Books in the Universitext series

This self-contained, comprehensive book tackles the principal problems and advanced questions of probability theory and random processes in 22 chapters, presented in a logical order but also suitable for dipping into.

In two comprehensive volumes, updated and revised in a second edition, this textbook spans elliptic, parabolic, and hyperbolic types, and several variables. This second part emphasizes functional analytic methods and applications to differential geometry.

The first of two volumes that comprehensively treat partial differential equations, this revised second edition focuses on geometric and complex variable methods involving integral representations. Topics such as Brouwer's mapping degree are treated in detail.

Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing.

This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics.

Split into two parts, part I presents a self-contained introduction to the dynamics of linear operators, while part II covers selected, largely independent topics from linear dynamics.

This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way.

This book presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. Includes a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields.

This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective.

Geodesic and Horocyclic Trajectories provides an introduction to the topological dynamics of classical flows. The text highlights gateways between some mathematical fields in an elementary framework, and describes the advantages of using them.

As well as offering the reader a complete theory of Sobolev spaces, this volume explains how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems.

Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. Additionally, some of the simplest variational methods are evolving as classical tools in the field of nonlinear differential equations.

Make the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups.

The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner.

This graduate/advanced undergraduate textbook contains a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups.

Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations.

Simply put, quantum calculus is ordinary calculus without taking limits. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics.

Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields.

In any case, for the development of a consistent and powerful mathematical theory, it seems to be necessary to concentrate solely on the internal problems and structures and to neglect the relations to other ?elds of scienti?c, even of mathematical study for a certain while.

This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.

Ordinary differential equations serve as mathematical models for many exciting real world problems. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections.

Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms.

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject;

The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". One of its main goals is to help the reader to see linear programming "behind the scenes".

This book uses a distinctly applied framework to present the most important topics in stochastic processes, including Gaussian and Markovian processes, Markov Chains, Poisson processes, Brownian motion and queueing theory.

Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not.

To the uninitiated, algebraic topology might seem fiendishly complex, but its utility is beyond doubt. No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained.

Also called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introduction to the Ito calculus. From the reviews:"Introduction to Stochastic Integration is exactly what the title says.

Based on lectures given by Professor Hlawka, this book covers diophantine approximation, uniform distribution of numbers, geometry of numbers and analytic numbers theory.

An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces.