Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowled…
The number theoretic properties of curves of genus 2 are attracting increasing attention. This book provides new insights into this subject; much of the material here is entirely new, and none has appeared in book form before. Included is an explici…
Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme. Alexander Grothendieck taught that algebraic cycles should be considered from a motivic point of view and in recent years this topic has spur…
Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory where the reversible group elements are those that are conjugate to their inverses. Howe…
Information propagation through peer-to-peer systems, online social systems, wireless mobile ad hoc networks and other modern structures can be modelled as an epidemic on a network of contacts. Understanding how epidemic processes interact with netw…
The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and bi…
The study of dissipative equations is an area that has attracted substantial attention over many years. Much progress has been achieved using a combination of both finite dimensional and infinite dimensional techniques, and in this book the authors…
Many areas of active research within the broad field of number theory relate to properties of polynomials, and this volume displays the most recent and most interesting work on this theme. The 2006 Number Theory and Polynomials workshop in Bristol d…
In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non…
Line graphs have the property that their least eigenvalue is greater than or equal to -2, a property shared by generalized line graphs and a finite number of so-called exceptional graphs. This book deals with all these families of graphs in the cont…
This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lowe…
This volume is devoted to the use of helices as a method for studying exceptional vector bundles, an important and natural concept in algebraic geometry. The work arises out of a series of seminars organised in Moscow by A. N. Rudakov. The first art…
Hilbert C*-modules are objects like Hilbert spaces, except that the inner product, instead of being complex valued, takes its values in a C*-algebra. The theory of these modules, together with their bounded and unbounded operators, is not only rich…
Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil a…
Many classical and modern results and quadratic forms are brought together in this book. The treatment is self-contained and of a totally elementary nature requiring only a basic knowledge of rings, fields, polynomials, and matrices, such that the w…
The field of geometric variational problems is fast-moving and influential. These problems interact with many other areas of mathematics and have strong relevance to the study of integrable systems, mathematical physics and PDEs. The workshop 'Varia…
The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, the last few years having seen the resolution of many longstanding conjectures. This volume contains important expositions and original w…
The surreal numbers form a system which includes both the ordinary real numbers and the ordinals. Since their introduction by J. H. Conway, the theory of surreal numbers has seen a rapid development revealing many natural and exciting properties. Th…
These volumes contain selected papers presented at the international conference on group theory held in St Andrews in 1989. The themes of the conference were combinatorial and computational group theory; four leading group theorists (J. A. Green, N.…
The biennial meetings at Sao Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to a wide variety of topics in both pure and applied mathematics. The t…
Durham Symposia traditionally constitute an excellent survey of recent developments in many areas of mathematics. The Symposium on stochastic analysis, which took place at the University of Durham in July 1990, was no exception. This volume is edite…
Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chie…
Many areas of mathematics were deeply influenced or even founded by Hermann Weyl, including geometric foundations of manifolds and physics, topological groups, Lie groups and representation theory, harmonic analysis and analytic number theory as wel…
Integration of differential equations is a central problem in mathematics and several approaches have been developed by studying analytic, algebraic, and algorithmic aspects of the subject. One of these is Differential Galois Theory, developed by Ko…
Tilting theory originates in the representation theory of finite dimensional algebras. Today the subject is of much interest in various areas of mathematics, such as finite and algebraic group theory, commutative and non-commutative algebraic geomet…
This 2007 volume contains survey articles based on the invited lectures given at the Twenty-first British Combinatorial Conference, held in July 2007 at the University of Reading. This biennial conference is a well-established international event an…
Written for mathematicians working with the theory of graph spectra, this book explores more than 400 inequalities for eigenvalues of the six matrices associated with finite simple graphs: the adjacency matrix, Laplacian matrix, signless Laplacian m…
The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology,…
This volume is a collection of articles based on the plenary talks presented at the 2005 meeting in Santander of the Society for the Foundations of Computational Mathematics. The talks were given by some of the foremost world authorities in computat…
This is an introduction to geometrical topics that are useful in applied mathematics and theoretical physics, including manifolds, metrics, connections, Lie groups, spinors and bundles, preparing readers for the study of modern treatments of mechani…
The use of geometric methods in classical mechanics has proven to be a fruitful exercise, with the results being of wide application to physics and engineering. Here Professor Marsden concentrates on these geometric aspects, and especially on symmet…
This volume comprises the proceedings of the 1995 Cardiff symposium on sieve methods, exponential sums, and their applications in number theory. Included are contributions from many leading international figures in this area which encompasses the ma…
The concepts of a locally presentable category and an accessible category have turned out to be useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition o…
This 2010 book was the first devoted to the theory of p-adic wavelets and pseudo-differential equations in the framework of distribution theory. This relatively recent theory has become increasingly important in the last decade with exciting applica…
This book comprises a collection of papers from participants at the IMCS Workshop on Computational and Geometric Aspects of Modern Algebra, held at Heriot-Watt University in 1998. Written by leading researchers, the papers cover a wide range of topi…
Hyperbolic geometry is a classical subject in pure mathematics which has exciting applications in theoretical physics. In this book leading experts introduce hyperbolic geometry and Maass waveforms and discuss applications in quantum chaos and cosmo…
The fifteenth British Combinatorial Conference took place in July 1995 at the University of Stirling. This volume consists of the papers presented by the invited lecturers at the meeting, and provides an up-to-date survey of current research activit…
In this book Professor Rees introduces and proves some of the main results of the asymptotic theory of ideals. The author’s aim is to prove his Valuation Theorem, Strong Valuation Theorem, and Degree Formula, and to develop their consequences.…
This volume contains a selection of the invited papers presented at a LMS Durham Symposium on modern developments in non-classical continuum mechanics. A major aim was to bring together workers in both the abstract and practical aspects of the subje…
With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present res…
This book is based on a course taught to an audience of undergraduate and graduate students at Oxford, and can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively litt…
Geometric group theory is a vibrant subject at the heart of modern mathematics. It is currently enjoying a period of rapid growth and great influence marked by a deepening of its fertile interactions with logic, analysis and large-scale geometry, an…
This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop’s school, but intuitionism. Russian constructivism and recursive analysis are also treated, with c…
This book, which was originally published in 1985 and has been translated and revised by the author from notes of a course, is an introduction to certain central ideas in group theory and geometry. Professor Lyndon emphasises and exploits the well-k…
This volume, dedicated to Professor A. Plans, concentrates on some important and contemporary themes in Banach space theory. The articles are by leading researchers and cover topics such as sequences, operators, eigenvalues, s-numbers and projection…
Recursion theory - now a well-established branch of pure mathematics, having grown rapidly over the last 35 years - deals with the general (abstract) theory of those operations which we conceive as being `computable' by idealized machines. The theor…
The theory of prehomogeneous vector spaces is a relatively new subject although its origin can be traced back through the works of Siegel to Gauss. The study of the zeta functions related to prehomogeneous vector spaces can yield interesting informa…
In the past few years elliptic curve cryptography has moved from a fringe activity to a major challenger to the dominant RSA/DSA systems. Elliptic curves offer major advances on older systems such as increased speed, less memory and smaller key size…
A thorough account of the methods that underlie the theory of subalgebras of finite von Neumann algebras, this book contains a substantial amount of current research material and is ideal for those studying operator algebras. The conditional expecta…
This book is devoted to the asymptotic properties of solutions of stochastic evolution equations in infinite dimensional spaces. It is divided into three parts: Markovian dynamical systems; invariant measures for stochastic evolution equations; inva…