixteen points proposition, and homogeneous coordinates. The text examines the fundamental proposition of projective geometry and order, including cyclic order of the projective line, order and coordinates, geometry over an ordered ternary field, cyclically ordered sets, and fundamental proposition. The manuscript is a valuable source of data for mathematicians and researchers interested in axiomatic projective geometry.

  • Non-Linear Transformations of Stochastic Processes

    • 1st Edition
    • P. I. Kuznetsov + 2 more
    • English
    Non-Linear Transformations of Stochastic Processes focuses on the approaches, methodologies, transformations, and computations involved in the non-linear transformations of stochastic processes. The selection first underscores some problems of the theory of stochastic processes and the transmission of random functions through non-linear systems. Discussions focus on the transformation of moment functions for the general non-linear transformation; conversion formulas for correlation functions; transformation of moment functions for the simplest type of non-linear transformation; and normalization of the linear system of probability distribution laws. The text then ponders on quasi-moment functions in the theory of random processes and correlation functions in the theory of the Brownian motion generalization of the Fokker-Planck equation. The manuscript elaborates on the correlation functions of random sequences of rectangular pulses; method of determining the envelope of quasi-harmonic fluctuations; and the problem of measuring electrical fluctuations with the aid of thermoelectric devices. The book then examines the effect of signal and noise on non-linear elements and the approximate method of calculating the correlation function of stochastic signals. The selection is a dependable source of information for researchers interested in the non-linear transformations of stochastic processes.

  • Tables of Weber Functions

    Mathematical Tables, Vol. 1
    • 1st Edition
    • I. Ye. Kireyeva + 1 more
    • English
    Tables of Weber Functions contains values for Weber functions or functions of a parabolic cylinder. Investigators at the Computing Centre of the Academy of Sciences, U.S.S.R. confirm these tables which have been calculated by a computer. The wave equation, expressed in parabolic coordinates, occurs in quantum mechanics, radio physics, aerodynamics, hydrodynamics and other fields. Each section of the tables contains values of the real and imaginary parts of the function Dp[x(i + i)]for 51-55 successive values of x, as determined by the interpolation with respect to x, and four values of p. On the left side are given the values of up(x) and vp(x) for positive values of x, and on the right for negative x with the same absolute values. The book contains twenty groups of sections corresponding to values of

  • The Office of the Future

    Communication and Computers
    • 1st Edition
    • Ronald P. Uhlig + 2 more
    • English
    Monograph Series of the International Council for Computer Communications, Volume 1: The Office of the Future: Communication and Computers focuses on the advancements in the processes, technologies, techniques, principles, and approaches involved in communication and computers, including computer based tools, data gathering and information retrieval, and office automation. The publication first elaborates on the automated office of the future, tools to support the communication activity, and text editing tools for generating, organizing, analyzing, and transforming information. Discussions focus on generating, organizing, and analyzing information, basic message system concepts, impact of computer networks, and other processes in the office. The text then examines the integration of computer based tools, data gathering and information retrieval tools, coordination tools in the office of the future, and tools to support office processes. The manuscript ponders on the integration of the spoken word with interactive computer based office support systems, underlying technology, digital channel, and software aspects of the office environment utilizing the micro-processor. Topics include single board computer, advances in digital computer communications technology, future directions for digital networks, bandwidth availability, and storage and retrieval of voice information. The book is a dependable source of data for computer science experts and researchers interested in the relationship of communication and computers.

  • Topological Spaces

    • 1st Edition
    • H. J. Kowalsky
    • English
    Topological Spaces focuses on the applications of the theory of topological spaces to the different branches of mathematics. The book first offers information on elementary principles, topological spaces, and compactness and connectedness. Discussions focus on locally compact spaces, local connectedness, fundamental concepts and their reformulations, lattice of topologies, axioms of separation, fundamental concepts of set theory, and ordered sets and lattices. The manuscript then ponders on mappings and extensions and characterization of topological spaces, including completely regular spaces, transference of topologies, Wallman compactification, and embeddings. The publication takes a look at metric and uniform spaces and applications of topological groups. Topics include the Stone-Weierstrass Approximation Theorem, extensions and completions of topological groups, topological rings and fields, extension and completion of uniform spaces, uniform continuity and uniform convergence, metric spaces, and metritization. The text is a valuable reference for mathematicians and researchers interested in the study of topological spaces.

  • Functional Analysis and Numerical Mathematics

    • 1st Edition
    • Lothar Collatz
    • English
    Functional Analysis and Numerical Mathematics focuses on the structural changes which numerical analysis has undergone, including iterative methods, vectors, integral equations, matrices, and boundary value problems. The publication first examines the foundations of functional analysis and applications, including various types of spaces, convergence and completeness, operators in Hilbert spaces, vector and matrix norms, eigenvalue problems, and operators in pseudometric and other special spaces. The text then elaborates on iterative methods. Topics include the fixed-point theorem for a general iterative method in pseudometric spaces; special cases of the fixed-point theorem and change of operator; iterative methods for differential and integral equations; and systems of equations and difference methods. The manuscript takes a look at monotonicity, inequalities, and other topics, including monotone operators, applications of Schauder's theorem, matrices and boundary value problems of monotone kind, discrete Chebyshev approximation and exchange methods, and approximation of functions. The publication is a valuable source of data for mathematicians and researchers interested in functional analysis and numerical mathematics.

