Search results for ""author american mathem american mathem""

Emil Artin was one of the great mathematicians of the twentieth century. He had the rare distinction of having solved two of the famous problems posed by David Hilbert in 1900. He showed that every positive definite rational function of several variables was a sum of squares. This book gathers a selection of his writings.

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Presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. This book also presents the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras.

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Includes discussion of smoothness, differentiability, and analyticity, the idea of local coordinates and coordinate transformation, and a detailed explanation of the Whitney imbedding theorem (both in weak and in strong form). This book describes the notion of the area of a figure on the plane and the volume of a solid body in space.

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Although division algebras are a very classical object, this book presents this 'classical' material in a new way, highlighting various approaches and fresh theorems, and illuminating the connections with a variety of areas in mathematics. It is based on lectures on division algebras given at a conference held at Colorado State University.

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Presents a comprehensive exposition of the modern theory of valued and ordered fields. This title presents the classical aspects of such fields: their arithmetic, topology, and Galois theory. It emphasizes the close connections and interplay between valuations and orderings, and to a large extent, studies them in a unified manner.

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Presents proceedings from the AMS short course, Trends in Optimization 2004, held at the Joint Mathematics Meetings in Phoenix (AZ). This book describes Lovasz's fundamental algorithm for producing a short vector in a lattice by basis reduction.

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Ideas from quantum field theory and string theory have had considerable impact on mathematics. In 1996-97 the Institute for Advanced Study (Princeton, NJ) organized a special year-long program designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. These volumes are a written record of the program.

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Presents a coherent account of matrix theory with a view to applications in mathematics, theoretical physics, statistics, and electrical engineering.

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Throughout the history of mathematics, maximum and minimum problems have played an important role in the evolution of the field. This book presents fifteen 'stories' that acquaint readers with the central concepts of the theory of maxima and minima, as well as with its illustrious history.

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A monograph that is concerned with Galois theoretical embedding problems of so-called Brauer type with a focus on 2-groups and on finding explicit criteria for solvability and explicit constructions of the solutions. It also considers questions of reducing the embedding problems and reformulating the solvability criteria.

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Offers an easily accessible form a coherent account of matrix theory with a view to applications in mathematics, theoretical physics, statistics, and electrical engineering. This title includes individual chapters that have been kept as far as possible independent of each other.

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Aims to give an exposition of generalized (co)homology theories that can be read by mathematicians who are not experts in algebraic topology. This work starts with basic notions of homotopy theory and then introduces the axioms of generalized (co)homology theory. It focuses on spectral sequences and their use in generalized cohomology theories.

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Traces the thread of pi through the long history of mathematics. This book touches upon many major subjects in mathematics: geometry (of course), number theory, Galois theory, probability, transcendental numbers, analysis, and, as their crown jewel, the theory of elliptic functions, which connects many of the other subjects.

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The concept of 'wave packet analysis' originates in Carleson's famous proof of almost everywhere convergence of Fourier series of $L^2$ functions. This work emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main development.

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The influence of Thurston's hyperbolization theorem on the geometry and topology of 3-manifolds has been tremendous. This book presents a proof of the hyperbolization theorem for 3-manifolds that fiber over the circle, following the plan of Thurston's original proof, though the double limit theorem is dealt with in a different way.

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Presents an exposition of spherical functions on compact symmetric spaces, from the viewpoint of Cartan-Selberg. This title treats compact symmetric pairs, spherical representations for compact symmetric pairs, the fundamental groups of compact symmetric spaces, and the radial part of an invariant differential operator.

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Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This book provides a general perspective on coarse structures. It discusses results on asymptotic dimension and uniform embeddings into Hilbert space.

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Suitable for readers who want to learn about the Newtonian $N$-body problem, this book contains simple explanations of the apparent 'looping' orbit of Mars and the unexpected 'Sunrise, Sunset' behavior as viewed from Mercury. It also covers the weird dynamics exhibited by Saturn's F-ring.

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Studies boundary value problems are from two points of view; solvability, unique or otherwise, and the effect of various smoothness properties of the given functions on the smoothness of the solutions. This title includes various chapters that introduce the various function spaces typical of modern Russian-style functional analysis.

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Contains the developments in a central theme of research on analysis of one complex variable. This book includes material that is based on lectures at the University of Michigan. It clarifies how certain basic properties of the space at hand are reflected in the geometry of interpolating and sampling sequences.

