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.

Books Journals

2731-2740 of 3351 results in All results

The Theory of Finitely Generated Commutative Semigroups

1st Edition
January 1, 1965
L. Rédei
I. N. Sneddon + 2 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 5 5 9 4 - 4

The Theory of Finitely Generated Commutative Semigroups describes a theory of finitely generated commutative semigroups which is founded essentially on a single "fundamental theorem" and exhibits resemblance in many respects to the algebraic theory of numbers. The theory primarily involves the investigation of the F-congruences (F is the the free semimodule of the rank n, where n is a given natural number). As applications, several important special cases are given. This volume is comprised of five chapters and begins with preliminaries on finitely generated commutative semigroups before turning to a discussion of the problem of determining all the F-congruences as the fundamental problem of the proposed theory. The next chapter lays down the foundations of the theory by defining the kernel functions and the fundamental theorem. The elementary properties of the kernel functions are then considered, along with the ideal theory of free semimodules of finite rank. The final chapter deals with the isomorphism problem of the theory, which is solved by reducing it to the determination of the equivalent kernel functions. This book should be of interest to mathematicians as well as students of pure and applied mathematics.

Mathematical Problems and Puzzles

1st Edition
January 1, 1965
S. Straszewicz
I. N. Sneddon + 1 more
English
eBook
9 7 8 - 1 - 4 8 3 2 - 8 0 3 1 - 8

Popular Lectures in Mathematics, Volume 12: Mathematical Problems and Puzzles: From the Polish Mathematical Olympiads contains sample problems from various fields of mathematics, including arithmetic, algebra, geometry, and trigonometry. The contest for secondary school pupils known as the Mathematical Olympiad has been held in Poland every year since 1949/50. This book is composed of two main parts. Part I considers the problems and solutions about integers, polynomials, algebraic fractions and irrational experience. Part II focuses on the problems of geometry and trigonometric transformation, along with their solutions. The provided solutions aim to extend the student’s knowledge of mathematics and train them in mathematical thinking. This book will prove useful to secondary school mathematics teachers and students.

Numerical Analysis

1st Edition
January 1, 1965
I. M. Khabaza
F. M. Arscott
English
eBook
9 7 8 - 1 - 4 8 3 1 - 3 9 5 6 - 2

Numerical Analysis is an elementary introduction to numerical analysis, its applications, limitations, and pitfalls. Methods suitable for digital computers are emphasized, but some desk computations are also described. Topics covered range from the use of digital computers in numerical work to errors in computations using desk machines, finite difference methods, and numerical solution of ordinary differential equations. This book is comprised of eight chapters and begins with an overview of the importance of digital computers in numerical analysis, followed by a discussion on errors in computations using desk machines. Subsequent chapters deal with recurrence relations and algebraic equations; basic properties of matrices; relaxation and finite difference methods; and numerical methods for unequal intervals. The derivation of Lagrange's interpolation polynomial is explained, together with curve fitting and the method of least squares, orthogonal polynomials, and integration methods. This monograph will be of interest to practicing engineers, mathematicians, and scientists as well as students.

Mathematical Analysis

1st Edition
January 1, 1965
G. Ye. Shilov
D. A. R. Wallace
English
eBook
9 7 8 - 1 - 4 8 3 1 - 8 5 3 7 - 8

Mathematical Analysis: A Special Course covers the fundamentals, principles, and theories that make up mathematical analysis. The title first provides an account of set theory, and then proceeds to detailing the elements of the theory of metric and normed linear spaces. Next, the selection covers the calculus of variations, along with the theory of Lebesgue integral. The text also tackles the geometry of Hilbert space and the relation between integration and differentiation. The last chapter of the title talks about the Fourier transform. The book will be of great use to individuals who want to expand and enhance their understanding of mathematical analysis.

Multidimensional Singular Integrals and Integral Equations

1st Edition
January 1, 1965
S. G. Mikhlin
I. N. Sneddon + 2 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 6 4 4 9 - 6

Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.

