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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.

  • Sets: Naïve, Axiomatic and Applied

    A Basic Compendium with Exercises for Use in Set Theory for Non Logicians, Working and Teaching Mathematicians and Students
    • 1st Edition
    • D. Van Dalen + 2 more
    • I. N. Sneddon
    • English
    Sets: Naïve, Axiomatic and Applied is a basic compendium on naïve, axiomatic, and applied set theory and covers topics ranging from Boolean operations to union, intersection, and relative complement as well as the reflection principle, measurable cardinals, and models of set theory. Applications of the axiom of choice are also discussed, along with infinite games and the axiom of determinateness. Comprised of three chapters, this volume begins with an overview of naïve set theory and some important sets and notations. The equality of sets, subsets, and ordered pairs are considered, together with equivalence relations and real numbers. The next chapter is devoted to axiomatic set theory and discusses the axiom of regularity, induction and recursion, and ordinal and cardinal numbers. In the final chapter, applications of set theory are reviewed, paying particular attention to filters, Boolean algebra, and inductive definitions together with trees and the Borel hierarchy. This book is intended for non-logicians, students, and working and teaching mathematicians.

  • Some Modern Mathematics for Physicists and Other Outsiders

    An Introduction to Algebra, Topology, and Functional Analysis
    • 1st Edition
    • Paul Roman
    • English
    Some Modern Mathematics for Physicists and Other Outsiders: An Introduction to Algebra, Topology, and Functional Analysis, Volume 1 focuses on the operations, principles, methodologies, and approaches employed in algebra, topology, and functional analysis. The publication first offers information on sets, maps, and algebraic composition laws and systems. Discussions focus on morphisms of algebraic systems, sequences and families, cardinal numbers, ordered sets and maps, equivalence relations and maps, composite functions and inverses, operations with sets, and relations in sets. The text then ponders on special algebraic systems, topological spaces, and topological spaces with special properties. Topics include complete metric spaces, compact spaces, separable and connected spaces, homeomorphism and isometry, convergence, continuity, general structure of topological spaces, rings and fields, linear spaces, linear algebras, and nonassociative algebras. The book elaborates on the theory of integration and measure spaces, including measurable spaces, general properties of the integral, and measureable functions. The publication is a valuable reference for theoretical physicists, research engineers, and scientists who are concerned with structural problems.

  • Statistical Analysis

    A Computer Oriented Approach
    • 1st Edition
    • A. A. Afifi + 1 more
    • English
    Statistical Analysis: A Computer Oriented Approach discusses the probabilistic foundations of statistics, the standard statistical inference procedures, regression, and correlation analysis. The book also explains the analysis of variance and multivariate analysis, with an emphasis on the applications and interpretations of statistical tools. The text defines computer terminologies, coding sheets, format statements, and packaged statistical programs or software. Software and other related programs are tools for data analysis: the "frequency count program" analyzes discrete observations; and the "descriptive program" investigates one continuous variable. Other similar tools are the "descriptive program with strata" that evaluates more than one continuous random variable, and the "crosstabulation program" that reviews contingency tables. The book also explains the general linear model which is applied to the estimators and tests of hypotheses for simple and multiple linear regression models. The text shows how different packaged computer programs can be used to perform analyses of variance. For example, the factorial programs can analyze special designs of randomized blocks, replicated randomized blocks, and nested designs. For other special designs, including the split plot and Latin square designs, the investigator can make adaptations to the standard factorial program. The book is intended for students of statistical inference, computer programming, and readers interested in advanced mathematics.

  • Annual Review in Automatic Programming

    International Tracts in Computer Science and Technology and Their Application
    • 1st Edition
    • Richard Goodman
    • English
    Annual Review in Automatic Programming focuses on the techniques of automatic programming used with digital computers. Topics covered range from the design of machine-independent programming languages to the use of recursive procedures in ALGOL 60. A multi-pass translation scheme for ALGOL 60 is described, along with some commercial source languages. The structure and use of the syntax-directed compiler is also considered. Comprised of 12 chapters, this volume begins with a discussion on the basic ideas involved in the description of a computing process as a program for a computer, expressed in a formal symbolic language such as ALGOL 60. The emphasis is on the information conveyed by the program constituents (semantics), rather than the particular form used (syntax). Subsequent chapters focus on generalized ALGOL; the design of machine-independent programming languages; JOVIAL, a programming language for real-time command systems; and a complete ALGOL translator, expressed in ALGOL itself. A detailed description of the compiler compiler is also presented, together with the Rapidwrite program. The final chapter is devoted to file processing in SEAL (Standard Electronic Accounting Language). This monograph will be of interest to computer programmers.