  • Lacunary Polynomials Over Finite Fields

    • 1st Edition
    • L. Rédei
    • English
    Lacunary Polynomials Over Finite Fields focuses on reducible lacunary polynomials over finite fields, as well as stem polynomials, differential equations, and gaussian sums. The monograph first tackles preliminaries and formulation of Problems I, II, and III, including some basic concepts and notations, invariants of polynomials, stem polynomials, fully reducible polynomials, and polynomials with a restricted range. The text then takes a look at Problem I and reduction of Problem II to Problem III. Topics include reduction of the marginal case of Problem II to that of Problem III, proposition on power series, proposition on polynomials, and preliminary remarks on polynomial and differential equations. The publication ponders on Problem III and applications. Topics include homogeneous elementary symmetric systems of equations in finite fields; divisibility maximum properties of the gaussian sums and related questions; common representative systems of a finite abelian group with respect to given subgroups; and difference quotient of functions in finite fields. The monograph also reviews certain families of linear mappings in finite fields, appendix on the degenerate solutions of Problem II, a lemma on the greatest common divisor of polynomials with common gap, and two group-theoretical propositions. The text is a dependable reference for mathematicians and researchers interested in the study of reducible lacunary polynomials over finite fields.

  • Test Bank for College Algebra

    • 2nd Edition
    • Bernard Kolman + 2 more
    • English
    Test Bank for College Algebra, Second Edition is a supplementary material for the text, College Algebra, Second Edition. The book is intended for use by mathematics teachers. The book contains standard tests for each chapter in the textbook. Each set of test aims to evaluate the level of understanding the student has achieved during the course. The answers for each chapter test and the final exam are found at the end of the book. Mathematics teachers teaching college algebra will find the book very useful.

  • Nonlinear Phenomena in Mathematical Sciences

    Proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, Held at the University of Texas at Arlington, Arlington, Texas, June 16–20, 1980
    • 1st Edition
    • V. Lakshmikantham
    • English
    Nonlinear Phenomena in Mathematical Sciences contains the proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, held at the University of Texas at Arlington, on June 16-20,1980. The papers explore trends in nonlinear phenomena in mathematical sciences, with emphasis on nonlinear functional analytic methods and their applications; nonlinear wave theory; and applications to medical and life sciences. In the area of nonlinear functional analytic methods and their applications, the following subjects are discussed: optimal control theory; periodic oscillations of nonlinear mechanical systems; Leray-Schauder degree theory; differential inequalities applied to parabolic and elliptic partial differential equations; bifurcation theory, stability theory in analytical mechanics; singular and ordinary boundary value problems, etc. The following topics in nonlinear wave theory are considered: nonlinear wave propagation in a randomly homogeneous media; periodic solutions of a semilinear wave equation; asymptotic behavior of solutions of strongly damped nonlinear wave equations; shock waves and dissipation theoretical methods for a nonlinear Schr?dinger equation; and nonlinear hyperbolic Volterra equations occurring in viscoelasticity. Applications to medical and life sciences include mathematical modeling in physiology, pharmacokinetics, and neuro-mathematics, along with epidemic modeling and parameter estimation techniques. This book will be helpful to students, practitioners, and researchers in the field of mathematics.

  • Modern General Topology

    • 2nd Edition
    • Jun-Iti Nagata
    • N. G. De Bruijn + 2 more
    • English
    Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VII: Modern General Topology focuses on the processes, operations, principles, and approaches employed in pure and applied mathematics, including spaces, cardinal and ordinal numbers, and mappings. The publication first elaborates on set, cardinal and ordinal numbers, basic concepts in topological spaces, and various topological spaces. Discussions focus on metric space, axioms of countability, compact space and paracompact space, normal space and fully normal space, subspace, product space, quotient space, and inverse limit space, convergence, mapping, and open basis and neighborhood basis. The book then ponders on compact spaces and related topics, as well as product of compact spaces, compactification, extensions of the concept of compactness, and compact space and the lattice of continuous functions. The manuscript tackles paracompact spaces and related topics, metrizable spaces and related topics, and topics related to mappings. Topics include metric space, paracompact space, and continuous mapping, theory of inverse limit space, theory of selection, mapping space, imbedding, metrizability, uniform space, countably paracompact space, and modifications of the concept of paracompactness. The book is a valuable source of data for mathematicians and researchers interested in modern general topology.

  • Graph Theory and Computing

    • 1st Edition
    • Ronald C. Read
    • English
    Graph Theory and Computing focuses on the processes, methodologies, problems, and approaches involved in graph theory and computer science. The book first elaborates on alternating chain methods, average height of planted plane trees, and numbering of a graph. Discussions focus on numbered graphs and difference sets, Euclidean models and complete graphs, classes and conditions for graceful graphs, and maximum matching problem. The manuscript then elaborates on the evolution of the path number of a graph, production of graphs by computer, and graph-theoretic programming language. Topics include FORTRAN characteristics of GTPL, design considerations, representation and identification of graphs in a computer, production of simple graphs and star topologies, and production of stars having a given topology. The manuscript examines the entropy of transformed finite-state automata and associated languages; counting hexagonal and triangular polyominoes; and symmetry of cubical and general polyominoes. Graph coloring algorithms, algebraic isomorphism invariants for graphs of automata, and coding of various kinds of unlabeled trees are also discussed. The publication is a valuable source of information for researchers interested in graph theory and computing.