Mathematical Analysis

1st Edition
January 1, 1965
I.G. Aramanovich + 2 more
I. N. Sneddon
English
eBook
9 7 8 - 1 - 4 8 3 1 - 5 6 2 4 - 8

Mathematical Analysis: Differentiation and Integration is devoted to two basic operations of mathematical analysis, differentiation and integration. The problems directly connected with the operations of differentiation and integration of functions of one or several variables are discussed, together with elementary generalizations of these operations. This volume is comprised of seven chapters and begins by considering the differentiation of functions of one variable and of n variables, paying particular attention to derivatives and differentials as well as their properties. The next chapter deals with composite and implicit functions of n variables in connection with differentiation, along with the representation of functions in the form of superpositions. Subsequent chapters offer detailed accounts of systems of functions and curvilinear coordinates in a plane and in space; the integration of functions; and improper integrals. The final chapter examines the transformation of differential and integral expressions. This book will be a useful resource for mathematicians and mathematics students.

The Method of Summary Representation for Numerical Solution of Problems of Mathematical Physics

1st Edition
Volume 79
January 1, 1965
G. N. Polozhii
I. N. Sneddon + 2 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 8 5 4 6 - 0

Pure and Applied Mathematics, Volume 79: The Method of Summary Representation for Numerical Solution of Problems of Mathematical Physics presents the numerical solution of two-dimensional and three-dimensional boundary-value problems of mathematical physics. This book focuses on the second-order and fourth-order linear differential equations. Organized into two chapters, this volume begins with an overview of ordinary finite-difference equations and the general solutions of certain specific finite-difference equations. This text then examines the various methods of successive approximation that are used exclusively for solving finite-difference equations. This book discusses as well the established formula of summary representation for certain finite-difference operators that are associated with partial differential equations of mathematical physics. The final chapter deals with the formula of summary representation to enable the researcher to write the solution of the corresponding systems of linear algebraic equations in a simple form. This book is a valuable resource for mathematicians and physicists.

Solution of Cubic and Quartic Equations

1st Edition
January 1, 1965
S. Neumark
English
eBook
9 7 8 - 1 - 4 8 3 1 - 8 5 5 7 - 6

Solution of Cubic and Quartic Equations presents the classical methods in solving cubic and quartic equations to the highest possible degree of efficiency. This book suggests a rapid and efficient method of computing the roots of an arbitrary cubic equation with real coefficients, by using specially computed 5-figure tables. The method of factorizing an arbitrary quartic equation by an appropriate use of a resolvent cubic is also discussed. Section 4 of this text gives several numerical examples that show the rapidity of the procedures suggested. This publication is valuable to mathematicians and students intending to acquire knowledge of the cubic and quartic equations.

An Introduction to Digital Computing

1st Edition
January 1, 1965
F. H. George
English
eBook
9 7 8 - 1 - 4 8 3 1 - 8 0 8 2 - 3

An Introduction to Digital Computing provides information pertinent to the fundamental aspects of digital computing. This book represents a major step towards the universal availability of programmed material. Organized into four chapters, this book begins with an overview of the fundamental workings of the computer, including the way it handles simple arithmetic problems. This text then provides a brief survey of the basic features of a typical computer that is divided into three sections, namely, the input and output system, the memory system for data storage, and a processing system. Other chapters focus on programming and on the workings of the computer control unit. This book discusses as well the various arithmetic codes such as binary, decimal, octal, duodecimal, and hexadecimal codes. The final chapter deals with some of the more detailed workings of the control unit. This book is a valuable resource for university students and computer specialists.

Computer Arithmetic

1st Edition
January 1, 1965
F. H. George
F. H. George
English
eBook
9 7 8 - 1 - 4 8 3 1 - 8 0 9 1 - 5

Computer Arithmetic provides information pertinent to the fundamental aspects of a digital computer. This book discusses how the control unit uses the arithmetic unit to produce, under commands, the answers asked by the user. Organized into four chapters, this book begins with an overview of the binary code and provides a preview of the use of other arithmetic codes outside the computer. This text then explains in detail the codes employed in the representation of numbers inside the computer. Other chapters consider the number systems as well as other related matters to be able to understand computer arithmetic. This book discusses as well the signed numbers and their conversations, as well as the problems of scaling. The final chapter deals with the methods of fixed- and floating-point arithmetic, rounding off, and overflow. This book is a valuable resource for sixth form as well as university students who are interested in arithmetic codes.