E. T. Whittaker, G. N. Watson

This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principal transcendental functions.

Anatole Katok, Boris Hasselblatt

This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with all main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book contains over 400 systematic exercises aimed at students and researchers in mathematics at all levels from advanced undergraduate up. Scientists and engineers working in applied dynamics, nonlinear science, and chaos will also find many fresh insights in this concrete and clear presentation.

Boris Hasselblatt, Anatole Katok

The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. Its concepts, methods and paradigms have greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This elegant introduction to the subject combines mathematical rigor with copious examples of important applications, covering topics ranging from Newtonian mechanics to coding theory. It will be a valuable first textbook for senior undergraduate and beginning graduate students of mathematics, physics, and engineering.

N. L. Carothers

This is a short course on classical Banach space theory. It is a natural follow-up to a first course on functional analysis. The topics covered have proven useful in many contemporary research arenas such as harmonic analysis, the theory of frames and wavelets, signal processing, economics, and physics. The book is intended for use in an advanced topics course or seminar, or for independent study. It offers a gentler introduction than can be found in the existing literature, even including elementary exercises. In addition, the text includes references to expository articles and suggestions for further reading.

Yitzhak Katznelson

First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. This new edition has been revised by the author, to include several new sections and a new appendix.

Ron Blei

This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The book is primarily aimed at students with a basic background in graduate analysis. Also of interest to computer scientists, physicists, statisticians, biologists and economists.

Mark J. Ablowitz, Athanassios S. Fokas

Complex variables provide powerful methods for attacking many difficult problems, and it is the aim of this book to provide a thorough grounding in these methods and their application. Part I of this text provides an introduction to the subject, including residue calculus and transform methods. Part II moves on to conformal mappings, and the study of Riemann-Hilbert problems. An extensive array of examples and exercises are included. This new edition has been improved throughout and is ideal for use in undergraduate and introductory graduate level courses in complex variables.

R. Daniel Mauldin, Mariusz Urbanski

The main focus of this book is the development of the theory of Graph Directed Markov Systems. This far reaching generalisation of the theory of conformal iterated systems can be applied in many situations, including the theory of dynamical systems. This text is very timely and is written by acknowledged experts in the field. The authors have included much of the necessary background material to increase the appeal of this book to graduate students as well as researchers. There is also an extensive list of references suggesting further reading.

George Boros, Victor Moll

The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in 19th century analysis and it has now been revived with the appearance of symbolic languages. In this book, the authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics, including analysis, number theory, algebra and combinatorics. The questions discussed here are as old as calculus itself. This will be a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.

Peter R. Cromwell

Knots and links are studied by mathematicians, and are also finding increasing application in chemistry and biology. Many naturally occurring questions are often simple to state, yet finding the answers may require ideas from the forefront of research. This readable and richly illustrated book explores selected topics in depth in a way that makes contemporary mathematics accessible to an undergraduate audience. Also included are discussion sections that cover historical aspects, motivation, possible extensions, and applications. The many examples and exercises show both the power and limitations of the techniques developed.

Jonathan R. Partington

This book presents an introduction to the common ground between operator theory and linear systems theory. Pure mathematical topics are included such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view.

Jean Bertoin

This is an up-to-date and comprehensive account of the theory of Lévy processes. This branch of modern probability theory has been developed over recent years and has many applications in such areas as queues, mathematical finance and risk estimation. Professor Bertoin uses the interplay between the probabilistic structure and analytic tools to give a quick and concise treatment of the core theory, with the minimum of technical requirements. This will become the standard reference on the subject for all working probability theorists.

Ken-iti Sato

Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book provides the reader with comprehensive basic knowledge of Lévy processes, and at the same time serves as an introduction to stochastic processes in general. The author gives special emphasis to the correspondence between Lévy processes and infinitely divisible distributions, and treats many special subclasses such as stable or semi-stable processes. All serious students of random phenomena will find that this book has much to offer.

E. T. Jaynes, Edited by G. Larry Bretthorst

This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a variety of problems. It contains many exercises and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.

N. L. Carothers

This is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus the course consists of three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. The book is written in an informal style, offering motivation and overview of new ideas with complete proofs. The author includes historical commentary, recommends articles of interest to non-specialists, and provides exercises and suggestions for further study.

R. M. Dudley

This classic graduate textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The new edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.

C. T. C. Wall

Even the simplest singularities of planar curves, e.g. where the curve crosses itself, or where it forms a cusp, are best understood in terms of complex numbers. The full treatment uses techniques from algebra, algebraic geometry, complex analysis and topology and leads to the study of singularities in higher dimensions. This book is designed to introduce graduate students to this attractive area of mathematics. It is based on a MSc course taught by the author and also is an original synthesis, with new views and results not found elsewhere.

Karen M. Brucks, Henk Bruin

One-dimensional dynamics owns many deep results and avenues of active mathematical research. Numerous inroads to this research exist for the advanced undergraduate or beginning graduate student. This book provides glimpses into one-dimensional dynamics with the hope that the results presented illuminate the beauty and excitement of the field. Much of this material is covered nowhere else in textbook format, some aspects are mini new research topics in themselves, and novel connections are drawn with other research areas both inside and outside the text. The material presented here is not meant to be approached in a linear fashion, but anybody with an interest in dynamics, novice or expert alike, will find many topics of interest within.

Henk Tijms

Mastering the concepts of probability can cast new light on situations where randomness and chance appear to rule. In this book, which uses lotteries and casino games to provide lots of examples, the author demystifies much of probability theory, including betting systems, the central limit theorem and the Bayesian approach. Written with wit and clarity, this book is for anyone who is not put off by a few numbers and some high-school algebra. It is also ideally suited to students of all disciplines taking their first course in probability.