  • Additive and Polynomial Representations

    • 1st Edition
    • David H. Krantz + 2 more
    • English
    Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utilization of constructive methods, and as a series of isomorphism theorems leading to consistent numerical solutions. The text also explains the counting of units in relation to an empirical relational structure which contains a concatenation operation. The book notes some special variants which arise in connection with relativity and thermodynamics. The text cites examples from physics and psychology for which additive conjoint measurement provides a possible method of fundamental measurement. The book will greatly benefit mathematicians, econometricians, and academicians in advanced mathematics or physics.

  • Mathematical Logic and Formalized Theories

    A Survey of Basic Concepts and Results
    • 2nd Edition
    • Robert L. Rogers
    • English
    Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results focuses on basic concepts and results of mathematical logic and the study of formalized theories. The manuscript first elaborates on sentential logic and first-order predicate logic. Discussions focus on first-order predicate logic with identity and operation symbols, first-order predicate logic with identity, completeness theorems, elementary theories, deduction theorem, interpretations, truth, and validity, sentential connectives, and tautologies. The text then tackles second-order predicate logic, as well as second-order theories, theory of definition, and second-order predicate logic F2. The publication takes a look at natural and real numbers, incompleteness, and the axiomatic set theory. Topics include paradoxes, recursive functions and relations, Gödel's first incompleteness theorem, axiom of choice, metamathematics of R and elementary algebra, and metamathematics of N. The book is a valuable reference for mathematicians and researchers interested in mathematical logic and formalized theories.

  • Introduction to Parallel Algorithms and Architectures

    Arrays · Trees · Hypercubes
    • 1st Edition
    • F. Thomson Leighton
    • English
    Introduction to Parallel Algorithms and Architectures: Arrays Trees Hypercubes provides an introduction to the expanding field of parallel algorithms and architectures. This book focuses on parallel computation involving the most popular network architectures, namely, arrays, trees, hypercubes, and some closely related networks. Organized into three chapters, this book begins with an overview of the simplest architectures of arrays and trees. This text then presents the structures and relationships between the dominant network architectures, as well as the most efficient parallel algorithms for a wide variety of problems. Other chapters focus on fundamental results and techniques and on rigorous analysis of algorithmic performance. This book discusses as well a hybrid of network architecture based on arrays and trees called the mesh of trees. The final chapter deals with the most important properties of hypercubes. This book is a valuable resource for readers with a general technical background.

  • Group Theory and Its Applications

    • 1st Edition
    • Ernest M. Loebl
    • English
    Group Theory and Its Applications focuses on the applications of group theory in physics and chemistry. The selection first offers information on the algebras of lie groups and their representations and induced and subduced representations. Discussions focus on the functions of positive type and compact groups; orthogonality relations for square-integrable representations; group, topological, Borel, and quotient structures; and classification of semisimple lie algebras in terms of their root systems. The text then takes a look at the generalization of Euler's angles and projective representation of the Poincare group in a quaternionic Hilbert space. The manuscript ponders on group theory in atomic spectroscopy, group lattices and homomorphism, and group theory in solid state physics. Topics include band theory of solids, lattice vibrations in solids, stationary states in the quantum theory of matter, coupled tensors, and shell structure. The text then examines the group theory of harmonic oscillators and nuclear structure and de Sitter space and positive energy. The selection is a dependable reference for physicists and chemists interested in group theory and its applications.

  • NonEuclidean Geometry

    • 1st Edition
    • Herbert Meschkowski
    • D. Allan Bromley + 2 more
    • English
    Noneuclidean Geometry focuses on the principles, methodologies, approaches, and importance of noneuclidean geometry in the study of mathematics. The book first offers information on proofs and definitions and Hilbert's system of axioms, including axioms of connection, order, congruence, and continuity and the axiom of parallels. The publication also ponders on lemmas, as well as pencil of circles, inversion, and cross ratio. The text examines the elementary theorems of hyperbolic geometry, particularly noting the value of hyperbolic geometry in noneuclidian geometry, use of the Poincaré model, and numerical principles in proving hyperparallels. The publication also tackles the issue of construction in the Poincaré model, verifying the relations of sides and angles of a plane through trigonometry, and the principles involved in elliptic geometry. The publication is a valuable source of data for mathematicians interested in the principles and applications of noneuclidean geometry.

  • A Course of Higher Mathematics

    Integration and Functional Analysis, Volume 5
    • 1st Edition
    • V. I. Smirnov
    • A. J. Lohwater
    • English
    A Course of Higher Mathematics, Volume V focuses on the theory of integration and elements of functional analysis. This book is organized into five chapters. Chapter I discusses the theory of the classical Stieltjes integral and space C of continuous functions, while Chapter II deals with the foundations of the metric theory of functions of a real variable and Lebesgue-Stieltjes integral. The theory of completely additive set functions and case of the one-dimensional Hellinger integral are analyzed in Chapter III. Chapter IV contains an exposition of the foundations of the general theory of metric and normed spaces. The general theory of Hilbert space is covered in Chapter V. This volume is suitable for engineers, physicists, and students of pure mathematics.

