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.

  • Symplectic Geometry

    • 1st Edition
    • Carl Ludwig Siegel
    • English
    Symplectic Geometry focuses on the processes, methodologies, and numerical approaches involved in symplectic geometry. The book first offers information on the symplectic and discontinuous groups, symplectic metric, and hermitian forms. Numerical calculations are presented to show the values and transformations of these groups. The text then examines the fundamental domain of the modular group and the volume of the fundamental domain of the modular group. Equations and matrices are provided to show the fundamental domain and volume of the fundamental domain of the modular group. The publication ponders on commensurable groups and unit groups of quinary quadratic forms. Numerical analyses are also offered to show the values and characteristics of commensurable and unit groups. The text is a helpful reference for researchers interested in symplectic geometry.

  • 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.

  • 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.

  • A Course in Ordinary and Partial Differential Equations

    • 1st Edition
    • Zalman Rubinstein
    • English
    A Course in Ordinary and Partial Differential Equations discusses ordinary differential equations and partial differential equations. The book reviews the solution of elementary first-order differential equations, existence theorems, singular solutions, and linear equations of arbitrary order. It explains the solutions of linear equations with constant coefficients, operational calculus, and the solutions of linear differential equations. It also explores the techniques of computing for the solution of systems of linear differential equations, which is similar to the solutions of linear equations of arbitrary order. The text proves that if the coefficients of some differential equations possess certain restricted types of singularities, the solution will have Taylor series expansions about the singular points. The investigator can calculate a divergent series whose partial sums numerically approximate the solution for large x if the point in question is infinity, of which the series will be a Taylor series of negative powers of x. The book also explains the Fourier transform, its applications to partial differential equations, as well as the Hilbert space approach to partial differential equations. The book is a stimulating material for mathematicians, for professors, or for students of pure and applied mathematics, physics, or engineering.

  • Digital Computer Design

    Logic, Circuitry, and Synthesis
    • 1st Edition
    • Edward L. Braun
    • English
    Digital Computer Design: Logic, Circuitry, and Synthesis focuses on the logical structure, electronic realization, and application of digital information processors. The manuscript first offers information on numerical symbols, fundamentals of computing aids, quantization, representation of numbers in an electronic digital computer, and computer applications. The text then ponders on the nature of automatic computation and Boolean algebra. Discussions focus on the advantages of a Boolean algebraic description of a digital computer; clock pulse generators and timing circuits; sequential switching networks; elements of information processing systems and types of digital computers; and automatic sequencing methods. The book elaborates on circuit descriptions of switching and storage elements and large capacity storage systems. Topics include static magnetic storage, dynamic delay line storage, cathode-ray storage, vacuum tube systems of circuit logic, and magnetic core systems of circuit logic. The publication also examines the system design of GP computers, digital differential analyzer, and the detection and correction of errors. The text is a valuable source of data for mathematicians and engineers interested in digital computer design.

  • Mathematical Methods and Theory in Games, Programming, and Economics

    Volume 2: The Theory of Infinite Games
    • 1st Edition
    • Samuel Karlin
    • Z. W. Birnbaum
    • English
    Mathematical Methods and Theory in Games, Programming, and Economics, Volume II provides information pertinent to the mathematical theory of games of strategy. This book presents the mathematical tools for manipulating and analyzing large sets of strategies. Organized into nine chapters, this volume begins with an overview of the fundamental concepts in game theory, namely, strategy and pay-off. This text then examines the identification of strategies with points in Euclidean n-space, which is a convenience that simplifies the mathematical analysis. Other chapters provide a discussion of the theory of finite convex games. This book discusses as well the extension of the theory of convex continuous games to generalized convex games, which leads to the characterization that such games possess optimal strategies of finite type. The final chapter deals with the components of a simple two-person poker game. This book is a valuable resource for mathematicians, statisticians, economists, social scientists, and research workers.

  • Generalized Functions

    Applications of Harmonic Analysis
    • 1st Edition
    • I. M. Gel'fand + 1 more
    • English
    Generalized Functions, Volume 4: Applications of Harmonic Analysis is devoted to two general topics—developments in the theory of linear topological spaces and construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces. This volume specifically discusses the bilinear functionals on countably normed spaces, Hilbert-Schmidt operators, and spectral analysis of operators in rigged Hilbert spaces. The general form of positive generalized functions on the space S, continuous positive-definite functions, and conditionally positive generalized functions are also deliberated. This publication likewise considers the mean of a generalized random process, multidimensional generalized random fields, simplest properties of cylinder sets, and definition of Gaussian measures. This book is beneficial to students, specialists, and researchers aiming to acquire knowledge of functional analysis.

  • Euclidean and Affine Transformations

    Geometric Transformations
    • 1st Edition
    • P. S. Modenov + 1 more
    • Henry Booker + 2 more
    • English
    Geometric Transformations, Volume 1: Euclidean and Affine Transformations focuses on the study of coordinates, trigonometry, transformations, and linear equations. The publication first takes a look at orthogonal transformations, including orthogonal transformations of the first and second kinds; representations of orthogonal transformations as the products of fundamental orthogonal transformations; and representation of an orthogonal transformation of space as a product of fundamental orthogonal transformations. The text then examines similarity and affine transformations. Topics include properties of affine mappings, Darboux's lemma and its consequences, affine transformations in coordinates, homothetic transformations, similarity transformations of the plane in coordinates, and similarity mapping. The book takes a look at the representation of a similarity transformation as the product of a homothetic transformation and an orthogonal transformation; application of affine transformations to the investigation of properties of the ellipse; and representation of any affine transformation as a product of affine transformations of the simplest types. The manuscript is a valuable reference for high school teachers and readers interested in the Euclidean and affine transformations.

  • Linear Algebra

    • 1st Edition
    • R. R. Stoll + 1 more
    • English
    Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understanding some of the examples and exercises. This book sets itself apart from other similar textbooks through its dedication to the principle that, whenever possible, definitions and theorems should be stated in a form which is independent of the notion of the dimension of a vector space. A second feature of this book which is worthy of mention is the early introduction of inner product spaces and the associated metric concepts. Students soon feel at ease with this class of spaces because they share so many properties with physical space when equipped with a rectangular coordinate system. Finally, the book includes a chapter concerned with several applications to other fields of the theory that have been developed.

  • Projective Transformations

    Geometric Transformations
    • 1st Edition
    • P. S. Modenov + 1 more
    • Henry Booker + 2 more
    • English
    Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserv... transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.

Related subjects