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Presents a study of problems related to the theory of infinite-dimensional dynamical systems. This work studies their properties for various non-autonomous equations of mathematical physics: the 2D and 3D Navier-Stokes systems, reaction-diffusion systems, dissipative wave equations, the complex Ginzburg-Landau equation, and others.

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Hermann Weyl was one of the most influential mathematicians of the twentieth century. This title contains the proceedings of the AMS Symposium on the Mathematical Heritage of Hermann Weyl, held in May 1987 at Duke University. It is suitable for mathematicians, theoretical physicists, and other scientists.

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Contains the proceedings of the Algebraic Geometry Conference on Classification of Algebraic Varieties, held in May 1992 at the University of L'Aquila in Italy. This work discusses a variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics.

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There are incredibly rich connections between classical analysis and number theory. This title uncovers interesting combinatorial identities by means of the function theory on Riemann surfaces related to the principal congruence subgroups $\Gamma(k)$. It is suitable for a graduate course or for independent reading.

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Presents elementary models of transport in continuous media and a corresponding body of mathematical technique. This title includes physical topics such as convection and diffusion as the simplest models of transport; local conservation laws with sources as the general framework of continuum mechanics; and momentum and energy transport.

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Offers an introduction to the theory of finite fields and to some of their many practical applications. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields. Each of the remaining chapters details applications.

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Treats various selected topics in differential geometry. This book includes a paper written jointly with V Guillemin at the beginning of a period of intense interest in the equivalence problem.

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The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St Petersburg's school of mathematical physics in the 1980s. The book gives an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras.

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Focuses on normed vector spaces and their important examples, Banach spaces and Hilbert spaces. This work covers topics including perturbation classes, measures of noncompactness, strictly singular operators and operator constants.

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Jacques Hadamard, among the greatest mathematicians of the twentieth century, made signal contributions to a number of fields. This title offers solutions to the problems in the first part of Hadamard's work (""Lessons in Geometry I Plane Geometry""). It is suitable for high school teachers, gifted high school students, and college students.

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Hodge theory originated as an application of harmonic theory to the study of the geometry of compact complex manifolds. This book consists of expositions of various aspects of modern Hodge theory.

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Understanding and working with the models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Covering the topic of financial modelling and optimization, this book helps readers obtain a self-contained introduction to the underlying mathematics. It is suitable as a graduate textbook.

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The correspondence between Einstein metrics and their conformal boundaries has been the focus of great interest. This book shows this correspondence in the wider context of asymptotically symmetric Einstein metrics, that is Einstein metrics whose curvature is asymptotic to that of a rank one symmetric space.

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In addition to the standard topics, this volume contains many topics not often found in an algebra book, such as inequalities, and the elements of substitution theory. Especially extensive is Chrystal's treatment of the infinite series, infinite products, and (finite and infinite) continued fractions.

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The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean curvature is zero at each point is a minimal surface, and it is known that such surfaces are models for soap film. This book presents many examples of constant mean curvature surfaces.

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Presents the proceedings of the conference on 'Trends in Mathematical Physics' held at the University of Tennessee. The conference drew international experts from mathematical and computational physics. The following topics were addressed: superstrings and quantum gravity, pattern formation, and crystallographic topology.

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Reproduces the doctoral thesis written by a remarkable mathematician, Sergei V Kerov. This book discusses the properties of the distribution of the normalized cycle length in a random permutation and the limiting shape of a random (with respect to the Plancherel measure) Young diagram.

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Contains many topics in algebra such as inequalities, and the elements of substitution theory. This volume includes over 2,400 exercises with solutions. It also gives a treatment of the infinite series, infinite products, and (finite and infinite) continued fractions.

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Presents the translation from the Japanese textbook for the grade 10 course, 'Basic Mathematics'. This book covers algebra (including quadratic functions, equations, and inequalities), trigonometric functions, and plane coordinate geometry.

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Based on courses taught by the author at Moscow State University, this book features such topics as the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. It contains many examples illustrating the general theory presented, as well as multiple exercises to help the reader.

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Intended for graduate students who have completed standard courses in linear algebra and abstract algebra, this title provides a single source for the basic facts about the classical groups and also includes the required geometrical background information from the first principles.

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