  • The Frame Problem in Artificial Intelligence

    Proceedings of the 1987 Workshop
    • 1st Edition
    • Frank M. Brown
    • English
    The Frame Problem in Artificial Intelligence: Proceedings of the 1987 Workshop focuses on the approaches, principles, and concepts related to the frame problem in artificial intelligence (AI). The selection first tackles the definition of the frame problem, circumscription approaches and criticisms, modal logic approaches, and syntactic consistency approaches. The text then takes a look at two frame problems, frame problem in AI, and the frame problem in AI histories, including frame problem defined, mathematical frame problem, commonsense frame problem, and the problems of qualification and extended prediction and their relation to the frame problem. The publication examines tense-logic-based mitigation of the frame problem, unframing the frame problem, a truth maintenance based approach to the frame problem, and qualification problem. Topics include possible worlds, qualification and possible worlds, epistemological issues, truth maintenance, contradiction handling, application of intensional logic, development and implementation of chronolog, and approaches to solving the frame problem. The selection is a dependable source of data for researchers interested in the frame problem.

  • Properties and Operations

    • 1st Edition
    • I. M. Gel'fand + 1 more
    • English
    Generalized Functions, Volume 1: Properties and Operations provides a systematic development of the theory of generalized functions and problems in analysis connected with it. This book focuses on the concept of a convenient link that connects many aspects of analysis, functional analysis, theory of differential equations, representation theory of locally compact Lie groups, and theory of probability and statistics. This volume is essentially devoted to algorithmic questions of the theory, covering many applications of generalized functions to various problems of analysis. The topics discussed include the local properties of generalized functions, differentiation as a continuous operation, and Fourier Transforms of test functions. The wave equation in space of odd dimension, derivation of Green's theorem, and reducible singular points are also described. This publication is a good reference for mathematicians, researchers, and students concerned with generalized functions.

  • Entire Functions

    • 1st Edition
    • A. I. Markushevich
    • English
    Entire Functions focuses on complex numbers and the algebraic operations on them and the basic principles of mathematical analysis. The book first elaborates on the concept of an entire function, including the natural generalization of the concept of a polynomial and power series. The text then takes a look at the maximum absolute value and the order of an entire function, as well as calculations for the coefficients of power series representing a given function, use of integrals, and complex numbers. The publication elaborates on the zeros of an entire function and the fundamental theorem of algebra and Picard’s little theorem. Calculations for the zeros of an entire function and numerical representations of Liouville's theorem and Picard’s little theorem are presented. The book also examines algebraic relationships and addition theorems, including an explanation of Weierstrass' theorem and Picard’s little theorem. The manuscript is a vital reference for students interested in the numerical approaches involved in entire functions.

  • Computer Programming

    A Mixed Language Approach
    • 3rd Edition
    • Marvin L. Stein + 1 more
    • English
    Computer Programming: A Mixed Language Approach describes computer programming from a mixed language perspective. More specifically, it examines how to make effective use of the hardware and software aspects of the total system using the mixed languages that are a composite of the absolute machine languages and the more facile problem-oriented languages. In addition to the absolute machine language required by the computer "hardware" and the problem-oriented language provided by the "software" of symbolic assembly programs and compilers, a third kind of programming language is considered, namely, the symbolic machine language. Comprised of nine chapters, this book illustrates mixed language programming using Fortran and the Fortran Symbolic Assembly Program. The discussion begins by describing a modern digital computer and introducing the general theory of number systems. Subsequent chapters focus on the way in which computing machines are organized to perform their functions; how a computer executes the sequence of instructions and performs a given calculation, a process known as coding; and non-arithmetic instructions used on computers. Subroutines, input-output, and assembly of complete programs are also explored. The final chapter is devoted to Fortran and programs written completely in Fortran, as well as executive programs and programs in mixed languages. This monograph is intended for both professional programmers-to-be and non-professionals in computer programming.

  • Discrete Computational Structures

    • 1st Edition
    • Robert R. Korfhage
    • Werner Rheinboldt
    • English
    Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasizes combinatorics and probability. Examples show different techniques of the general process of enumerating objects. Combinatorics cover permutations, enumerators for combinations, Stirling numbers, cycle classes of permutations, partitions, and compositions. The book cites as example the interplay between discrete mathematics and computing using a system of distinct representatives (SDR) problem. The problem, originating from group theory, graph theory, and set theory can be worked out by the student with a network model involving computers to generate and analyze different scenarios. The book is intended for sophomore or junior level, corresponding to the course B3, "Introduction to Discrete Structures," in the ACM Curriculum 68, as well as for mathematicians or professors of computer engineering and advanced mathematics.

