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

Euler is one of the greatest and most prolific mathematicians of all time. This book examines his work and its relation to current mathematics. It also treats the progression of ideas regarding divergent series from Euler to many parts of modern analysis and quantum physics.

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Presents an exposition of fixed point theory. This work focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property. It aims to show how fixed point theory uses combinatorial ideas related to decomposition of figures into distinct parts called faces, which adjoin each other in a regular fashion.

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Focuses on the spectral theory for evolution operators and evolution semigroups, a subject tracing its origins to the classical results of J Mather on hyperbolic dynamical systems and J Howland on nonautonomous Cauchy problems. This book includes a collection of examples from different areas of analysis, PDEs, and dynamical systems.

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Modular forms appear in many ways in number theory. This book details various roles that modular forms and $q$-series play in number theory, such as applications and connections to basic hypergeometric functions, Gaussian hypergeometric functions, super-congruences, Weierstrass points on modular curves, singular moduli, and class numbers.

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Covers Diophantine analysis. Besides the familiar cases of Diophantine equations, this book also covers partitions, representations as a sum of two, three, four or $n$ squares, Waring's problem in general and Hilbert's solution of it, and perfect squares in arithmetical and geometrical progressions.

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Emphasizes on functions rather than on geometric or physical applications.

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Discusses the differential geometric aspects of complex manifolds. This work contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. It discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles. It also gives a brief account of the surface classification theory.

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Contains 10 articles that explores topics ranging from Fermat's Last Theorem to Computational Fluid Dynamics. This volume includes articles on: a fresh mathematical method that's taking Wall Street by storm 'Ultra-parallel' supercomputing with DNA, and how a mathematician found the famous flaw in the Pentium chip.

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Presents a basic collection of principles, techniques, and applications needed to conduct independent research in gauge theory and its use in geometry and topology. This title includes self-contained computations of the Seiberg-Witten invariants of most simply connected algebraic surfaces using Witten's factorization method.

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Contains lectures from the CBMS Regional Conference held at Harvey Mudd College, June 1977. This monograph consists of applications to nonlinear differential equations of the author's coincidental degree. It includes an bibliography covering many aspects of the modern theory of nonlinear differential equations and the theory of nonlinear analysis.

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By studying algebraic varieties over a field, this book demonstrates how the notion of schemes is necessary in algebraic geometry. It gives a definition of schemes and describes some of their elementary properties.

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Presents an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide an account of the introductory portions of this important and technically difficult subject.

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Contains papers written by participants of the special session on value distribution theory and complex dynamics held in Hong Kong at the First Joint International Meeting of the AMS and the Hong Kong Mathematical Society in December 2000. This book discusses non-Archimedean analogs of Picard's theorems.

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A translation from the Latin of the third and last edition of ""Waring's Meditationes Algebraicae"".

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Presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. This title is suitable for graduate students and researchers interested in quantum mechanics and Schrodinger operators.

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A monograph that develops the spectral theory of an $n$th order non-self-adjoint two-point differential operator $L$ in the Hilbert space $L^2[0,1]$. It lays the mathematical foundation in the first part, where the spectral theory is developed for closed linear operators and Fredholm operators.

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The theory of partitions, founded by Euler, has led in a natural way to the idea of basic hypergeometric series, also known as Eulerian series. These series were first studied systematically by Heine, but many early results are attributed to Euler, Gauss, and Jacobi. This book provides a simple approach to basic hypergeometric series.

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In addition to the standard topics, this volume includes 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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Presents a comprehensive study of the algebraic theory of quadratic forms, from classical theory to the developments, including results and proofs. Written from the viewpoint of algebraic geometry, this book includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible.

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The laws of thermodynamics happen to be an extremely powerful tool for understanding the objects of holomorphic dynamical systems. This book develops a 'thermodynamic formalism', bringing together notions that are a priori unrelated. It describes this formalism both from the physical and mathematical point of view.

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Contains articles published from 1970 to 1990 in the Russian journal, ""Kvant"". This collection represents the Russian tradition of expository mathematical writing. It is designed to be used by students and teachers who love mathematics and want to study its various aspects, thus deepening and expanding the school curriculum.

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Introduces readers to the language of generating functions, which is the main language of enumerative combinatorics. This book starts with definitions, simple properties, and many examples of generating functions. It discusses topics such as formal grammars, generating functions in several variables, and the exclusion-inclusion principle.

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Introduces a systematic approach to the construction and analysis of semi simple $p$-adic groups. This book presents an overview of the representation theory of GL$_n$ over finite groups.

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Presents a comprehensive exposition of the theory of linear operators on Banach spaces and Banach lattices. This book offers a presentation that includes various developments in operator theory and draws together results that are spread over the vast literature. It contains over 600 exercises to help students master the material developed.

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Presents the analysis of optimal control problems for systems described by partial differential equations. This book covers cases where the controlled system corresponds to well-posed or ill-posed boundary value problems, which can be linear or nonlinear.

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Deals with problems of approximation of continuous or bounded functions of several variables by linear superposition of functions that are from the same class and have fewer variables.

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Based on lectures given by the author at the University of Chicago in 1956, this work covers such topics as recurrence, the ergodic theorems, and a general discussion of ergodicity and mixing properties. It is suitable for use for a one-semester course in ergodic theory or for self-study.

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Presents an account of noncommutative Noetherian rings. This book covers the major developments from the 1950s, stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras, PI rings, differential operators, and localization theory.

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Covers the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August. This work includes Kirby's problem list, which contains a description of the progress made on each of the problems and includes a bibliography. It is suitable for those interested in the many areas of topology.

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Presents some gratuitous generalities on scientific method as it relates to diffusion theory. This book defines Brownian motion by the characterization of P Levy, and then constructed in three basic ways and these are proved to be equivalent in the appropriate sense.

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Presents an approach to algebraic geometry of curves that is treated as the theory of algebraic functions on the curve. This book discusses such topics as the theory of divisors on a curve, the Riemann-Roch theorem, $p$-adic completion, and extensions of the fields of functions (covering theory) and of the fields of constants.

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In May 1974, the American Mathematical Society sponsored a special symposium on the mathematical consequences of the Hilbert problems, held at Northern Illinois University, DeKalb, Illinois. This title contains the proceedings of that symposium and includes papers corresponding to the invited addresses with one exception.

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Contains the proceedings of a symposium honoring the memory of Josiah Willard Gibbs, one of the giants of theoretical physics. This book provides perspectives on Gibbs, the man, and on the place his work occupies in the history of science.

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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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