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

Decomposition of Multivariate Probabilities

1st Edition
June 20, 2014
Roger Cuppens
Z. W. Birnbaum + 1 more
English
eBook
9 7 8 1 4 8 3 2 1 7 6 4 2

Decomposition of Multivariate Probability is a nine-chapter text that focuses on the problem of multivariate characteristic functions. After a brief introduction to some useful results on measures and integrals, this book goes on dealing with the classical theory and the Fourier-Stieltjes transforms of signed measures. The succeeding chapters explore the multivariate extension of the well-known Paley-Wiener theorem on functions that are entire of exponential type and square-integrable; the theory of infinitely divisible probabilities and the classical results of Hin?in; and the decompositions of analytic characteristic functions. Other chapters are devoted to the important problem of the description of a specific class on n-variate probabilities without indecomposable factors. The final chapter studies the problem of ?-decomposition of multivariate characteristic functions. This book will prove useful to mathematicians and advance undergraduate and graduate students.

Algebra and Trigonometry

1st Edition
May 10, 2014
Harley Flanders + 1 more
English
eBook
9 7 8 1 4 8 3 2 7 1 0 4 0

Algebra and Trigonometry presents the essentials of algebra and trigonometry with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered. Comprised of 11 chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of algebraic notation and practical manipulative skills such as factoring, using exponents and radicals, and simplifying rational expressions is highlighted, along with the most common mistakes in algebra. The reader is then introduced to the solution of linear, quadratic, and other types of equations and systems of equations, as well as the solution of inequalities. Subsequent chapters deal with the most basic functions: polynomial, rational, exponential, logarithm, and trigonometric. Trigonometry and the inverse trigonometric functions and identities are also presented. The book concludes with a review of progressions, permutations, combinations, and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

Algebra

1st Edition
May 10, 2014
Harley Flanders + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 5 0 8 7

Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms. Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of algebraic notation and practical manipulative skills such as factoring, using exponents and radicals, and simplifying rational expressions is highlighted, along with the most common mistakes in algebra. The reader is then introduced to the solution of linear, quadratic, and other types of equations and systems of equations, as well as the solution of inequalities. Subsequent chapters deal with the most basic functions of algebra: polynomial, rational, exponential, and logarithm. The book concludes with a review of sequences, permutations and combinations, and the binomial theorem, as well as summation and mathematical induction. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

Stochastic Differential Equations and Applications

1st Edition
June 20, 2014
Avner Friedman
Z. W. Birnbaum + 1 more
English
eBook
9 7 8 1 4 8 3 2 1 7 8 7 1

Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume is divided into nine chapters. Chapters 1 to 5 deal with the basic theory of stochastic differential equations, including discussions of the Markov processes, Brownian motion, and the stochastic integral. Chapter 6 examines the connections between solutions of partial differential equations and stochastic differential equations, while Chapter 7 describes the Girsanov’s formula that is useful in the stochastic control theory. Chapters 8 and 9 evaluate the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity. This book is intended primarily for undergraduate and graduate mathematics students.

Sequential Statistical Procedures

1st Edition
June 20, 2014
Z. Govindarajulu
Z. W. Birnbaum + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 3 3 2 8

Probability and Mathematical Statistics, Volume 26: Sequential Statistical Procedures provides information pertinent to the sequential procedures that are concerned with statistical analysis of data. This book discusses the fundamental aspects of sequential estimation. Organized into four chapters, this volume begins with an overview of the essential feature of sequential procedure. This text then examines the sequential probability ratio test procedure and provides a method of constructing a most powerful test for a simple hypothesis versus simple alternative-testing problem. Other chapters consider the problem of testing a composite hypothesis against a composite alternative. This book discusses as well the theory of sequential tests that is appropriate for distinguishing between two simple or composite hypotheses. The final chapter deals with the theory of sequential estimation. This book is a valuable resource for graduate students, research workers, and users of sequential procedures.

An Introduction to Group Representation Theory

1st Edition
Volume 116
November 5, 1975
S. Keown
English
eBook
9 7 8 0 0 8 0 9 5 6 2 5 1

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.

General Systems Theory: Mathematical Foundations

1st Edition
Volume 113
March 21, 1975
M. D. Mesarovic + 1 more
English
eBook
9 7 8 0 0 8 0 9 5 6 2 2 0

Statistical Inference and Related Topics

1st Edition
May 10, 2014
Madan Lal Puri
English
eBook
9 7 8 1 4 8 3 2 5 7 6 0 0

Statistical Inference and Related Topics, Volume 2 presents the proceedings of the Summer Research Institute on Statistical Inference for Stochastic Processes, held in Bloomingdale, Indiana on July 31 to August 9, 1975. This book focuses on the theory of statistical inference for stochastic processes. Organized into 15 chapters, this volume begins with an overview of the case of continuous distributions with one real parameter. This text then reviews some results for multidimensional empirical processes and Brownian sheets when they are indexed by families of sets. Other chapters consider a class of cubic spline estimators of probability density functions over a finite interval. This book discusses as well the method to construct nonelimination type sequential procedures to select a subset containing all the superior populations. The final chapter deals with Markov sequences, which are among the most interesting available for study with a rich theory and varied applications. This book is a valuable resource for graduate students and research workers.

Studies in Topology

1st Edition
May 10, 2014
Nick M. Stavrakas + 1 more
English
eBook
9 7 8 1 4 8 3 2 5 9 1 1 6

Studies in Topology is a compendium of papers dealing with a broad portion of the topological spectrum, such as in shape theory and in infinite dimensional topology. One paper discusses an approach to proper shape theory modeled on the "ANR-systems" of Mardesic-Segal, on the "mutations" of Fox, or on the "shapings" of Mardesic. Some papers discuss homotopy and cohomology groups in shape theory, the structure of superspace, on o-semimetrizable spaces, as well as connected sets that have one or more disconnection properties. One paper examines "weak" compactness, considered as either a strengthening of absolute closure or a weakening of relative compactness (subject to entire topological spaces or to subspaces of larger spaces). To construct spaces that have only weak properties, the investigator can use the various productivity theorems of Scarborough and Stone, Saks and Stephenson, Frolik, Booth, and Hechler. Another paper analyzes the relationship between "normal Moore space conjecture" and productivity of normality in Moore spaces. The compendium is suitable for mathematicians, physicists, engineers, and other professionals involved in topology, set theory, linear spaces, or cartography.

Theory of Optimal Search

1st Edition
Volume 118
January 20, 1976
LAWRENCE D. STONE
English
eBook
9 7 8 0 0 8 0 9 5 6 2 7 5

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