  • Modern Data Analysis

    • 1st Edition
    • Robert L. Launer + 1 more
    • English
    Modern Data Analysis contains the proceedings of a Workshop on Modern Data Analysis held in Raleigh, North Carolina, on June 2-4, 1980 under the auspices of the United States Army Research Office. The papers review theories and methods of data analysis and cover topics ranging from single and multiple quantile-quantile (Q-Q) plotting procedures to biplot display and pencil-and-paper exploratory data analysis methods. Projection pursuit methods for data analysis are also discussed. Comprised of nine chapters, this book begins with an introduction to styles of data analysis techniques, followed by an analysis of single and multiple Q-Q plotting procedures. Problems involving extreme-value data and the behavior of sample averages are considered. Subsequent chapters deal with the use of smelting in guiding re-expression; geometric data analysis; and influence functions and regression diagnostics. The final chapter examines the use and interpretation of robust analysis of variance for the general non-full-rank linear model. The procedures are described in terms of their mathematical structure, which leads to efficient computational algorithms. This monograph should be of interest to mathematicians and statisticians.

  • General Topology and Its Relations to Modern Analysis and Algebra 2

    Proceedings of the Second Prague Topological Symposium, 1966
    • 1st Edition
    • Z. Frolík + 2 more
    • English
    General Topology and Its Relations to Modern Analysis and Algebra II is comprised of papers presented at the Second Symposium on General Topology and its Relations to Modern Analysis and Algebra, held in Prague in September 1966. The book contains expositions and lectures that discuss various subject matters in the field of General Topology. The topics considered include the algebraic structure for a topology; the projection spectrum and its limit space; some special methods of homeomorphism theory in infinite-dimensional topology; types of ultrafilters on countable sets; the compactness operator in general topology; and the algebraic generalization of the topological theorems of Bolzano and Weierstrass. This publication will be found useful by all specialists in the field of Topology and mathematicians interested in General Topology.

  • Topology

    Volume I
    • 1st Edition
    • K. Kuratowski
    • English
    Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete spaces. Great use is made of closure algebra. Comprised of three chapters, this volume begins with a discussion on general topological spaces as well as their specialized aspects, including regular, completely regular, and normal spaces. Fundamental notions such as base, subbase, cover, and continuous mapping, are considered, together with operations such as the exponential topology and quotient topology. The next chapter is devoted to the study of metric spaces, starting with more general spaces, having the limit as its primitive notion. The space is assumed to be metric separable, and this includes problems of cardinality and dimension. Dimension theory and the theory of Borei sets, Baire functions, and related topics are also discussed. The final chapter is about complete spaces and includes problems of general function theory which can be expressed in topological terms. The book includes two appendices, one on applications of topology to mathematical logics and another to functional analysis. This monograph will be helpful to students and practitioners of algebra and mathematics.

  • Mathematical Theory of Probability and Statistics

    • 1st Edition
    • Richard von Mises
    • Hilda Geiringer
    • English
    Mathematical Theory of Probability and Statistics focuses on the contributions and influence of Richard von Mises on the processes, methodologies, and approaches involved in the mathematical theory of probability and statistics. The publication first elaborates on fundamentals, general label space, and basic properties of distributions. Discussions focus on Gaussian distribution, Poisson distribution, mean value variance and other moments, non-countable label space, basic assumptions, operations, and distribution function. The text then ponders on examples of combined operations and summation of chance variables characteristic function. The book takes a look at the asymptotic distribution of the sum of chance variables and probability inference. Topics include inference from a finite number of observations, law of large numbers, asymptotic distributions, limit distribution of the sum of independent discrete random variables, probability of the sum of rare events, and probability density. The text also focuses on the introduction to the theory of statistical functions and multivariate statistics. The publication is a dependable source of information for researchers interested in the mathematical theory of probability and statistics

  • Mathematical Methods

    Linear Algebra / Normed Spaces / Distributions / Integration
    • 1st Edition
    • Jacob Korevaar
    • English
    Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions. The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector spaces, and delta sequences and convergence and approximation. The text then examines the Lebesgue integral, including approximation of integrable functions and applications, integration of sequences and series, functions of bounded variation and the Stieltjes integral, and multiple integrals. Curves and integrals, holomorphic functions and integrals in the complex plane, and multiple integrals are also discussed. The book is a valuable reference for students in the physical sciences, mathematics students interested in applications, and mathematically oriented engineering students.

  • A Survey of Combinatorial Theory

    • 1st Edition
    • Jagdish N. Srivastava
    • English
    A Survey of Combinatorial Theory covers the papers presented at the International Symposium on Combinatorial Mathematics and its Applications, held at Colorado State University (CSU), Fort Collins, Colorado on September 9-11, 1971. The book focuses on the principles, operations, and approaches involved in combinatorial theory, including the Bose-Nelson sorting problem, Golay code, and Galois geometries. The selection first ponders on classical and modern topics in finite geometrical structures; balanced hypergraphs and applications to graph theory; and strongly regular graph derived from the perfect ternary Golay code. Discussions focus on perfect ternary Golay code, finite projective and affine planes, Galois geometries, and other geometric structures. The book then examines the characterization problems of combinatorial graph theory, line-minimal graphs with cyclic group, circle geometry in higher dimensions, and Cayley diagrams and regular complex polygons. The text discusses combinatorial problems in finite Abelian groups, dissection graphs of planar point sets, combinatorial problems and results in fractional replication, Bose-Nelson sorting problem, and some combinatorial aspects of coding theory. The text also reviews the enumerative theory of planar maps, balanced arrays and orthogonal arrays, existence of resolvable block designs, and combinatorial problems in communication networks. The selection is a valuable source of information for mathematicians and researchers interested in the combinatorial theory.

