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

2661-2670 of 3351 results in All results

Algebraic Methods of Mathematical Logic

1st Edition
January 1, 1967
Ladislav Rieger
English
eBook
9 7 8 - 1 - 4 8 3 2 - 7 0 5 2 - 4

Algebraic Methods of Mathematical Logic focuses on the algebraic methods of mathematical logic, including Boolean algebra, mathematical language, and arithmetization. The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-mathematical parallelism and its natural limits; practical applications of methods of mathematical logic; and principal mathematical tools of mathematical logic. The text then elaborates on the language of mathematics and its symbolization and recursive construction of the relation of consequence. Discussions focus on recursive construction of the relation of consequence, fundamental descriptively-semantic rules, mathematical logic and mathematical language as a material system of signs, and the substance and purpose of symbolization of mathematical language. The publication examines expressive possibilities of symbolization; intuitive and mathematical notions of an idealized axiomatic mathematical theory; and the algebraic theory of elementary predicate logic. Topics include the notion of Boolean algebra based on joins, meets, and complementation, logical frame of a language and mathematical theory, and arithmetization and algebraization. The manuscript is a valuable reference for mathematicians and researchers interested in the algebraic methods of mathematical logic.

Random Matrices and the Statistical Theory of Energy Levels

1st Edition
January 1, 1967
M. L. Mehta
English
eBook
9 7 8 - 1 - 4 8 3 2 - 5 8 5 6 - 0

Random Matrices and the Statistical Theory of Energy Levels focuses on the processes, methodologies, calculations, and approaches involved in random matrices and the statistical theory of energy levels, including ensembles and density and correlation functions. The publication first elaborates on the joint probability density function for the matrix elements and eigenvalues, including the Gaussian unitary, symplectic, and orthogonal ensembles and time-reversal invariance. The text then examines the Gaussian ensembles, as well as the asymptotic formula for the level density and partition function. The manuscript elaborates on the Brownian motion model, circuit ensembles, correlation functions, thermodynamics, and spacing distribution of circular ensembles. Topics include continuum model for the spacing distribution, thermodynamic quantities, joint probability density function for the eigenvalues, stationary and nonstationary ensembles, and ensemble averages. The publication then examines the joint probability density functions for two nearby spacings and invariance hypothesis and matrix element correlations. The text is a valuable source of data for researchers interested in random matrices and the statistical theory of energy levels.

Boundary Value Problems

1st Edition
January 1, 1966
F. D. Gakhov
I. N. Sneddon + 2 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 6 4 9 8 - 4

Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value are explained. The Riemann boundary value problem is emphasized in considering the theory of boundary value problems of analytic functions. The book then analyzes the application of the Riemann boundary value problem as applied to singular integral equations with Cauchy kernel. A second fundamental boundary value problem of analytic functions is the Hilbert problem with a Hilbert kernel; the application of the Hilbert problem is also evaluated. The use of Sokhotski's formulas for certain integral analysis is explained and equations with logarithmic kernels and kernels with a weak power singularity are solved. The chapters in the book all end with some historical briefs, to give a background of the problem(s) discussed. The book will be very valuable to mathematicians, students, and professors in advanced mathematics and geometrical functions.

The Monte Carlo Method

1st Edition
January 1, 1966
Yu.A. Shreider
English
eBook
9 7 8 - 1 - 4 8 3 1 - 5 5 5 7 - 9

The Monte Carlo Method: The Method of Statistical Trials is a systematic account of the fundamental concepts and techniques of the Monte Carlo method, together with its range of applications. Some of these applications include the computation of definite integrals, neutron physics, and in the investigation of servicing processes. This volume is comprised of seven chapters and begins with an overview of the basic features of the Monte Carlo method and typical examples of its application to simple problems in computational mathematics. The next chapter examines the computation of multi-dimensional integrals using the Monte Carlo method. Some examples of statistical modeling of integrals are analyzed, together with the accuracy of the computations. Subsequent chapters focus on the applications of the Monte Carlo method in neutron physics; in the investigation of servicing processes; in communication theory; and in the generation of uniformly distributed random numbers on electronic computers. Methods for organizing statistical experiments on universal digital computers are discussed. This book is designed for a wide circle of readers, ranging from those who are interested in the fundamental applications of the Monte Carlo method, to those who are concerned with comparatively limited problems of the peculiarities of simulating physical processes.

Applied Calculus

1st Edition
January 1, 1966
D. J. Bell
F. H. George
English
eBook
9 7 8 - 1 - 4 8 3 1 - 8 0 8 3 - 0

Applied Calculus, Volume 1 provides information pertinent to the fundamental principles of the calculus to problems that occur in Science and Technology. This book illustrates the use of the calculus to determine the motion of different systems, to find the areas and volumes of certain figures, and to determine the turning points on a curve. Organized into four chapters, this volume begins with an overview of the idea of the slope or gradient of a curve to derive further information from the distance-time graph. This text then examines the notation of the calculus to derive the equations of motion for a particle moving in a straight line with uniform acceleration. Other chapters consider the equation of the tangent of the curve. This book discusses as well the importance of an interval along the curve. The final chapter deals with the maximum and the minimum point on a curve. This book is a valuable resource for students.

