Bøger i London Mathematical Society Student Texts serien

This book concentrates on discrete aspects of functional analysis, including Fourier series, sequence spaces, and matrix maps. It is suitable for advanced undergraduates and above, and is an excellent textbook for capstone courses in mathematical analysis as well as beginning graduate courses in measure theory and functional analysis.

This introductory book on braid groups and related topics keeps prerequisites to a minimum, with appendices providing a detailed guide to the more advanced notions required. A special emphasis is placed on the algorithmic aspects of braids. A range of exercises allow students to test their knowledge, with solutions available.

This book provides a quick yet detailed introduction to set theory and forcing, building the reader's intuition about it as well as rigorousness. Part II discusses contemporary issues in the theory of forcing, including previously unpublished results and open questions.

Noncommutative geometry combines themes from algebra, analysis and geometry and has many applications to physics. This book focuses on cyclic theory, containing background not found in published papers. It is intended for Ph.D. students in analysis and geometry, and researchers using K-theory, cyclic theory, differential geometry and index theory.

This advanced volume of lecture notes presents an open problem at the frontier of research into operator algebra theory, based on the author's university lecture courses and written in a widely accessible style for researchers and Ph.D. students with little experience in the area.

The original edition of this book, written for beginning graduate students, was the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including chapters on Hecke algebras and Green functions.

Recent years have seen rapid progress in the field of approximate groups, with the emergence of a varied range of applications. Written by a leader in the field, this text for both beginning graduate students and researchers collects, for the first time in book form, the main concepts and techniques into a single, self-contained introduction.

The theory of semigroups of operators is a topic with great intellectual beauty and wide-ranging applications. This graduate-level introduction presents the essential elements of the theory, introducing the key notions and establishing the central theorems. A mixture of applications are included and further development directions are indicated.

Graduate students and researchers in modular representation theory, especially block theory, will find this systematic introduction indispensable. The two volumes include detailed treatments of classic material as well as more modern developments which have not appeared in any book before, giving readers a comprehensive overview of the subject.

Homotopical or ( ,1)-categories have become a significant framework in many areas of mathematics. This book gives an introduction to the different approaches to these structures and the comparisons between them from the perspective of homotopy theory.

This detailed account of analysis on Polish spaces contains results that apply to probability theory and a gentle introduction to optimal transportation. Containing more than 200 elementary exercises, it is a useful resource for advanced mathematical students and also for researchers in mathematical analysis.

A two-volume advanced text for graduate students. This first volume covers the theory of Fourier analysis.

A self-contained and concise introduction to recent developments, particularly those of a geometric and topological nature, in the theory of random graphs. Such material is seldom covered in the formative study of young combinatorialists and probabilists, making this essential reading for beginning researchers in these fields.

For students and researchers interested in algebraic combinatorics, this book not only provides an introduction to the geometries arising from vector spaces over finite fields but also shows how these geometries can be applied to various combinatorial objects. More than 100 exercises and solutions are provided.

Geometric discrepancy theory is a rapidly growing modern field. This book provides a complete introduction to the topic with exposition based on classical number theory and Fourier analysis, but assuming no prior knowledge of either. Ideal as a guide to the subject for advanced undergraduate or beginning graduate students.

A description of how non-commutative geometry could provide a means to attack the Riemann Hypothesis, one of the most important unsolved problems in mathematics. The book will be of interest to graduate students in analytic and algebraic number theory, and provides a strong foundation for further research in this area.

The only book entirely devoted to Joseph Liouville's elementary method in number theory, this gentle introduction explains his method in a clear and straightforward manner, including many applications. This is an extremely valuable resource suitable for advanced undergraduate and beginning graduate students, and researchers in number theory.

Three chapters introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each is accessible to beginning graduate students in group theory and will appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.

This straightforward introduction gives a self-contained account of Clifford algebras suitable for research students, final year undergraduates and working mathematicians and physicists. It includes the necessary background material about multilinear algebra, real quadratic spaces and finite-dimensional real algebras and many applications in mathematics and physics.

A coherent account of the computational methods used to solve diophantine equations. Topics include local methods, sieving, descent arguments, the LLL algorithm, Baker's theory of linear forms in logarithms, and problems associated with curves. Useful exercises and bibliography are included. Suitable for graduate students and research workers.

Gives a complete description of representation theorems with direct proofs for both classes of Hardy spaces. Clear and concise, it features over 300 exercises and is ideal for advanced undergraduate and graduate students taking courses in Advanced Complex Analysis, Function Theory or Theory of Hardy Spaces.

This book presents a modern, geometric approach to group theory. An accessible and engaging approach to the subject, with many exercises and figures to develop geometric intuition. Ideal for advanced undergraduates, it will also interest graduate students and researchers as a gentle introduction to geometric group theory.

Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors develop all the necessary basic theory, including the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. Applications to holomorphic dynamics are discussed including new results and accessible open problems.

Kahler geometry is of substantial interest to both mathematicians and physicists and this graduate text provides a self-contained introduction to the subject. Topics discussed include complex manifolds and holomorphic vector bundles; Kahler manifolds and Hodge and Dolbeault theories; compact Kahler manifolds and a proof of the famous Kahler identities.

The aim of this book is to provide an elementary but up-to-date introduction to the representation theory of algebras. Representation-finite and representation-infinite cases are both covered in detail with many concrete examples to illustrate the theory. The treatment is accessible to beginning graduate students and researchers in related areas.

A 2001 account of Algebraic Number Theory, a field which has grown to touch many other areas of pure mathematics. Encompasses everything that graduate students and pure mathematicians interested in the subject are likely to need. Many exercises and an annotated reading list are included.

This book provides a motivated introduction to sieve theory. Rather than focus on technical details which obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. Suitable for a senior level undergraduate course or an introductory graduate course in analytic number theory.