  • Matrix Calculus

    • 3rd Edition
    • E. Bodewig
    • English
    Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well as the decomposition of the matrix into two triangular matrices, choice of another pivotal element, Gauss-Doolittle process, Aitken's triple product, neighbor systems, errors and exactness of the solution, and complex systems. The publication also elaborates on the characteristic equation of the iteration processes, type of convergence of the iteration methods, speeding-up convergence by changing matrix, and methods for electronic computers. The determination of eigenvectors, pure methods, progressive algorithms, and deflation are also discussed. The manuscript is a helpful reference for researchers interested in matrix calculus.

  • Introductory Statistics for Psychology

    The Logic and the Methods
    • 1st Edition
    • Gustav Levine
    • English
    Introductory Statistics for Psychology: The Logic and the Methods presents the concepts of experimental design that are carefully interwoven with the statistical material. This book emphasizes the verbalization of conclusions to experiments, which is another means of communicating the reasons for statistical analyses. Organized into 17 chapters, this book begins with an overview of alternative ways of stating the conclusions from a significant interaction. This text then presents the analysis of variance and introduces the summation sign and its use. Other chapters consider frequency distribution as any presentation of data that offers the frequency with which each score occurs. This book discusses as well the differences in and among people, which are a constant source of variability in test scores, and in most other measurements of people. The final chapter deals with the working knowledge of arithmetic and elementary algebra. This book is a valuable resource for students and psychologists.

  • Calculus and Its Applications

    • 1st Edition
    • P. Mainardi + 1 more
    • English
    Calculus and its Applications provides information pertinent to the applications of calculus. This book presents the trapping technique in defining geometrical and physical entities that are usually regarded as limits of sums. Organized into 20 chapters, this book begins with an overview of the notion of average speed that seems to appear first as a qualitative concept. This text then presents the concepts of external and internal parameters to increase the appreciation of parametric functions. Other chapters consider separable differential equations with more detail than usual with their suitability in describing physical laws. This book discusses as well the study of variable quantities whose magnitude is determined by the magnitudes of several other variables. The final chapter deals with a homogeneous differential equation and auxiliary equations consisting imaginary roots. This book is a valuable resource for mathematicians and students. Readers whose interests span a variety of fields will also find this book useful.

  • Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations

    • 1st Edition
    • V. L. Zaguskin
    • English
    Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations provides information pertinent to algebraic and transcendental equations. This book indicates a well-grounded plan for the solution of an approximate equation. Organized into six chapters, this book begins with an overview of the solution of various equations. This text then outlines a non-traditional theory of the solution of approximate equations. Other chapters consider the approximate methods for the calculation of roots of algebraic equations. This book discusses as well the methods for making roots more accurate, which are essential in the practical application of Berstoi's method. The final chapter deals with the methods for the solution of simultaneous linear equations, which are divided into direct methods and methods of successive approximation. This book is a valuable resource for students, engineers, and research workers of institutes and industrial enterprises who are using mathematical methods in the solution of technical problems.

  • Geometry of Numbers

    • 1st Edition
    • C. G. Lekkerkerker
    • N. G. De Bruijn + 2 more
    • English
    Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VIII: Geometry of Numbers focuses on bodies and lattices in the n-dimensional euclidean space. The text first discusses convex bodies and lattice points and the covering constant and inhomogeneous determinant of a set. Topics include the inhomogeneous determinant of a set, covering constant of a set, theorem of Minkowski-Hlawka, packing of convex bodies, successive minima and determinant of a set, successive minima of a convex body, extremal bodies, and polar reciprocal convex bodies. The publication ponders on star bodies, as well as points of critical lattices on the boundary, reducible, and irreducible star bodies and reduction of automorphic star bodies. The manuscript reviews homogeneous and inhomogeneous s forms and some methods. Discussions focus on asymmetric inequalities, inhomogeneous forms in more variables, indefinite binary quadratic forms, diophantine approximation, sums of powers of linear forms, spheres and quadratic forms, and a method of Blichfeldt and Mordell. The text is a dependable reference for researchers and mathematicians interested in bodies and lattices in the n-dimensional euclidean space.

  • Young Tableaux in Combinatorics, Invariant Theory, and Algebra

    An Anthology of Recent Work
    • 1st Edition
    • Joseph P.S. Kung
    • English
    Young Tableaux in Combinatorics, Invariant Theory, and Algebra: An Anthology of Recent Work is an anthology of papers on Young tableaux and their applications in combinatorics, invariant theory, and algebra. Topics covered include reverse plane partitions and tableau hook numbers; some partitions associated with a partially ordered set; frames and Baxter sequences; and Young diagrams and ideals of Pfaffians. Comprised of 16 chapters, this book begins by describing a probabilistic proof of a formula for the number f? of standard Young tableaux of a given shape f?. The reader is then introduced to the generating function of R. P. Stanley for reverse plane partitions on a tableau shape; an analog of Schensted's algorithm relating permutations and triples consisting of two shifted Young tableaux and a set; and a variational problem for random Young tableaux. Subsequent chapters deal with certain aspects of Schensted's construction and the derivation of the Littlewood-Richardso... rule for the multiplication of Schur functions using purely combinatorial methods; monotonicity and unimodality of the pattern inventory; and skew-symmetric invariant theory. This volume will be helpful to students and practitioners of algebra.

