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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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464 results in London Mathematical Society Lecture Note Series

Page 7 of 24

Differentiable Germs and Catastrophes
  • Theodor Bröcker
  • Translated by L. Lander
  • Published online:
    05 May 2013
    Print publication:
    17 July 1975
  • These notes give a fairly elementary introduction to the local theory of differentiable mappings. Sard's Theorem and the Preparation Theorem of Malgrange and Mather are the basic tools and these are proved first. There follows a number of illustrations including: the local part of Whitney's Theorem on mappings of the plane into the plane, quadratic differentials, the Instability Theorem of Thom, one of Mather's theorems on finite determinacy and a glimpse of the theory of Toujeron. The later part of the book develops Mather's theory of unfoldings of singularities. Its application to Catastrophe theory is explained and the Elementary Catastrophes are illustrated by many pictures. The book is suitable as a text for courses to graduates and advanced undergraduates but may also be of interest to mathematical biologists and economists.

Surveys in Combinatorics 2009
  • Edited by Sophie Huczynska, James D. Mitchell, Colva M. Roney-Dougal
  • Published online:
    05 May 2013
    Print publication:
    09 July 2009
  • This volume contains survey articles based on the invited lectures given at the Twenty-second British Combinatorial Conference, held in July 2009 at the University of St Andrews. This biennial conference is a well-established international event, with speakers from all over the world. By its nature this volume provides an up-to-date overview of current research activity in several areas of combinatorics, including graph theory, design theory and packing problems. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results, and give a unique preview of the most recent developments. The book provides a valuable survey of the present state of knowledge in combinatorics. It will be useful to research workers and advanced graduate students, primarily in mathematics but also in computer science, statistics and engineering.

Singularities
  • Edited by Jean-Paul Brasselet
  • Published online:
    05 May 2013
    Print publication:
    07 July 1994
  • Singularity theory encompasses many different aspects of geometry and topology, and an overview of these is represented here by papers given at the International Singularity Conference held in 1991 at Lille. The conference attracted researchers from a wide variety of subject areas, including differential and algebraic geometry, topology, and mathematical physics. Some of the best known figures in their fields participated, and their papers have been collected here. Contributors to this volume include G. Barthel, J. W. Bruce, F. Delgado, M. Ferrarotti, G. M. Greuel, J. P. Henry, L. Kaup, B. Lichtin, B. Malgrange, M. Merle, D. Mond, L. Narvaez, V. Neto, A. A. Du Plessis, R. Thom and M. Vaquié. Research workers in singularity theory or related subjects will find that this book contains a wealth of valuable information on all aspects of the subject.

Commutative Algebra
  • Durham 1981
  • Edited by R. Y. Sharp
  • Published online:
    05 May 2013
    Print publication:
    27 January 1983
  • This book is concerned with the research conducted in the late 1970s and early 1980s in the theory of commutative Neotherian rings. It consists of articles by invited speakers at the Symposium of Commutative Algebra held at the University of Durham in July 1981; these articles are all based on lectures delivered at the Symposium. The purpose of this book is to provide a record of at least some aspects of the Symposium, which several of the world leaders in the field attended. Several articles are included which provide surveys, incorporating historical perspective, details of progress made and indications of possible future lines of investigation. The book will be of interest to scholars of commutative and local algebra.

Number Theory and Cryptography
  • J. H. Loxton
  • Published online:
    05 May 2013
    Print publication:
    19 April 1990
  • In this volume, originally published in 1990, are included papers presented at two meetings; one a workshop on Number Theory and Cryptography, and the other, the annual meeting of the Australian Mathematical Society. Questions in number theory are of military and commercial importance for the security of communication, as they are related to codes and code-breaking. Papers in the volume range from problems in pure mathematics whose study has been intensified by this connection, through interesting theoretical and combinatorial problems which arise in the implementation, to practical questions that come from banking and telecommunications. The contributors are prominent within their field. The whole volume will be an attractive purchase for all number theorists, 'pure' or 'applied'.