Advances in Programming and Non-Numerical Computation

1st Edition
January 1, 1966
L. Fox
English
eBook
9 7 8 - 1 - 4 8 3 1 - 5 9 1 9 - 5

Advances in Programming and Non-Numerical Computation is the third volume of the Proceedings of Summer Schools organized by the Oxford University Computing Laboratory and the Delegacy for Extra-Mural Studies. The 27 lectures summarized in this volume were from 1963 Summer School. The book is organized two parts, keeping the theories of programming separate from the uses of programs. In the first part, an introduction gives a succinct historical account of the development of programming since the invention of the digital computer, and the other four chapters discuss the theory and the developing practice of methods of communicating with the computer, particularly for non-numerical purposes. The second provides a summary of possible non-numerical work, and more detail on three particular applications, in theorem-proving, game-playing, and learning, and information retrieval. It is hoped that this book provides a suitable introduction for a final year student seeking interesting research possibilities not too closely connected with his undergraduate work. It should also give to the intelligent layman, who is prepared to do some non-trivial reading, ideas about just what a machine can do, how it does it, and some of the methods, and the problems, of making further advances.

The Number Systems and Operations of Arithmetic

1st Edition
January 1, 1966
Orval M. Klose
W. J. Langford + 1 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 3 7 0 9 - 4

The Number Systems and Operations of Arithmetic was written for the single purpose of explaining to elementary school teachers (both in-service and in-training) the nature of those basic principles of mathematics which form the foundations and structural framework of arithmetic, and how the familiar formal algorithms of arithmetic stem from these structural principles. The book is organized into two parts. Part I on number systems covers the origin of numerical thinking; natural operations with the natural numbers; natural laws for the natural operations; the inverse operations and convergence and the number systems generated by these operations; and classification of the number systems as abstract systems. Part II on computational algorithms discusses computations with natural numbers, rational numbers, real numbers, and complex numbers. The ""answers"" to all the exercises are also provided in the main body of the text and it is hoped that the student will form the habit of looking there for them.

Lambda-Matrices and Vibrating Systems

1st Edition
January 1, 1966
Peter Lancaster
I. N. Sneddon + 2 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 5 0 9 6 - 3

Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with latent vectors in common. The book then expounds on Lambda matrices and on some numerical methods for Lambda matrices. These methods explain developments of known approximations and rates of convergence. The text then addresses general solutions for simultaneous ordinary differential equations with constant coefficients. The results of some of the studies are then applied to the theory of vibration by applying the Lagrange method for formulating equations of motion, after the formula establishing the energies and dissipation functions are completed. The book describes the theory of resonance testing using the stationary phase method, where the test is carried out by applying certain forces to the structure being studied, and the amplitude of response in the structure is measured. The book also discusses other difficult problems. The text can be used by physicists, engineers, mathematicians, and designers of industrial equipment that incorporates motion in the design.

The Theory of Jets in an Ideal Fluid

1st Edition
Volume 93
January 1, 1966
M. I. Gurevich
J. P. Kahane + 2 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 8 5 8 2 - 8

Pure and Applied Mathematics, Volume 39: The Theory of Jets in an Ideal Fluid provides a general idea of the theory of jets. This book serves as an introduction to the classical problems in the theory and provides some knowledge of the fundamentals of hydromechanics. Organized into 12 chapters, this volume begins with an overview of the theory of plane, steady flow of an ideal, incompressible fluid. This text then examines the jet flow of an unbounded current about a flat plate, placed perpendicular to the flow. Other chapters consider a number of problems involving the plane flow of fluid out of vessels. This book discusses as well the physical importance of Brillouin's condition and also the problem of cavitational flow. The final chapter deals with the flows of weightless fluid in order to know the effect of surface tension forces. This book is a valuable resource for marine and hydraulic engineers.

Model Answers in Pure Mathematics for A-Level Students

1st Edition
January 1, 1966
G.A. Pratt + 1 more
C. W. Schofield
English
eBook
9 7 8 - 1 - 4 8 3 1 - 5 5 5 6 - 2

Model Answers in Pure Mathematics for A-Level Students provides a set of solutions that indicate what is required and expected in an Advanced Level examination in Pure Mathematics. This book serves as a guide to the length of answer required, layout of the solution, and methods of selecting the best approach to any particular type of math problem. This compilation intends to supplement, not replace, the normal textbook and provides a varied selection of questions for practice in addition to the worked solutions. The subjects covered in this text include algebra, trigonometry, coordinate geometry, and calculus. This publication is valuable to students; working through and coping with the practice questions will help them face advanced mathematical examinations with confidence.