  • Philosophy and Foundations of Mathematics

    L. E. J. Brouwer
    • 1st Edition
    • A. Heyting
    • English
    L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.

  • Theory of Markov Processes

    • 1st Edition
    • E. B. Dynkin
    • T. Köváry
    • English
    Theory of Markov Processes provides information pertinent to the logical foundations of the theory of Markov random processes. This book discusses the properties of the trajectories of Markov processes and their infinitesimal operators. Organized into six chapters, this book begins with an overview of the necessary concepts and theorems from measure theory. This text then provides a general definition of Markov process and investigates the operations that make possible an inspection of the class of Markov processes corresponding to a given transition function. Other chapters consider the more complicated operation of generating a subprocess. This book discusses as well the construction of Markov processes with given transition functions. The final chapter deals with the conditions to be imposed on the transition function so that among the Markov processes corresponding to this function, there should be at least one. This book is a valuable resource for mathematicians, students, and research workers.

  • College Algebra and Trigonometry

    • 2nd Edition
    • Bernard Kolman + 1 more
    • English
    College Algebra and Trigonometry, Second Edition provides a comprehensive approach to the fundamental concepts and techniques of college algebra and trigonometry. The book incorporates improvements from the previous edition to provide a better learning experience. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, trigonometric functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appropriate page references; key ideas for review to stress the concepts; review exercises to provide additional practice; and progress tests to provide self-evaluation and reinforcement. The answers to all Review Exercises and Progress Tests appear in the back of the book. College students will find the book very useful and invaluable.

  • A First Course in Stochastic Processes

    • 1st Edition
    • Samuel Karlin
    • English
    A First Course in Stochastic Processes focuses on several principal areas of stochastic processes and the diversity of applications of stochastic processes, including Markov chains, Brownian motion, and Poisson processes. The publication first takes a look at the elements of stochastic processes, Markov chains, and the basic limit theorem of Markov chains and applications. Discussions focus on criteria for recurrence, absorption probabilities, discrete renewal equation, classification of states of a Markov chain, and review of basic terminologies and properties of random variables and distribution functions. The text then examines algebraic methods in Markov chains and ratio theorems of transition probabilities and applications. The manuscript elaborates on the sums of independent random variables as a Markov chain, classical examples of continuous time Markov chains, and continuous time Markov chains. Topics include differentiability properties of transition probabilities, birth and death processes with absorbing states, general pure birth processes and Poisson processes, and recurrence properties of sums of independent random variables. The book then ponders on Brownian motion, compounding stochastic processes, and deterministic and stochastic genetic and ecological processes. The publication is a valuable source of information for readers interested in stochastic processes.

  • Nonlinear Systems and Applications

    An International Conference
    • 1st Edition
    • V. Lakshmikantham
    • English
    Nonlinear Systems and Applications: An International Conference contains the proceedings of an International Conference on Nonlinear Systems and Applications held at the University of Texas at Arlington, on July 19-23, 1976. The conference provided a forum for reviewing advances in nonlinear systems and their applications and tackled a wide array of topics ranging from abstract evolution equations and nonlinear semigroups to controllability and reachability. Various methods used in solving equations are also discussed, including approximation techniques for delay systems. Most of the applications are in the area of the life sciences. Comprised of 59 chapters, this book begins with a discussion on monotonically convergent upper and lower bounds for classes of conflicting populations, followed by an analysis of constrained problems. The reader is then introduced to approximation techniques for delay systems in biological models; differential inequalities for Liapunov functions; and stability or chaos in discrete epidemic models. Subsequent chapters deal with nonlinear boundary value problems for elliptic systems; bounds for solutions of reaction-diffusion equations; monotonicity and measurability; and periodic solutions of some integral equations from the theory of epidemics. This monograph will be helpful to students, practitioners, and researchers in the field of mathematics.

  • Arithmetic for the Mature Student

    • 1st Edition
    • F. H. George
    • F. H. George
    • English
    Arithmetic for the Mature Student provides information pertinent to the basic operations of arithmetic, including addition, subtraction, multiplication, and division. This book covers a variety of topics, including percentages, fractions, and factors. Organized into five chapters, this book begins with an overview of the instructions on how to use the book. This text then explains arithmetic, which is made up of a set of rules for performing jobs with ordinary numbers. Other chapters consider adding, subtracting, multiplying, and dividing numbers that come between 0 and 1. This book discusses as well an alternative notation for describing fractions. The final chapter deals with that particular type of standard fraction called a percentage. This book is a valuable resource for students in arithmetic.

