Books in Mathematics and applied mathematics

Nomography

1st Edition
Volume 42
July 21, 2014
Edward Otto
English
eBook
9 7 8 1 4 8 3 2 2 2 7 8 3

Nomography deals with geometrical transformations, particularly projective transformations of a plane. The book reviews projective plane and collineation transformations in geometrical and algebraical terms. The geometrical approach aims at permitting the use of elementary geometrical methods in drawing collineation nomograms consisting of three rectilinear scales. The algebraical treatment concerns nomograms containing curvilinear scales. The text explains functional scales that include the graph of a function and a logarithmic scale. The book explores equations which can be represented by elementary methods without the use of a system of coordinates, some equations that require algebraic calculations, as well as nomograms with a binary field (lattice nomograms). The text investigates collineation monograms of many variables, elementary geometrical methods of joining nomograms, and also of nomograms consisting of two parts to be superimposed on each other. In addition to the Massau method and the criterion of Saint Robert, the book also applies the criteria of nomogrammability of a function to address mathematical problems related to the analysis of the methods in constructing nomograms. The book can be useful for mathematicians, geometricians, engineers, and researchers working in the physical sciences who use graphical calculations in their work.

Introduction to Higher Algebra

1st Edition
Volume 37
July 18, 2014
A. Mostowski + 1 more
I. N. Sneddon + 2 more
English
eBook
9 7 8 1 4 8 3 2 8 0 3 5 6

Introduction to Higher Algebra is an 11-chapter text that covers some mathematical investigations concerning higher algebra. After an introduction to sets of functions, mathematical induction, and arbitrary numbers, this book goes on considering some combinatorial problems, complex numbers, determinants, vector spaces, and linear equations. These topics are followed by discussions of the determination of polynomials in ne variable, rings of real and complex polynomials, and algebraic and transcendental numbers. The final chapters deal with the polynomials in several variables, symmetric functions, the theory of elimination, and the quadratic and Hermitian forms. This book will be of value to mathematicians and students.

Generalized Analytic Functions

1st Edition
Volume 25
July 17, 2014
I. N. Vekua
I. N. Sneddon + 2 more
English
eBook
9 7 8 1 4 8 3 1 8 4 6 7 8

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.

Mathematical Techniques of Operational Research

1st Edition
Volume 38
July 17, 2014
L. S. Goddard
I. N. Sneddon + 2 more
English
eBook
9 7 8 1 4 8 3 1 8 0 6 0 1

Mathematical Techniques of Operational Research is a seven-chapter text that covers the principles and applications of various mathematical tools and models to for operational research. Chapter I provides the basic mathematical ideas used in later chapters. Chapters II and III deal with linear programming, including the special cases of transportation and assignment, as well as their applications such as the Trim Problem. Chapters IV and V discuss the theory of queues and describe the general stationary properties of the single-channel queue, and of simple queues in series and in parallel. These chapters also examine some transient properties of queues. Chapter VI focuses on machine interference, which is an aspect of queueing theory, while Chapter VII deals with the important and mathematically subject of Stock Control or Inventory Theory. This book is intended primarily to graduate mathematicians, business manages, and industrial leaders.

Abelian Groups

3rd Edition
Volume 12
July 15, 2014
L. Fuchs
J. P. Kahane + 2 more
English
eBook
9 7 8 1 4 8 3 2 8 0 9 0 5

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.

Linear Representations of the Lorentz Group

1st Edition
Volume 63
July 15, 2014
M. A. Naimark
H. K. Farahat
English
eBook
9 7 8 1 4 8 3 1 8 4 9 8 2

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.

Mathematical Analysis

1st Edition
Volume 69
July 15, 2014
L. A. Lyusternik + 1 more
English
eBook
9 7 8 1 4 8 3 1 9 4 3 6 3

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.

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

1st Edition
Volume 97
July 15, 2014
L. Redei
I. N. Sneddon + 1 more
English
eBook
9 7 8 1 4 8 3 2 8 2 7 0 1

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.

Some Topics in Complex Analysis

1st Edition
Volume 86
July 15, 2014
E. G. Phillips
I. N. Sneddon + 2 more
English
eBook
9 7 8 1 4 8 3 2 8 2 7 2 5

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.

The Theory of Lebesgue Measure and Integration

1st Edition
Volume 15
July 14, 2014
S. Hartman + 1 more
I. N. Sneddon + 2 more
English
eBook
9 7 8 1 4 8 3 2 8 0 3 3 2

The Theory of Lebesgue Measure and Integration deals with the theory of Lebesgue measure and integration and introduces the reader to the theory of real functions. The subject matter comprises concepts and theorems that are now considered classical, including the Yegorov, Vitali, and Fubini theorems. The Lebesgue measure of linear sets is discussed, along with measurable functions and the definite Lebesgue integral. Comprised of 13 chapters, this volume begins with an overview of basic concepts such as set theory, the denumerability and non-denumerability of sets, and open sets and closed sets on the real line. The discussion then turns to the theory of Lebesgue measure of linear sets based on the method of M. Riesz, together with the fundamental properties of measurable functions. The Lebesgue integral is considered for both bounded functions — upper and lower integrals — and unbounded functions. Later chapters cover such topics as the Yegorov, Vitali, and Fubini theorems; convergence in measure and equi-integrability; integration and differentiation; and absolutely continuous functions. Multiple integrals and the Stieltjes integral are also examined. This book will be of interest to mathematicians and students taking pure and applied mathematics.

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Abstract harmonic analysis

Algebra and number theory

Algebraic geometry

Algebraic topology

Analysis

Applied mathematics

Approximations and expansions

Associative rings and algebras

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Calculus of variations and optimal control optimization

Category theory homological algebra

Commutative rings and algebras

Computer science

Convex sets and related geometric topics

Differential geometry

Discrete mathematics combinatorics

Field theory and polynomials

Finite differences and functional equations

Fourier analysis

Functional analysis

Functions of a complex variable

General mathematical systems

General topology

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Global analysis analysis of manifolds

Group theory and generalizations

Integral equations

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Manifolds and cell complexes

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Operator theory

Order lattices ordered algebraic structures

Ordinary differential equations

Partial differential equations

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