Stochastic Differential Equations on Manifolds
  • K. D. Elworthy
  • Published online:
    05 May 2013
    Print publication:
    02 September 1982
  • The aims of this book, originally published in 1982, are to give an understanding of the basic ideas concerning stochastic differential equations on manifolds and their solution flows, to examine the properties of Brownian motion on Riemannian manifolds when it is constructed using the stochiastic development and to indicate some of the uses of the theory. The author has included two appendices which summarise the manifold theory and differential geometry needed to follow the development; coordinate-free notation is used throughout. Moreover, the stochiastic integrals used are those which can be obtained from limits of the Riemann sums, thereby avoiding much of the technicalities of the general theory of processes and allowing the reader to get a quick grasp of the fundamental ideas of stochastic integration as they are needed for a variety of applications.

Torsors, Étale Homotopy and Applications to Rational Points
  • Edited by Alexei N. Skorobogatov
  • Published online:
    05 May 2013
    Print publication:
    18 April 2013
  • Torsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and étale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the étale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the étale homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and homogeneous spaces, rational and K3 surfaces, geometric invariant theory, rational points, descent and the Brauer–Manin obstruction. Together, these give a state-of-the-art view of a broad area at the crossroads of number theory and algebraic geometry.

Aspects of Topology
  • In Memory of Hugh Dowker 1912–1982
  • Edited by I. M. James, E. H. Kronheimer
  • Published online:
    05 May 2013
    Print publication:
    31 January 1985
  • This is a memorial volume to the distinguished Canadian-born mathematician Hugh Dowker, one of the most highly regarded topologists in the United Kingdom and sometime Professor at Birkbeck College, London. The volume comprises specially written articles on various topological topics by experts in many countries who worked with Dowker at one time or another. These include survey, expository and research articles on general topology, algebraic topology and related subjects such as knot theory and graph theory. The volume will be of great interest to graduate students and professional mathematicians whose speciality is topology, in all its aspects.

Surveys in Combinatorics 2003
  • Edited by C. D. Wensley
  • Published online:
    05 May 2013
    Print publication:
    24 July 2003
  • The British Combinatorial Conference is held every two years and is a key event for mathematicians worldwide working in combinatorics. In June 2003 the conference was held at the University of Wales, Bangor. The papers contained here are surveys contributed by the invited speakers and are of the high quality that befits the event. There is also a tribute to Bill Tutte who had a long-standing association with the BCC. The papers cover topics currently attracting significant research interest as well as some less traditional areas such as the combinatorics of protecting digital content. They will form an excellent resource for established researchers as well as graduate students who will find much here to inspire future work.

Several Complex Variables and Complex Manifolds I
  • Mike Field
  • Published online:
    05 May 2013
    Print publication:
    01 April 1982
  • This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds was first published in 1982. It was intended be a synthesis of those topics and a broad introduction to the field. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a further knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts were designed to provide an introduction to the more advanced works in the subject.

Twistors in Mathematics and Physics
  • Edited by T. N. Bailey, R. J. Baston
  • Published online:
    05 May 2013
    Print publication:
    23 August 1990
  • Twistor theory has become a diverse subject as it has spread from its origins in theoretical physics to applications in pure mathematics. This 1990 collection of review articles covers the considerable progress made in a wide range of applications such as relativity, integrable systems, differential and integral geometry and representation theory. The articles explore the wealth of geometric ideas which provide the unifying themes in twistor theory, from Penrose's quasi-local mass construction in relativity, to the study of conformally invariant differential operators, using techniques of representation theory.

Surveys in Combinatorics, 1999
  • Edited by J. D. Lamb, D. A. Preece
  • Published online:
    05 May 2013
    Print publication:
    01 July 1999
  • The British Combinatorial Conference is one of the most well known meetings for combinatorialists. This volume collects the invited talks from the 1999 conference held at the University of Kent and together these span a broad range of combinatorial topics. The nine talks are from: S. Ball, J. Dinitz, M. Dyer, K. Metsch, J. Pach, R. Thomas, C. Thomassen, N. Wormald, plus a special contribution from W. T. Tutte. All researchers into combinatorics will find this volume an outstanding and up-to-date resource.

Analysis and Logic

Syzygies
  • E. Graham Evans, Phillip Griffith
  • Published online:
    05 May 2013
    Print publication:
    15 August 1985
  • The aim of this book, which was originally published in 1985, is to cover from first principles the theory of Syzygies, building up from a discussion of the basic commutative algebra to such results as the authors' proof of the Syzygy Theorem. In the last three chapters applications of the theory to commutative algebra and algebraic geometry are given.

Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds
  • Mark Pollicott
  • Published online:
    05 May 2013
    Print publication:
    04 February 1993
  • Pesin theory consists of the study of the theory of non-uniformly hyperbolic diffeomorphisms. The aim of this book is to provide the reader with a straightforward account of this theory, following the approaches of Katok and Newhouse. The notes are divided into two parts. The first develops the basic theory, starting with general ergodic theory and introducing Liapunov exponents. Part Two deals with the applications of Pesin theory and contains an account of the existence (and distribution) of periodic points. It closes with a look at stable manifolds, and gives some results on absolute continuity. These lecture notes provide a unique introduction to Pesin theory and its applications. The author assumes that the reader has only a good background of undergraduate analysis and nothing further, so making the book accessible to complete newcomers to the field.

Geometry of Riemann Surfaces
  • Edited by Frederick P. Gardiner, Gabino González-Diez, Christos Kourouniotis
  • Published online:
    05 May 2013
    Print publication:
    11 February 2010
  • Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, fractal geometry, conformal dynamics, discrete groups, geometric group theory, algebraic curves and their moduli, various kinds of deformation theory, coding, thermodynamic formalism, and topology of three-dimensional manifolds. This collection of articles, authored by leading authorities in the field, comprises 16 expository essays presenting original research and expert surveys of important topics related to Riemann surfaces and their geometry. It complements the body of recorded research presented in the primary literature by broadening, re-working and extending it in a more focused and less formal framework, and provides a valuable commentary on contemporary work in the subject. An introductory section sets the scene and provides sufficient background to allow graduate students and research workers from other related areas access to the field.

Finite Group Algebras and their Modules
  • P. Landrock
  • Published online:
    05 April 2013
    Print publication:
    29 December 1983
  • Originally published in 1983, the principal object of this book is to discuss in detail the structure of finite group rings over fields of characteristic, p, P-adic rings and, in some cases, just principal ideal domains, as well as modules of such group rings. The approach does not emphasize any particular point of view, but aims to present a smooth proof in each case to provide the reader with maximum insight. However, the trace map and all its properties have been used extensively. This generalizes a number of classical results at no extra cost and also has the advantage that no assumption on the field is required. Finally, it should be mentioned that much attention is paid to the methods of homological algebra and cohomology of groups as well as connections between characteristic 0 and characteristic p.

Algebraic Varieties
  • G. Kempf
  • Published online:
    05 April 2013
    Print publication:
    09 September 1993
  • In this book Professor Kempf gives an introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint. By taking this view he is able to give a clean and lucid account of the subject which will be easily accessible to all newcomers to algebraic varieties, graduate students or experts from other fields alike. Anyone who goes on to study schemes will find that this book is an ideal preparatory text.

Algebraic, Extremal and Metric Combinatorics 1986
  • Edited by M. M. Deza, P. Frankl, I. G. Rosenberg
  • Published online:
    05 April 2013
    Print publication:
    25 August 1988
  • This book represents a comprehensive overview of the present state of progress in three related areas of combinatorics. It comprises selected papers from a conference held at the University of Montreal. Topics covered in the articles include association schemes, extremal problems, combinatorial geometrics and matroids, and designs. All the papers contain new results and many are extensive surveys of particular areas of research. Particularly valuable will be Ivanov's paper on recent Soviet research in these areas. Consequently this volume will be of great attraction to all researchers in combinatorics and to research students requiring a rapid introduction to some of the open problems in the subject.

Geometric Galois Actions
  • Volume 1, Around Grothendieck's Esquisse d'un Programme
  • Edited by Leila Schneps, Pierre Lochak
  • Published online:
    05 April 2013
    Print publication:
    10 July 1997
  • The first of two companion volumes on anabelian algebraic geometry, this book contains the famous, but hitherto unpublished manuscript 'Esquisse d'un Programme' (Sketch of a Program) by Alexander Grothendieck. This work, written in 1984, fourteen years after his retirement from public life in mathematics, together with the closely connected letter to Gerd Faltings, dating from 1983 and also published for the first time in this volume, describe a powerful program of future mathematics, unifying aspects of geometry and arithmetic via the central point of moduli spaces of curves; it is written in an artistic and informal style. The book also contains several articles on subjects directly related to the ideas explored in the manuscripts; these are surveys of mathematics due to Grothendieck, explanations of points raised in the Esquisse, and surveys on progress in the domains described there.

Page 7 of 24