  • Gait Analysis

    An Introduction
    • 1st Edition
    • Michael W. Whittle
    • English
    Gait Analysis: An Introduction focuses on the systematic study of human walking and its contributions in the medical management of diseases affecting the locomotor system. The book first covers normal gait and pathological gait. Discussions focus on common pathologies affecting gait, amputee gait, walking aids, particular gait abnormalities, gait in the elderly and the young, moments of force, energy consumption, gait cycle, muscular activity during gait, and optimization of energy usage. The manuscript then elaborates on the methods of gait analysis, including visual gait analysis, general gait parameters, timing the gait cycle, direct motion measurement systems, electrogoniometers, electromyography, accelerometers, gyroscopes, and force platforms. The publication tackles the applications of gait analysis, as well as clinical gait and scientific gait analysis, normal ranges for gait parameters, conversions between measurement units, and computer program for general gait parameters. The manuscript is a valuable source of data for students of physical therapy, bioengineering, orthopedics, rheumatology, neurology, and rehabilitation.

  • Data Modelling and Process Modelling using the most popular Methods

    Covering SSADM, Yourdon, Inforem, Bachman, Information Engineering and 'Activity/Object' Diagramming Techniques
    • 1st Edition
    • Rosemary Rock-Evans
    • English
    Computer Weekly Professional Series: Data modeling and Process modeling: Using the Most Popular Methods focuses on the processes, methodologies, and approaches employed in data modeling and process modeling. The book first offers information on data modeling, how to do data modeling, and process modeling. Discussions focus on diagrammatic representation, main concepts of process modeling, merging the models, refining the data model, diagrammatic techniques, fundamental rules of data modeling, and other deliverables of data modeling. The text then examines how to do process modeling and improving a system using analysis deliverables. Topics include problems, causes and effects, events, obligations and objectives, verification methods, and refining the results. The manuscript reviews elementary activities, including structured text and access paths, updating the data model from the access paths and structured English, and other useful detailed deliverables of an elementary activity. The publication is a valuable source of data for researchers interested in data modeling and process modeling.

  • Information Structure Design for Databases

    A Practical Guide to Data Modelling
    • 1st Edition
    • Andrew J. Mortimer
    • English
    Computer Weekly Professional Series: Information Structure Design for Databases: A Practical Guide to Data modeling focuses on practical data modeling covering business and information systems. The publication first offers information on data and information, business analysis, and entity relationship model basics. Discussions cover degree of relationship symbols, relationship rules, membership markers, types of information systems, data driven systems, cost and value of information, importance of data modeling, and quality of information. The book then takes a look at entity relationship modeling connections, one-to-one relationship, and entity relationship modeling advanced topics, including connection traps, resolving many-to-many relationships, four combinations of membership, and entity merging. The text examines logical data dictionary, data flow diagrams, entity life history, and developing database applications. Topics include data modeling during development, waterfall approach, iterative development, sequence, selection, illegal data flow linkages, conservation of data, second normal form rule, and denormalization. The book is a valuable reference for researchers interested in data modeling.

  • Exploring Artificial Intelligence

    Survey Talks from the National Conferences on Artificial Intelligence
    • 1st Edition
    • Howard E. Shrobe
    • English
    Exploring Artificial Intelligence: Survey Talks from the National Conference on Artificial Intelligence provides information pertinent to the distinct subareas of artificial intelligence research. This book discusses developments in machine learning techniques. Organized into six parts encompassing 16 chapters, this book begins with an overview of intelligent tutoring systems, which describes how to guide a student to learn new concepts. This text then links closely with one of the concerns of intelligent tutoring systems, namely how to interact through the utilization of natural language. Other chapters consider the various aspects of natural language understanding and survey the huge body of work that tries to characterize heuristic search programs. This book discusses as well how computer programs can create plans to satisfy goals. The final chapter deals with computational facilities that support. This book is a valuable resource for cognitive scientists, psychologists, domain experts, computer scientists, instructional designers, expert teachers, and research workers.

  • Theoretical Numerical Analysis

    • 1st Edition
    • Burton Wendroff
    • English
    Theoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics. The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation. The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matrix eigenvalue problems, matrix inversion by triangular decomposition, homogeneous boundary value problems, and initial value problems. The publication takes a look at partial differential equations, including heat equation, stability, maximum principle, and first order systems. The manuscript is a vital source of data for mathematicians and researchers interested in theoretical numerical analysis.

  • L. E. J. Brouwer Collected Works

    Geometry, Analysis, Topology and Mechanics
    • 1st Edition
    • Hans Freudenthal
    • English
    L. E. J. Brouwer Collected Works, Volume 2: Geometry, Analysis, Topology, and Mechanics focuses on the contributions and principles of Brouwer on geometry, topology, analysis, and mechanics, including non-Euclidean spaces, integrals, and surfaces. The publication first ponders on non-Euclidean spaces and integral theorems, lie groups, and plane transition theorem. Discussions focus on remarks on multiple integrals, force field of the non-Euclidean spaces with negative curvature, difference quotients and differential quotients, characterization of the Euclidean and non-Euclidean motion groups, and continuous one-one transformations of surfaces in themselves. The book also takes a look at vector fields on surfaces and new methods in topology, including continuous vector distributions on surfaces and orthogonal trajectories of the orbits of a one parameter plane projective group. The book then ponders on mechanics and topology of surfaces, as well as the motion of a particle on the bottom of a rotating vessel under the influence of gravitational force. The publication is a valuable reference for researchers interested in geometry, topology, analysis, and mechanics.

Related subjects