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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.

  • Generalized Analytic Functions

    • 1st Edition
    • Volume 25
    • I. N. Vekua
    • I. N. Sneddon + 2 more
    • English
    Generalized Analytic Functions is concerned with foundations of the general theory of generalized analytic functions and some applications to problems of differential geometry and theory of shells. Some classes of functions and operators are discussed, along with the reduction of a positive differential quadratic form to the canonical form. Boundary value problems and infinitesimal bendings of surfaces are also considered. Comprised of six chapters, this volume begins with a detailed treatment of various problems of the general theory of generalized analytic functions as as well as boundary value problems. The reader is introduced to some classes of functions and functional spaces, with emphasis on functions of two independent variables. Subsequent chapters focus on the problem of reducing a positive differential quadratic form to the canonical form; basic properties of solutions of elliptic systems of partial differential equations of the first order, in a two-dimensional domain; and some boundary value problems for an elliptic system of equations of the first order and for an elliptic equation of the second order, in a two-dimensional domain. The final part of the book deals with problems of the theory of surfaces and the membrane theory of shells. This book is intended for students of advanced courses of the mechanico-mathematic... faculties, postgraduates, and research workers.

  • Abelian Groups

    • 3rd Edition
    • Volume 12
    • L. Fuchs
    • J. P. Kahane + 2 more
    • English
    Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations. Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups. This book is intended for young research workers and students who intend to familiarize themselves with abelian groups.

  • Mathematical Analysis

    Functions, Limits, Series, Continued Fractions
    • 1st Edition
    • Volume 69
    • L. A. Lyusternik + 1 more
    • English
    Mathematical Analysis: Functions, Limits, Series, Continued Fractions provides an introduction to the differential and integral calculus. This book presents the general problems of the theory of continuous functions of one and several variables, as well as the theory of limiting values for sequences of numbers and vectors. Organized into six chapters, this book begins with an overview of real numbers, the arithmetic linear continuum, limiting values, and functions of one variable. This text then presents the theory of series and practical methods of summation. Other chapters consider the theory of numerical series and series of functions and other analogous processes, particularly infinite continued fractions. This book discusses as well the general problems of the reduction of functions to orthogonal series. The final chapter deals with constants and the most important systems of numbers, including Bernoulli and Euler numbers. This book is a valuable resource for mathematicians, engineers, and research workers.

  • Linear Representations of the Lorentz Group

    • 1st Edition
    • Volume 63
    • M. A. Naimark
    • H. K. Farahat
    • English
    Linear Representations of the Lorentz Group is a systematic exposition of the theory of linear representations of the proper Lorentz group and the complete Lorentz group. This book consists of four chapters. The first two chapters deal with the basic material on the three-dimensional rotation group, on the complete Lorentz group and the proper Lorentz group, as well as the theory of representations of the three-dimensional rotation group. These chapters also provide the necessary basic information from the general theory of group representations. The third chapter is devoted to the representations of the proper Lorentz group and the complete Lorentz group, while the fourth chapter examines the theory of invariant equations. This book will prove useful to mathematicians and students.

  • Some Topics in Complex Analysis

    • 1st Edition
    • Volume 86
    • E. G. Phillips
    • I. N. Sneddon + 2 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 86, Some Topics in Complex Analysis deals with a variety of topics related to complex analysis. This book discusses the method of comparison, periods of an integral, generalized Joukowski transformations, and Koebe's distortion theorems. The deductions from the maximum-modulus principle, canonical products and genus of an I.F., and Weierstrass's primary factors are also reviewed. This text likewise considers Mittag-Leffler's theorem, summation of series by the calculus of residues, definition of regular functions by integrals, and Riemann zeta function. This publication is a good reference for students and specialists researching in the field of applied and pure mathematics.

  • Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein

    • 1st Edition
    • Volume 97
    • L. Redei
    • I. N. Sneddon + 1 more
    • English
    Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein aims to remedy the deficiency in geometry so that the ideas of F. Klein obtain the place they merit in the literature of mathematics. This book discusses the axioms of betweenness, lattice of linear subspaces, generalization of the notion of space, and coplanar Desargues configurations. The central collineations of the plane, fundamental theorem of projective geometry, and lines perpendicular to a proper plane are also elaborated. This text likewise covers the axioms of motion, basic projective configurations, properties of triangles, and theorem of duality in projective space. Other topics include the point-coordinates in an affine space and consistency of the three geometries. This publication is beneficial to mathematicians and students learning geometry.

  • Introduction to Calculus

    • 2nd Edition
    • Volume 17
    • Kazimierz Kuratowski
    • A. J. Lohwater
    • English
    The English edition does not differ essentially from the Polish one. Among the more important supplements I should mention § 6.5 containing elementary information on the notation of mathematical logic. To this supplement I was inclined by the experience of many years. For many students (not for all, perhaps) the notation of definitions of certain notions by means of the logical symbols makes it easier to understand these notions (e.g. the notions of uniform continuity or uniform convergence). Besides that, this supplement is included in the book in such a manner that it can be omitted in reading the whole book. Among other changes introduced in the English text, I should mention the addition of a number of exercises and problems; in the second English edition, many of them have been collected in the Supplement. I am glad also to mention the simplification of certain proofs, and finally the removal of mistakes which were found in the primary text

  • Huygens' Principle and Hyperbolic Equations

    • 1st Edition
    • Volume 5
    • Gunther Paul
    • J. Coates + 1 more
    • English
    Huygens' Principle and Hyperbolic Equations is devoted to certain mathematical aspects of wave propagation in curved space-times. The book aims to present special nontrivial Huygens' operators and to describe their individual properties and to characterize these examples of Huygens' operators within certain more or less comprehensive classes of general hyperbolic operators. The materials covered in the book include a treatment of the wave equation for p-forms over a space of constant sectional curvature, the Riesz distributions, the Euler-Poisson-Darbou... over a Riemannian manifold, and plane wave manifolds. Physicists will find the book invaluable.

  • Recent Topics in Differential and Analytic Geometry

    • 1st Edition
    • Volume 18
    • T. Ochiai
    • English
    Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains. Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters consider the most recognized non-standard examples of compact homogeneous Einstein manifolds constructed via Riemannian submersions. This book discusses as well the natural compactification of the moduli space of polarized Einstein–Kähler orbitfold with a given Hilbert polynomials. The final chapter deals with solving a degenerate Monge–Ampère equation by constructing a family of Einstein–Kähler metrics on the smooth part of minimal varieties of general kind. This book is a valuable resource for graduate students and pure mathematicians.

  • Tables and Formulae for the Spherical Functions Pm – ½ + i t (Z)

    Mathematical Tables Series
    • 1st Edition
    • M. I. Zhurina + 1 more
    • English
    Tables and Formulae for the Spherical Functions Pm – ½ + i t (Z)

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