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

Abelian Groups

3rd Edition
Volume 12
January 1, 1960
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.

A Guide to Mathematical Tables

1st Edition
January 1, 1960
N. M. Burunova + 2 more
English
eBook
9 7 8 1 4 8 3 1 8 4 4 3 2

A Guide to Mathematical Tables is a supplement to the Guide to Mathematical Tables published by the U.S.S.R. Academy of Sciences in 1956. The tables contain information on subjects such as powers, rational and algebraic functions, and trigonometric functions, as well as logarithms and polynomials and Legendre functions. An index listing all functions included in both the Guide and the Supplement is included. Comprised of 15 chapters, this supplement first describes mathematical tables in the following order: the accuracy of the table (that is, the number of decimal places or significant figures); the limits of variation of the argument and the interval of the table; and the serial number of the book or journal in the reference material. The second part gives the author, title, publishing house, and date and place of publication for books, and the name of the journal, year of publication, series, volume and number, page and author and title of the article cited for journals. Topics range from exponential and hyperbolic functions to factorials, Euler integrals, and related functions. Sums and quantities related to finite differences are also tabulated. This book will be of interest to mathematicians and mathematics students.

An Introduction to Psychoanalytic Theory of Motivation

1st Edition
January 1, 1960
Walter Toman
English
eBook
9 7 8 1 4 8 3 1 8 4 5 5 5

An Introduction to Psychoanalytic Theory of Motivation details the fundamental concepts in applying the psychoanalytic theory in understanding motivation. The title addresses the short-comings of the psychoanalytic theory, particularly the lack of scientific literature. The first part of the text covers the critical concepts in psychoanalytic theory, such as the psychological forces, defense mechanisms, superego, and primal desires. In the second part, the selection details the theory at work; this part discusses the major stages of life from a psychoanalytic perspective. The text also talks about a system of psychopathology, along with the consideration to take in psychotherapy. The book will be of great interest to students, researchers, and practitioners of behavioral science.

Mathematical Tables

1st Edition
January 1, 1960
A. A. Abramov
English
eBook
9 7 8 1 4 8 3 2 1 4 5 6 6

Mathematical Tables of In ? (z) for Complex Argument is a compilation of tables of In ? (z), z = x + iy, calculated for steps in x and y of 0.01 and with an accuracy of one unit in the last (the sixth) decimal place. Interpolation is used to calculate In ? (z) for intermediate values and is carried out separately for the real and imaginary parts of In ? (z). Six places are retained in interpolation. This book first explains how the values of In ? (z) are calculated using the asymptotic formula in a wide lattice with step h = 0.16, and how the tables and the nomograph are used. The values in the lattice are interpolated successively at the centers of various symmetric figures. The calculation of In ? (z) outside the quadrangle is also considered. Formulas for the calculation of In ? (z) outside the given rectangle are listed. The nomograph is intended to facilitate the interpolation procedure. Some of the calculations (including the rounding off of the results to the sixth place and the calculation of second differences) are carried out with the aid of analytical computers. This monograph will be of interest to mathematicians and mathematics students.

Analytical Quadrics

1st Edition
Volume 14
January 1, 1960
Barry Spain
I. N. Sneddon + 2 more
English
eBook
9 7 8 1 4 8 3 1 3 8 2 9 9

Analytical Quadrics focuses on the analytical geometry of three dimensions. The book first discusses the theory of the plane, sphere, cone, cylinder, straight line, and central quadrics in their standard forms. The idea of the plane at infinity is introduced through the homogenous Cartesian coordinates and applied to the nature of the intersection of three planes and to the circular sections of quadrics. The text also focuses on paraboloid, including polar properties, center of a section, axes of plane section, and generators of hyperbolic paraboloid. The book also touches on homogenous coordinates. Concerns include intersection of three planes; circular sections of central quadric; straight line; and circle at infinity. The book also discusses general quadric and classification and reduction of quadric. Discussions also focus on linear systems of quadrics and plane-coordinates. The text is a valuable reference for readers interested in the analytical geometry of three dimensions.

Lincos

1st Edition
Volume 28
January 1, 1960
Lev D. Beklemishev
English
eBook
9 7 8 0 0 8 0 9 5 7 4 8 7

Axiomatics of Classical Statistical Mechanics

1st Edition
Volume 11
January 1, 1960
Rudolf Kurth
I. N. Sneddon + 2 more
English
eBook
9 7 8 1 4 8 3 1 9 4 7 8 3

Axiomatics of Classical Statistical Mechanics provides an understanding of classical statistical mechanics as a deductive system. This book presents the mechanical systems of a finite number of degrees of freedom. Organized into seven chapters, this book begins with an overview of the average behavior of mechanical systems. This text then examines the concept of a mechanical system and explains the equations of motion of the system. Other chapters consider an ensemble of mechanical systems wherein a Hamiltonian function and a truncated canonical probability density corresponds to each system. This book discusses as well the necessary and sufficient conditions that are given for the existence of statistically stationary states and for the approach of mechanical systems towards these states. The final chapter deals with the fundamental laws of thermodynamics. This book is a valuable resource for mathematicians.

Theory of Markov Processes

1st Edition
January 1, 1960
E. B. Dynkin
T. Köváry
English
eBook
9 7 8 1 4 8 3 2 2 6 1 0 1

Theory of Markov Processes provides information pertinent to the logical foundations of the theory of Markov random processes. This book discusses the properties of the trajectories of Markov processes and their infinitesimal operators. Organized into six chapters, this book begins with an overview of the necessary concepts and theorems from measure theory. This text then provides a general definition of Markov process and investigates the operations that make possible an inspection of the class of Markov processes corresponding to a given transition function. Other chapters consider the more complicated operation of generating a subprocess. This book discusses as well the construction of Markov processes with given transition functions. The final chapter deals with the conditions to be imposed on the transition function so that among the Markov processes corresponding to this function, there should be at least one. This book is a valuable resource for mathematicians, students, and research workers.

Homotopy Theory

1st Edition
Volume 8
January 1, 1959
Sze-tsen HU
English
eBook
9 7 8 0 0 8 0 8 7 3 1 6 9

Provability, Computability and Reflection

1st Edition
Volume 24
January 1, 1959
Lev D. Beklemishev
English
eBook
9 7 8 0 0 8 0 9 5 7 4 4 9

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