  • Applied Stochastic Processes

    • 1st Edition
    • G. Adomian
    • English
    Applied Stochastic Processes is a collection of papers dealing with stochastic processes, stochastic equations, and their applications in many fields of science. One paper discusses stochastic systems involving randomness in the system itself that can be a large dynamical multi-input, multi-output system. Examples of a large system are the national economy of a major country or when an acoustic wave is propagating as in the atmosphere, ocean, or sea. Another paper proves that only the average properties of the molecules of biology can be measured with precision in the test tube; and disputes a "simplistic" model of the cell as defined by a miniature Laplaces' universe. The paper notes that the way existing cells are constructed implies that quantum mechanical principles lead to certain questions (about simple experiments) having only statistical answers. Another paper addresses the detection of distributed, fluctuating targets in a reverberation limited, randomly time, and space varying transmission media. This approach is done by using the concepts of "random Green's functions" and the "stochastic Green's function." The collection will prove useful for cellular researchers, mathematicians, physicist, engineers, and academicians in the field of applied mathematics, statistics, and chemistry.

  • Minicomputer Research and Applications

    Proceedings of the First Conference of the HP/1000 International Users Group
    • 1st Edition
    • Helen K. Brown
    • English
    Minicomputer Research and Applications covers the proceedings of the First Conference of the HP/1000 International Users Group, held on August 25-27, 1980 in San Jose, California. The book focuses on the operations, applications, and functions of the HP/1000 computer driver. The selection first underscores an interactive color display station for IC layout and computer aided design in automatic control and logical automata. Discussions focus on automatic control, logical automata, organization of sirena, hardware and software configurations, interactive input support, and display processing. The text then examines a mini-based sculptured surface system and real-time performance analysis system for computers. The publication ponders on variations on a theme (RTE) by Hewlett-Packard, circumventing RTE system memory and disc restrictions, and the Gerber data management system. Topics include user interface, system security, command file, implementation of shared-EMA, and real-time executive modifications. The manuscript also elaborates on ultra low level programming using a high level language and future directions of the HP/1000. The selection is a dependable reference for readers interested in the HP/1000 computer driver.

  • Linear Associative Algebras

    • 1st Edition
    • Alexander Abian
    • English
    Linear Associative Algebras focuses on finite dimensional linear associative algebras and the Wedderburn structure theorems. The publication first elaborates on semigroups and groups, rings and fields, direct sum and tensor product of rings, and polynomial and matrix rings. The text then ponders on vector spaces, including finite dimensional vector spaces and matrix representation of vectors. The book takes a look at linear associative algebras, as well as the idempotent and nilpotent elements of an algebra, ideals of an algebra, total matrix algebras and the canonical forms of matrices, matrix representation of algebras, and division of algebras. The manuscript also tackles the Wedderburn structure theorems, including direct sum and tensor product decomposition of algebras, nilpotent algebras and the radical of an algebra, and structure of simple and semi-simple algebras. The publication is highly recommended for mathematicians and students interested in the Wedderburn structure theorems and finite dimensional linear associative algebras.

  • Vectors and Matrices

    • 1st Edition
    • Pamela Liebeck
    • C. Plumpton
    • English
    Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.

  • Algebraic and Classical Topology

    The Mathematical Works of J. H. C. Whitehead
    • 1st Edition
    • I. M. James
    • English
    Algebraic and Classical Topology contains all the published mathematical work of J. H. C. Whitehead, written between 1952 and 1960. This volume is composed of 21 chapters, which represent two groups of papers. The first group, written between 1952 and 1957, is principally concerned with fiber spaces and the Spanier-Whitehead S-theory. In the second group, written between 1957 and 1960, Whitehead returns to classical topology after a long interval, and participates in the renewed assault on the problems which fascinated him most. This book will prove useful to mathematicians.

  • Arithmetic Applied Mathematics

    • 1st Edition
    • Donald Greenspan
    • V. Lakshmikantham + 1 more
    • English
    Arithmetic Applied Mathematics deals with concepts of arithmetic applied mathematics and uses a computer, rather than a continuum, approach to the deterministic theories of particle mechanics. Models of classical physical phenomena are formulated from both Newtonian and special relativistic mechanics using only arithmetic. Definitions of energy and momentum are presented that are identical to those of continuum mechanics. Comprised of nine chapters, this book begins by exploring discrete modeling as it relates to Newtonian mechanics and special relativistic mechanics, paying particular attention to gravity. The reader is then introduced to long-range forces such as gravitation and short-range forces such as molecular attraction and repulsion; the N-body problem; and conservative and non-conservative models of complex physical phenomena. Subsequent chapters focus on the foundational concepts of special relativity; arithmetic special relativistic mechanics in one space dimension and three space dimensions; and Lorentz invariant computations. This monograph will be of interest to students and practitioners in the fields of mathematics and physics.

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