This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This first v…
This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second…
The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The…
The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen. The book is planned al…
Now in paperback, this classic book is addressed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that su…
Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The mathematics that underlies this discovery or that proceeded from it, known as the theory of Aperiodic Order, is the subj…
Traditional game theory has been successful at developing strategy in games of incomplete information: when one player knows something that the other does not. But it has little to say about games of complete information, for example, tic-tac-toe, s…
A series of important applications of combinatorics on words has emerged with the development of computerized text and string processing. The aim of this volume, the third in a trilogy, is to present a unified treatment of some of the major fields o…
In this treatise, the authors present the general theory of orthogonal polynomials on the complex plane and several of its applications. The assumptions on the measure of orthogonality are general, the only restriction is that it has compact support…
This revised and expanded new edition will continue to meet the needs for an authoritative, up-to-date, self contained, and comprehensive account of the rapidly growing field of basic hypergeometric series, or q-series. Simplicity, clarity, deductiv…
At the heart of this monograph is the Brunn-Minkowski theory. It can be used to great effect in studying such ideas as volume and surface area and the generalizations of these. In particular the notions of mixed volume and mixed area arise naturally…
Originally published in 1977, this volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separat…
This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs…
Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Internal Set Theory (IST) introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the book provides a careful devel…
This book is the first volume in a two-volume set, which will provide the complete proof of classification of two important classes of geometries, closely related to each other: Petersen and tilde geometries. There is an infinite family of tilde geo…
There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeatin…
This is a concise and elementary introduction to stochastic control and mathematical modelling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are inte…
The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with…
This is an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical no…
This treatise deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioural and social sciences. The authors have chosen to emphasize applications, thoug…
This treatise deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioural and social sciences. The authors have chosen to emphasise applications, thoug…
A Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence, with…
Originally published in 2000, this is the first volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and alg…
Dynamic data assimilation is the assessment, combination and synthesis of observational data, scientific laws and mathematical models to determine the state of a complex physical system, for instance as a preliminary step in making predictions about…
The first edition of this book was reviewed in 1982 as 'the most extensive treatment of Padé approximants actually available'. This second edition has been thoroughly updated, with a substantial chapter on multiseries approximants. Applications to s…
Originally published in 2000, this is the second volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and al…
This is the second volume in a two-volume set, which provides a complete self-contained proof of the classification of geometries associated with sporadic simple groups: Petersen and tilde geometries. The second volume contains a study of the repres…
Using Bishop's work on constructive analysis as a framework, this monograph gives a systematic, detailed and general constructive theory of probability theory and stochastic processes. It is the first extended account of this theory: almost all of t…
This is the first book devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of…
Spline functions are universally recognized as highly effective tools in approximation theory, computer-aided geometric design, image analysis, and numerical analysis. The theory of univariate splines is well known but this text is the first compreh…
Asymptotics and Mellin-Barnes Integrals provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical…
This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop th…
This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each…
This book focuses on the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. Large deviation probabili…
This work explores the role of probabilistic methods for solving combinatorial problems. These methods not only provide the means of efficiently using such notions as characteristic and generating functions, the moment method and so on but also let…
This 1997 work explores the role of probabilistic methods for solving combinatorial problems. These methods not only provide the means of efficiently using such notions as characteristic and generating functions, the moment method and so on but also…
This is the second volume of a two-volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. The author emphasizes the roles of *-algebra structure and explores the algebraic r…
This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material i…
This is an updated version of Gevrey’s classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems.…
The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become th…
This book is devoted to the study of classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields. The author shows how the application of the generalized scheme of allocation in the…
This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made a considerable contribution. This is an a…
The wave equation, a classical partial differential equation, has been studied and applied since the eighteenth century. Solving it in the presence of an obstacle, the scatterer, can be achieved using a variety of techniques and has a multitude of a…
Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. As the first book to deal exclusively with finite ordered sets, this book will be welcomed by graduate stu…
Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an…
The rapid development of the theories of Volterra integral and functional equations has been strongly promoted by their applications in physics, engineering and biology. This text shows that the theory of Volterra equations exhibits a rich variety o…
Some of the most beautiful mathematical objects found in the last forty years are the sporadic simple groups. But gaining familiarity with these groups presents problems for two reasons. Firstly, they were discovered in many different ways, so to un…
This is the concluding volume of the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten to reflect this. In particular the grow…
This is a revised edition of McEliece's classic. It is a self-contained introduction to all basic results in the theory of information and coding (invented by Claude Shannon in 1948). This theory was developed to deal with the fundamental problem of…
Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonorma…
Information content and programming semantics are just two of the applications of the mathematical concepts of order, continuity and domains. The authors develop the mathematical foundations of partially ordered sets with completeness properties of…
Algorithmic Aspects of Graph Connectivity is the first comprehensive book on this central notion in graph and network theory, emphasizing its algorithmic aspects. Because of its wide applications in the fields of communication, transportation, and p…
The complete theory of stochastic differential equations driven by jumps, their stability, and numerical approximation theories.
Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random m…
The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied…