Böcker i Cambridge Studies in Advanced Mathematics-serien

The first exposition of group representations and harmonic analysis for graduates for over twenty years.

This two-volume text in harmonic analysis is appropriate for advanced undergraduate students with a strong background in mathematical analysis and for beginning graduate students wishing to specialize in analysis. With numerous exercises and problems it is suitable for independent study as well as for use as a course text.

This book is based on Professor Harper's experience in teaching global methods in combinatorial optimization and is ideal for graduate students as well as experienced researchers. The author has increased the utility of the text for teaching by including worked examples, exercises and material about applications to computer science.

This second edition of a classic work has been considerably expanded and revised, now with complete proofs of all results, including several new theorems not included in the first edition, such as Talagrand's generic chaining approach to boundedness of Gaussian processes and Gine and Zinn's characterization of uniform Donsker classes.

Based on the author's graduate course on association schemes and the optimal design of scientific experiments, this book is accessible to both pure mathematicians and statisticians alike. It will appeal to researchers as an accessible reference work from which to learn about the statistical/combinatorial aspect of their work.

Levy processes are perhaps the most basic class of stochastic processes with a continuous time parameter. This book provides the reader with comprehensive basic knowledge of Levy processes, and at the same time serves as an introduction to stochastic processes in general.

The many different tools from different fields that are used in additive combinatorics are brought together in a self-contained and systematic manner. This graduate-level 2006 text will quickly allow students and researchers easy entry into the fascinating field of additive combinatorics.

The purpose of this book is to study the relation between the representation ring of a finite group and its integral cohomology by means of characteristic classes. In this way it is possible to extend the known calculations and prove some general results for the integral cohomology ring of a group G of prime power order.

This book is intended to be used with graduate courses in Banach space theory.

This book provides probabilists with sufficient background to begin applying PDEs to probability theory and probability theory to PDEs. It covers the theory of linear and second order PDEs of parabolic and elliptic type. While most of the techniques described have antecedents in probability theory, the book does cover a few purely analytic techniques.

This 2003 book discusses the basic properties of period maps and period domains.

This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. Written in an informal style, this is a contemporary introduction to the subject. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras.

This corrected and clarified second edition, first published in 2006, includes a new chapter on the Riemannian geometry of surfaces and provides an introduction to the geometry of curved spaces. Its main theme is the effect of the curvature of spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and on those new notions and ideas motivated by curvature itself.

This is an introduction to p-adic analysis, displaying the variety of applications of the subject. Dr Schikhof shows how p-adic and 'real' analysis differ, providing a large number of exercises. This book will therefore become a standard reference for professionals (especially in p-adic analysis, number theory and algebraic geometry) and welcomed as a textbook for students.

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with basic knowledge of classical analysis, complex variable theory, and algebra.

Two foremost researchers present important advances in stochastic process theory by linking well-understood (Gaussian) and less well-understood (Markov) classes of processes. It builds to this material through 'mini-courses' on the relevant ingredients, which assume only measure-theoretic probability. This original, readable 2006 book is for researchers and advanced graduate students.

This text provides the beginning graduate student, one with basic knowledge of real and functional analysis, with an account of p-summing and related operators. There are detailed expositions of the core results and highly non-trivial applications, for example to harmonic analysis, probability and measure theory and operator theory.

This book studies the geometric theory of polynomials and rational functions in the plane. Any theory in the plane should make full use of the complex numbers and thus the early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology and analysis.

To make the book accessible the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the new reader can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.

This book provides a comprehensive account of the key theory on which the Taylor-Wiles proof of Fermat's last theorem is based, presenting an overview of the theory of automorphic forms on linear algebraic groups. The book will appeal to graduate students and researchers in number theory and arithmetic algebraic geometry.

This textbook on the calculus of variations covers from the basics to the modern aspects of the theory. It is intended to equip the reader to read present research papers in the subject.

This 1989 monograph investigates groups acting on low-dimensional topological spaces, and for the most part the viewpoint is algebraic. A familiarity with group theory is sufficient background for the first third of the book, while the later chapters occasionally state without proof and then apply various facts which require knowledge of homological algebra and algebraic topology.

Develops Galois theory in a much more general context than the undegraduate-style Galois theory of fields. In particular, the relationship with category theory is emphasized. Treats work by leading researchers in the field, and includes a comprehensive bibliography and index. Will be interesting for algebraists and category theorists.

This work provides the reader with a solid foundation in set theory, while the inclusion of topics such as absoluteness, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing, will usher the advanced reader to the doorstep of the research literature.

The techniques used to solve non-linear problems differ greatly from those dealing with linear features. Deriving all the necessary theorems from first principles, this 2005 textbook should give upper undergraduates and graduate students a thorough understanding using as little background material as possible.

The goal of this book is to lead the reader to an understanding of recent results on the Inverse Galois Problem. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory.

This volume is a self-contained introduction to the ideas needed to understand 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.

This 2001 introduction to Fourier analysis and partial differential equations is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations, including the nonlinear Schroedinger and Kortweg-de Vries equations.

Cohomology of Drinfeld Modular Varieties provides an introduction, in two volumes, to both the subject of the title and the Langlands correspondence for function fields. It is based on courses given by the author and will be welcomed by workers in number theory and representation theory.

The authors' aim in this book is to unite the seemingly disparate topics of Clifford algebras, analysis on manifolds and harmonic analysis. They show how algebra, geometry and differential equations all play a more fundamental role in Euclidean Fourier analysis.