Bücher der Reihe Cambridge Studies in Advanced Mathematics

This book is about the basis of mathematical reasoning both in pure mathematics itself (particularly algebra and topology) and in computer science (how and what it means to prove correctness of programmes). It deliberately transcends disciplinary boundaries and challenges many established attitudes to the foundations of mathematics.

Yves Meyer stands the theory of wavelets firmly upon solid ground by basing his book on the fundamental work of Calderon, Zygmund and their collaborators. For anyone who would like an introduction to wavelets, this book will prove to be a necessary purchase.

This work consists of two courses on the moduli spaces of vector bundles. The first is introductory, and assumes very little background; the second is more advanced and takes the reader into current areas of research. This a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

Arising from a summer school course, this book develops the modern theory of rational varieties at a level that will particularly suit graduate students. The authors have written a state-of-the-art treatment with numerous exercises and solutions to help students reach the stage where they can begin to tackle contemporary research.

This book gives a quick introduction to the theory of foliations and Lie groupoids. It is based on the authors' extensive teaching experience and contains numerous examples and exercises making it ideal either for independent study or as the basis of a graduate course.

This book, first published in 2000, emphasizes the substantial role played by classical complex analysis in understanding holomorphic dynamics and gives an up-to-date coverage of the modern theory. The authors cover entire functions, Kleinian groups and polynomial automorphisms of several complex variables, as well as the case of rational functions.

The first rigorous treatment of tolerance graphs in book form. This book will act as a springboard for researchers, especially graduate students, to pursue new directions of investigation. With many examples and exercises it is also suitable for use as the text for a graduate course in graph theory.

The theory of automorphic forms is a cornerstone in modern number theory, an essential ingredient of the proof of Fermat's Last Theorem. This book presents the subject in a style which is accessible to graduate students entering the field, yet includes topics on the research frontier.

The first text devoted to the theory of natural dualities, this book provides an efficient path through a large body of results, examples and applications in this subject which is otherwise available only in scattered research papers. It is aimed at algebraists, category theorists and those who use algebra in their work, particularly those interested in non-classical logics.

This is the second of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras. Much of the material presented here has never appeared before in book form.

The main purpose of this book is to give a systematic treatment of the theory of stochastic differential equations.