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This series has established itself as a valuable source of information for professional mathematicians and research workers in all areas of mathematics. Most of the volumes are short monographs giving an authoritative account of the present state of knowledge of a topic of current interest. The treatment may be informal but importance is attached to clear yet rigorous exposition. The series also accepts conference proceedings and similar collective works that meet its general objectives.

  • Managing Editors: Endre Süli, University of Oxford
  • Associate Editors: Tim Austin, University of Warwick, Roger Heath-Brown, University of Oxford, Colva Roney-Dougal, University of St Andrews, Ulrike Tillmann, University of Oxford, Kasia A. Rejzner, University of York

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466 results in London Mathematical Society Lecture Note Series

Page 18 of 24

Representations of Rings over Skew Fields
  • A. H. Schofield
  • Published online:
    19 March 2010
    Print publication:
    18 April 1985
  • The first half of the book is a general study of homomorphisms to simple artinian rings; the techniques developed here should be of interest to many algebraists. The second half is a more detailed study of special types of skew fields which have arisen from the work of P. M. Cohn and the author. A number of questions are settled; a version of the Jacobian conjecture for free algebras is proved and there are examples of skew field extensions of different but finite left and right dimension.

The James Forest
  • Helga Fetter, Berta Gamboa de Buen
  • Preface by R. C. James
  • Published online:
    19 March 2010
    Print publication:
    05 June 1997
  • The James space J and the James tree space JT were constructed as counterexamples to several outstanding conjectures in Banach space theory. This book is a compendium of most of the known results about these spaces, frequently taken from the original sources, but presented in a unified and up to date fashion. Generalisations of J and JT are also discussed and other pathological Banach spaces are introduced. Specialists will welcome this book for its drawing together of classical material and recent results. Graduate students should also find that this book offers an excellent introduction to more advanced topics in Banach space theory.

Number Theory
  • Séminaire de théorie des nombres de Paris 1993–94
  • Edited by Sinnou David
  • Published online:
    19 March 2010
    Print publication:
    07 November 1996
  • The contributions in this book are based on the lectures delivered at the Seminaire de theorie des nombres de Paris during the academic year 93–94. It is the fifteenth annualvolume. This book covers the whole spectrum of number theory, and is composed of contributions from some of the best specialists worldwide. Together they constitute the latest developments in number theory that will be an invaluable resource for all workers in that area.

An Introduction to Independence for Analysts
  • H. G. Dales, W. H. Woodin
  • Published online:
    18 March 2010
    Print publication:
    10 December 1987
  • Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a naturally arising and deep question of analysis is independent of ZFC. It provides an accessible account of this result, and it includes a discussion, of Martin's Axiom and of the independence of CH.

Markov Processes and Related Problems of Analysis
  • E. B. Dynkin
  • Published online:
    18 March 2010
    Print publication:
    23 September 1982
  • The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics. Professor Dynkin has made many profound contributions to the subject and in this volume are collected several of his most important expository and survey articles. The content of these articles has not been covered in any monograph as yet. This account is accessible to graduate students in mathematics and operations research and will be welcomed by all those interested in stochastic processes and their applications.

Number Theory and Dynamical Systems
  • Edited by M. M. Dodson, J. A. G. Vickers
  • Published online:
    18 March 2010
    Print publication:
    09 November 1989
  • This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged last century from the study of the stability of the solar system where problems of small divisors associated with the near resonance of planetary frequencies arose. Previously the question of the stability of the solar system was answered in more general terms by the celebrated KAM theorem, in which the relationship between near resonance (and so Diophantine approximation) and stability is of central importance. Other examples of the connections involve the work of Szemeredi and Furstenberg, and Sprindzuk. As well as containing results on the relationship between number theory and dynamical systems, the book also includes some more speculative and exploratory work which should stimulate interest in different approaches to old problems.

