Offers a treatment of measure and integration that begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. This text also treats probabilistic concepts, in chapters on ergodic theory, probabil

Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. This book offers a modern perspectiv

Operator theory is a significant part of many important areas of modern mathematics: functional analysis, differential equations, index theory, representation theory, and mathematical physics. This text covers the central themes of operator theory. It is suitable for graduate students who have had a standard course in functional analysis.

Classical groups, named so by Hermann Weyl, are groups of matrices or quotients of matrix groups by small normal subgroups. Thus the story begins, as Weyl suggested, with the general linear group GLULn(V) of all invertible linear transformations of a vector space V over a field F. All further groups discussed are either subgroups of GLULn(V) or closely related quotient groups. Most of the classical groups consist of invertible linear transformations that respect a bilinear form having some geometric significance, for example, a quadratic form, a symplectic form, and so forth.

This work succinctly covers many topics of numerical methods. While it is basically a survey of the subject, it has enough depth for the student to walk away with the ability to implement the methods by writing computer programs or applying them to problems in physics or engineering.

Since at least the time of Poisson, mathematicians have pondered the notion of recurrence for differential equations. Solutions that exhibit recurrent behavior provide insight into the behavior of general solutions. This text provides a modern understandin

The first of two volumes on the qualitative theory of foliations, this comprehensive work has something to offer to a broad spectrum of readers, from beginners to advanced students and professional researchers. Offering illustrations and examples at varying degrees of difficulty, the text provides a full treatment of the theory of levels for foliated manifolds of codemension one.

A textbook for a one-semester graduate course in measure-theoretic probability theory. It presents an approach to develop the ideas that are absolutely central to modern probability theory. It offers topics that range from undergraduate probability and cla

Presents a comprehensive introduction to research on the applications of graph theory to real-world networks such as web graph. This book discusses both models of the web graph and algorithms for searching the web.

This text concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations.