Books in the Series on Concrete & Applicable Mathematics series

This is a book of problems in probability and their solutions. The work has been written for undergraduate students who have a background in calculus and wish to study probability. Probability theory is a key part of contemporary mathematics. The subject plays a key role in the insurance industry, modelling financial markets, and statistics in general including all those fields of endeavour to which statistics is applied (e.g. health, physical sciences, engineering, economics, social sciences). Every student majoring in mathematics at university ought to take a course on probability or mathematical statistics. Probability is now a standard part of high school mathematics, and teachers ought to be well versed and confident in the subject. Problem solving is important in mathematics. This book combines problem solving and probability.

Presents univariate and multivariate probabilistic inequalities with coverage on basic probabilistic entities like expectation, variance, moment generating function and covariance. This book deals with inequalities in information theory and the Csiszar's f-Divergence between probability measures.

Intends to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals.

Presents the theory of ordinary differential equations, with illustrative examples and interesting exercises. This book is suitable for undergraduate students who major in mathematics and have acquired a prerequisite knowledge of calculus and partly the knowledge of a complex variable, and are now reading advanced calculus and linear algebra.

A monograph that presents univariate and multivariate classical analyses of advanced inequalities. It examines the advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and Hardy-Opial type inequalities.

Provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. This book describes its generators and the link with stochastic differential equations in infinite dimensions.

This monograph presents the author's work of the last five years in approximation theory. The chapters are self-contained and can be read independently. Readers will find the topics covered are diverse and advanced courses can be taught out of this book.The first part of the book is dedicated to fractional monotone approximation theory introduced for the first time by the author, taking the related ordinary theory of usual differentiation at the fractional differentiation level with polynomials and splines as approximators. The second part deals with the approximation by discrete singular operators of the Favard style, for example, of the Picard and Gauss-Weierstrass types. Then, it continues in a very detailed and extensive chapter on approximation by interpolating operators induced by neural networks, a connection to computer science. This book ends with the approximation theory and functional analysis on time scales, a very modern topic, detailing all the pros and cons of this method.The results in this book are expected to find applications in many areas of pure and applied mathematics. So far, very little is written about fractional approximation theory which is at its infancy. As such, it is suitable for researchers, graduate students, and performing seminars as well as an invaluable resource for all science libraries.

An introductory course to the theory of distributions, as well as its applications in the resolution of partial differential equations (PDEs). It begins with a chapter on the fundamental spaces (or test function spaces), and concludes with a chapter on Sobolev spaces, which are known to be very important in the resolution of PDEs.

This volume is on initial boundary value problems for parabolic partial differential equations of second order.

"The material, forming a perfect integral whole, offers information that puts the reader at the forefront of current research and determines fruitful directions for future advanced study. Clarity of the text and rigorous proofs represent other features of this monograph. The monograph is addressed to researchers and graduate students specializing in pure and applied mathematics who are interested in a modern approach to discrete approximation theory."Mathematical Reviews Clippings In this monograph, we present the authors' recent work of the last seven years in Approximation Theory. Chapters are self-contained and can be read independently and advanced courses can be taught out of this book. Here our generalized discrete singular operators are of the following types: Picard, Gauss-Weierstrass and Poisson-Cauchy operators. We treat both the unitary and non-unitary, univariate and multivariate cases of these operators, which are not necessarily positive operators. The book's results are expected to find applications in many areas of pure and applied mathematics, and statistics. As such, it is suitable for researchers, graduate students, and seminars of related subjects, and serves well as an invaluable resource for all science libraries.