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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.

  • Annual Review in Automatic Programming

    International Tracts in Computer Science and Technology and Their Application, Vol. 2
    • 1st Edition
    • Richard Goodman
    • English
    Annual Review in Automatic Programming, Volume 2 is a collection of papers that discusses the controversy about the suitability of COBOL as a common business oriented language, and the development of different common languages for scientific computation. A couple of papers describes the use of the Genie system in numerical calculation and analyzes Mercury autocode in terms of a phrase structure language, such as in the source language, target language, the order structure of ATLAS, and the meta-syntactical language of the assembly program. Other papers explain interference or an "intermediate return" using ALGOL, the National-Elliot 803 Computer, and the MADCAP II. MADCAP II is A version of the automatic programming compiler for MANIAC II. One paper discusses the APT which serves as a common computer language for computational problems. Another paper explains SAKO which can bypass machine language almost entirely in the field of numerical and logical problems, particularly in programs using XYZ and ZAM II. A report of the Working Committee of the British Computer Society Discussion Group No. 5 concludes that COBOL is unnecessarily complex due to its close machine orientation. Computer engineers, computer instructors, programmers, and students of computer science will find the collection highly valuable.

  • Analytical Solution Methods for Boundary Value Problems

    • 1st Edition
    • A.S. Yakimov
    • English
    Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods.

  • Biostatistics and Computer-based Analysis of Health Data using R

    • 1st Edition
    • Christophe Lalanne + 1 more
    • English
    Biostatistics and Computer-Based Analysis of Health Data Using the R Software addresses the concept that many of the actions performed by statistical software comes back to the handling, manipulation, or even transformation of digital data. It is therefore of primary importance to understand how statistical data is displayed and how it can be exploited by software such as R. In this book, the authors explore basic and variable commands, sample comparisons, analysis of variance, epidemiological studies, and censored data. With proposed applications and examples of commands following each chapter, this book allows readers to apply advanced statistical concepts to their own data and software.

  • Fixed Point Theory and Graph Theory

    Foundations and Integrative Approaches
    • 1st Edition
    • Monther Alfuraidan + 1 more
    • English
    Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges. This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains. The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets.

  • Elements of Probability Theory

    • 1st Edition
    • L. Z. Rumshiskii
    • English
    Elements of Probability Theory focuses on the basic ideas and methods of the theory of probability. The book first discusses events and probabilities, including the classical meaning of probability, fundamental properties of probabilities, and the primary rule for the multiplication of probabilities. The text also touches on random variables and probability distributions. Topics include discrete and random variables; functions of random variables; and binomial distributions. The selection also discusses the numerical characteristics of probability distributions; limit theorems and estimates of the mean; and the law of large numbers. The text also describes linear correlation, including conditional expectations and their properties, coefficient of correlation, and best linear approximation to the regression function. The book presents tables that show the values of the normal probability integral, Poisson distribution, and values of the normal probability density. The text is a good source of data for readers and students interested in probability theory.

  • Programming—ALGOL

    • 1st Edition
    • D. J. Malcolme-Lawes
    • English
    Programming—ALGOL is an instructional book on how to write programs using the Algol language. The book starts with an introduction to computers. The Algol language, which runs on instructions typed or punched on strips of paper by the flexowriter, is explained. The text also compares the instructions used in Algol with words in the English language. The command instructions, calculation of numbers, and printing the output are discussed. After a brief introduction into what a program is, the book gives other commands to be added and improve the program. A sample program for repeating calculations is shown with different variables inputted to the program, and then arranging these for the output. The text then introduces the label and the block parts of the program, especially in procedures when several similar sets of commands are required. After the Algol syntax is explained, the different techniques used in programming are considered. In getting a problem into a form and making translation to Algol easier, the flow diagram is introduced. The process of actually running the program by compiling it, using data and program tapes, then begins. The text makes for interesting reading for computer programming instructors, students of introductory programing, and for readers who are interested in the history of computer programming.

  • Computers and Microprocessors

    Made Simple
    • 1st Edition
    • George H. Olsen + 1 more
    • English
    Computers and Microprocessors: Made Simple covers the basic concepts and applications of computers and microprocessors. The book discusses the basic concepts behind the architecture of a small digital computer including logic systems and the major functional blocks of the computer. The text also tackles the applications and operation of analog computers, electronic analog computers, and digital computers and its software (higher-level programming languages and flowcharts). Microprocessors are also discussed with regard to its evolution, architecture, types, and future trends. Students taking computer courses will find the book useful.

  • An Introduction to Mathematical Analysis

    International Series of Monographs on Pure and Applied Mathematics
    • 1st Edition
    • Robert A. Rankin
    • I. N. Sneddon + 2 more
    • English
    An Introduction to Mathematical Analysis is an introductory text to mathematical analysis, with emphasis on functions of a single real variable. Topics covered include limits and continuity, differentiability, integration, and convergence of infinite series, along with double series and infinite products. This book is comprised of seven chapters and begins with an overview of fundamental ideas and assumptions relating to the field operations and the ordering of the real numbers, together with mathematical induction and upper and lower bounds of sets of real numbers. The following chapters deal with limits of real functions; differentiability and maxima, minima, and convexity; elementary properties of infinite series; and functions defined by power series. Integration is also considered, paying particular attention to the indefinite integral; interval functions and functions of bounded variation; the Riemann-Stieltjes integral; the Riemann integral; and area and curves. The final chapter is devoted to convergence and uniformity. This monograph is intended for mathematics students.

  • A Collection of Problems in Analytical Geometry

    Three-Dimensional Analytical Geometry
    • 1st Edition
    • D. V. Kletenik
    • W. J. Langford + 1 more
    • English
    A Collection of Problems in Analytical Geometry, Part II: Three-Dimensional Analytical Geometry is a collection of problems dealing with analytical geometry in the field of theoretical mechanics. The book discusses rectangular Cartesian coordinates in three-dimensional space and the division of an interval in a given ratio. The sample questions concern problems dealing with isosceles triangles, vertices, and center of gravity of equal masses. The book defines the concept of a vector and then lists problems concerning the triangle law and the scalar product of two vectors. Other problems focus on the equations of a surface and a curve and on questions related to the intersection of three surfaces. The text lists other problems such as the equation of a plane, the direction-vector of a straight line, and miscellaneous problems pertaining to the equations of a plane, of a straight line, and of a sphere in a direction-vector. The selection is useful for professors in analytical geometry and for other courses in physic-mathematics and general engineering.

  • A Course of Higher Mathematics

    International Series of Monographs In: Pure and Applied Mathematics, Volume 3, Part 1
    • 1st Edition
    • V. I. Smirnov
    • I. N. Sneddon + 2 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 59: A Course of Higher Mathematics, III/I: Linear Algebra focuses on algebraic methods. The book first ponders on the properties of determinants and solution of systems of equations. The text then gives emphasis to linear transformations and quadratic forms. Topics include coordinate transformations in three-dimensional space; covariant and contravariant affine vectors; unitary and orthogonal transformations; and basic matrix calculus. The selection also focuses on basic theory of groups and linear representations of groups. Representation of a group by linear transformations; linear representations of the unitary group in two variables; linear representations of the rotation group; and Abelian groups and representations of the first degree are discussed. Other considerations include integration over groups, Lorentz transformations, permutations, and classes and normal subgroups. The text is a vital source of information for students, mathematicians, and physicists.

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