Search results for ""MP-AMM American Mathematical""

Contains papers presented by speakers at the AMS-IMS-SIAM Joint Summer Research Conference on Conformal Field Theory, Topological Field Theory and Quantum Groups, held at Mount Holyoke College in June 1992. This work deals with one aspect of conformal field theory, namely, vertex operator algebras or superalgebras and their representations.

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Algebraic Geometry has been at the centre of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of exercises, plus some background information and explanations, starting with conics and ending with sheaves and cohomology.

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Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, and applies this theory to various special examples.

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There is a deep and fundamental relationship between the differential equations that occur in the calculus of variations and partial differential equations of the first order: in particular, to each such partial differential equation there correspond variational problems. This book discusses this basic fact.

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A collection of one hundred short essays, that offers a tour through contemporary and everyday mathematics. It includes topics that range from pure mathematics to applications of mathematics to observations about the mathematics that surrounds us in daily life. It is suitable for those who read the science section of a newspaper or magazine.

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Develops three related tools that are useful in the analysis of partial differential equations (PDEs), arising from the classical study of singular integral operators: pseudodifferential operators, paradifferential operators, and layer potentials. This work focuses on the treatment of PDE in the presence of relatively little regularity.

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Contains twenty-two papers presented at the International Conference in Combinatorics, held in Jerusalem in May 1993. This title describes developments in algebraic combinatorics, enumeration, graph and hypergraph theory, combinatorial geometry, and geometry of polytopes and arrangements.

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We have been curious about numbers - and prime numbers - since antiquity. One notable direction this century in the study of primes has been the influx of ideas from probability. This book intends to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness.

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Contains a collection of papers devoted primarily to transcendental number theory and diophantine approximations. This title includes a text of the author's invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki.

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Resolution of Singularities has long been considered as being a difficult to access area of mathematics. This volume is intended for readers who are not yet experts but always wondered about the intricacies of resolution. It provides a gentle and comprehensive introduction to this amazing field.

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A collection of papers that addresses a variety of problems and approaches for predicting spatial effects in ecological systems. It discusses the spatial dynamics of natural systems and the impact of economic and sociological changes, as well as the adaptation methods from statistical lattice physics.

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The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. There have been striking developments in the mathematics of 3-dimensional manifolds. This book introduces some of these important developments.

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Oliver Heaviside is probably best known to the majority of mathematicians for the Heaviside function in the theory of distribution. His main research activity concerned the theory of electricity and magnetism. This book brings together many of Heaviside's published and unpublished notes and short articles written between 1891 and 1912.

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Deals with the interplay of computational commutative algebra and the theory of convex polytopes. This title centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties.

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This flexible text is organised into two parts: Part I treats the theory of measure and integration over abstract measure spaces; Part II is more specialised, and includes regular measures on locally compact spaces, the Riesz-Markoff theorem on the measure-theoretic representation of positive linear forms, and Haar measure on a locally compact group.

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Focuses on the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. This title begins with an introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem. It then gives a presentation of homogeneous spaces in which the main goal is to find formulas for their curvature.

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The goal of this book is to analyse in detail Ulam's problem for increasing subsequences of random permutations, and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. The book is self-contained, and develops enough of the theory from each area that a general reader can learn the subject directly from the text.

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Presents the proceedings of a conference held at the University of California at Riverside in February 1995, that focused on the interplay between the theory of Lie algebras of prime characteristic, quantum groups and Lie superalgebras.

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Offers an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. This book contains over 230 exercises (with solutions) that illustrate and expand the material. It is suitable for first-year graduate students who have background in real analysis.

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Covers key topics of numerical methods. This book includes such topics as interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic.

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Tries to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources to produce new and significant mathematics - mathematics unforeseen from the motivating problem. This book focuses on aperiodic tilings; the best-known example is the 'kite and dart' tiling.

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This is the second volume of the book on the proof of Fermat's Last Theorem by Wiles and Taylor (the first volume is published in the same series). Here the detail of the proof announced in the first volume is fully exposed. The book also includes basic materials and constructions in number theory and arithmetic geometry that are used in the proof.

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This is the first book to be devoted entirely to the potential theory of the heat equation, and thus deals with time dependent potential theory. Its purpose is to give a logical, mathematically precise introduction to a subject where previously many proofs were not written in detail, due to their similarity with those of the potential theory of Laplace's equation.

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Explores concepts such as the index of composition and the index of isolation of an integer. This book displays several tables of particular families of numbers, including the list of all 88 narcissistic numbers and the list of the eight known numbers which are not prime powers but which can be written as the sum of cubes of their prime factors.

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Presents complex algebraic curves. This book covers a range of topics from conics and cubics to theta functions, Jacobians, and questions of moduli. It is suitable for those preparing a course on the topic of complex curves.

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Contains papers presented at the conference on Banach Algebras and Several Complex Variables held June 21-24, 1983, to honor Professor Charles E Rickart upon his retirement from Yale University. This work includes articles that present advances in topics related to Banach algebras, function algebras and infinite dimensional holomorphy.

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Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group.

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Provides an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises, it will acquaint the non-expert with the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties.

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The field of differential topology underwent a dramatic development period between 1955 and 1965. This collection of articles contains original papers and expository lectures. It includes commentary by the author, filling in some of the historical context, and outlining developments in the field. It provides an understanding of the subject.

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Presents an introduction to probability and statistics. This book covers topics that include the axiomatic setup of probability theory, polynomial distribution, finite Markov chains, distribution functions and convolution, the laws of large numbers (weak and strong), characteristic functions, the central limit theorem, and Markov processes.

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Presents a view about the experience of being a department head.

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Presents an introduction to differential geometry through differential forms, emphasizing their applications in various areas of mathematics and physics. This work focuses on Stokes' theorem, the classical integral formulas and their applications to harmonic functions and topology.

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In a very broad sense, 'spaces' are objects of study in geometry, and 'functions' are objects of study in analysis. There are, however, deep relations between functions defined on a space and the shape of the space, and the study of these relations is the main theme of Morse theory. This book describes Morse theory for finite dimensions.

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The study of the zeroes of polynomials, which for one variable is essentially algebraic, becomes a geometric theory for several variables. This book looks at the classic entry point to the subject: plane algebraic curves. It presents an introduction to algebraic geometry, which assumes the standard undergraduate mathematical topics.

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Explains the problems that must be resolved in order to procure a rigorous development of the calculus and shows the student how to deal with those problems. Starting with the real line, this book also covers finite-dimensional spaces and metric spaces.

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