Uniform Algebras and Jensen Measures
  • T. W. Gamelin
  • Published online:
    18 March 2010
    Print publication:
    01 March 1979
  • These lecture notes are devoted to an area of current research interest that bridges functional analysis and function theory. The unifying theme is the notion of subharmonicity with respect to a uniform algebra. The topics covered include the rudiments of Choquet theory, various classes of representing measures, the duality between abstract sub-harmonic functions and Jensen measures, applications to problems of approximation of plurisubharmonic functions of several complex variables, and Cole's theory of estimates for conjugate functions. Many of the results are published here for the first time in monograph form.

Elliptic Structures on 3-Manifolds
  • Charles Benedict Thomas
  • Published online:
    17 March 2010
    Print publication:
    21 August 1986
  • This volume will give a systematic exposition of known results for free actions by finite groups on S. The text begins with preliminary material on Seifert manifolds and group classification. This is followed by sections dealing with related topics including free bZe/2 and bZe/3 actions on lens/prism manifolds, the reduction theorem and tangential structure.

Spectral Asymptotics in the Semi-Classical Limit
  • M. Dimassi, J. Sjostrand
  • Published online:
    17 March 2010
    Print publication:
    16 September 1999
  • Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course.

Classification Theory of Polarized Varieties
  • Takao Fujita
  • Published online:
    17 March 2010
    Print publication:
    23 August 1990
  • A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas. Readers are assumed to have some background in algebraic geometry, including sheaf cohomology, and for them this work will provide an illustration of the power of modern abstract techniques applied to concrete geometric problems. Thus the book helps the reader not only to understand about classical objects but also modern methods, and so it will be useful not only for experts but also non-specialists and graduate students.

Localization in Noetherian Rings
  • A. V. Jategaonkar
  • Published online:
    17 March 2010
    Print publication:
    13 March 1986
  • This monograph first published in 1986 is a reasonably self-contained account of a large part of the theory of non-commutative Noetherian rings. The author focuses on two important aspects: localization and the structure of infective modules. The former is presented in the opening chapters after which some new module-theoretic concepts and methods are used to formulate a new view of localization. This view, which is one of the book's highlights, shows that the study of localization is inextricably linked to the study of certain injectives and leads, for the first time, to some genuine applications of localization in the study of Noetherian rings. In the last part Professor Jategaonkar introduces a unified setting for four intensively studied classes of Noetherian rings: HNP rings, PI rings, enveloping algebras of solvable Lie algebras, and group rings of polycyclic groups. Some appendices summarize relevant background information about these four classes.

Surveys in Combinatorics
  • Edited by B. Bollobás
  • Published online:
    17 March 2010
    Print publication:
    09 August 1979
  • Combinatorics is an active field of mathematical study and the British Combinatorial Conference, held biennially, aims to survey the most important developments by inviting distinguished mathematicians to lecture at the meeting. The contributions of the principal lecturers at the Seventh Conference, held in Cambridge, are published here and the topics reflect the breadth of the subject. Each author has written a broadly conceived survey, not limited to his own work, but intended for wide readership. Important aspects of the subject are emphasized so that non-specialists will find them understandable. Topics covered include graph theory, matroids, combinatorial set theory, projective geometry and combinatorial group theory. All those researching into any aspect of Combinatorics and its applications will find much in these articles of use and interest.

Van der Corput's Method of Exponential Sums
  • S. W. Graham, Grigori Kolesnik
  • Published online:
    17 March 2010
    Print publication:
    25 January 1991
  • This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums. These arise in many problems in analytic number theory. It is the first cohesive account of much of this material and will be welcomed by graduates and professionals in analytic number theory. The authors show how the method can be applied to problems such as upper bounds for the Riemann-Zeta function. the Dirichlet divisor problem, the distribution of square free numbers, and the Piatetski-Shapiro prime number theorem.

Isolated Singular Points on Complete Intersections
  • E. J. N. Looijenga
  • Published online:
    17 March 2010
    Print publication:
    01 March 1984
  • Singularity theory is not a field in itself, but rather an application of algebraic geometry, analytic geometry and differential analysis. The adjective 'singular' in the title refers here to singular points of complex-analytic or algebraic varieties or mappings. A tractable (and very natural) class of singularities to study are the isolated complete intersection singularities, and much progress has been made over the past decade in understanding these and their deformations.

Surveys in Contemporary Mathematics
  • Edited by Nicholas Young, Yemon Choi
  • Published online:
    16 March 2010
    Print publication:
    15 November 2007
  • Young scientists in Russia are continuing the outstanding tradition of Russian mathematics in their home country, in spite of the post-Soviet diaspora. This collection, the second of two, showcases the recent achievements of young Russian mathematicians and the strong research groups they are associated with. The first collection focused on geometry and number theory; this one concentrates on combinatorial and algebraic geometry and topology. The articles are mainly surveys of the recent work of the research groups and contain a substantial number of new results. Topics covered include algebraic geometry over Lie groups, cohomological aspects of toric topology, the Borsuk partition problem, and embedding and knotting of manifolds in Euclidean spaces. The authors are A. E. Guterman, I. V. Kazachkov, A. V. Malyutin, D. V. Osipov, T. E. Panov, A. M. Raigorodskii, A. B. Skopenkov and V. V. Ten.

Interaction Models
  • Norman L. Biggs
  • Published online:
    16 March 2010
    Print publication:
    24 November 1977
  • This book is based on a set of lectures given to a mixed audience of physicists and mathematicians. The desire to be intelligible to both groups is the underlying preoccupation of the author. Physicists nowadays are particularly interested in phase transitions. The typical situation is that a system of interacting particles exhibits an abrupt change of behaviour at a certain temperature, although the local forces between the particles are thought to be smooth functions of temperature. This account discusses the theory behind a simple model of such phenomena. An important tool is the mathematical discipline known as the Theory of Graphs. There are five chapters, each subdivided into sections. The first chapter is intended as a broad introduction to the subject, and it is written in a more informal manner than the rest. Notes and references for each chapter are given at the end of the chapter.

Combinatorics
  • H. N. V. Temperley
  • Published online:
    16 March 2010
    Print publication:
    03 September 1981
  • The articles collected here are the texts of the invited lectures given at the Eighth British Combinatorial Conference held at University College, Swansea. The contributions reflect the scope and breadth of application of combinatorics, and are up-to-date reviews by mathematicians engaged in current research. This volume will be of use to all those interested in combinatorial ideas, whether they be mathematicians, scientists or engineers concerned with the growing number of applications.

Graphs, Codes and Designs
  • P. J. Cameron, J. H. van Lint
  • Published online:
    16 March 2010
    Print publication:
    31 July 1980
  • This book is concerned with the relations between graphs, error-correcting codes and designs, in particular how techniques of graph theory and coding theory can give information about designs. A major revision and expansion of a previous volume in this series, this account includes many examples and new results as well as improved treatments of older material. So that non-specialists will find the treatment accessible the authors have included short introductions to the three main topics. This book will be welcomed by graduate students and research mathematicians and be valuable for advanced courses in finite combinatorics.

Symmetric Designs
  • An Algebraic Approach
  • Eric S. Lander
  • Published online:
    16 March 2010
    Print publication:
    20 January 1983
  • Symmetric designs are an important class of combinatorial structures which arose first in the statistics and are now especially important in the study of finite geometries. This book presents some of the algebraic techniques that have been brought to bear on the question of existence, construction and symmetry of symmetric designs – including methods inspired by the algebraic theory of coding and by the representation theory of finite groups – and includes many results. Rich in examples and containing over 100 problems, the text also provides an introduction to many of the modern algebraic approaches used, through six lengthy appendices and supplementary problems. The book will be of interest to both combinatorialists and algebraists, and could be used as a course text for a graduate course.

Surveys in Combinatorics, 1993
  • Edited by K. Walker
  • Published online:
    16 March 2010
    Print publication:
    29 July 1993
  • This volume comprises the invited lectures given at the 14th British Combinatorial Conference. The lectures survey many topical areas of current research activity in combinatorics and its applications, and also provide a valuable overview of the subject, for both mathematicians and computer scientists.

Page 18 of 24