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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Presents a general theory of iteration algorithms for the numerical solution of equations and systems of equations. This book investigates the relationship between the quantity and the quality of information that is used by an algorithm.

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Much has been written on the theory of discontinuous groups and automorphic functions since 1880, when the subject received its first formulation. This book intends to bring together in one place both the classical and modern aspects of the theory, and to present them clearly and in a modern language and notation.

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Covers developments in the theory of Teichmuller spaces and offers references to the literature on Teichmuller spaces and quasiconformal mappings. This work describes how quasiconformal mappings have revitalized the subject of complex dynamics. It illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds.

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It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.

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Intends to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. The book reviews some basic geometry, but it is assumed that the reader has a general background in differential geometry. It also includes a chapter containing open problems and conjectures.

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Starting from classical arithmetical questions on quadratic forms, this book takes the reader step by step through the connections with lattice sphere packing and covering problems. As a model for polyhedral reduction theories of positive definite quadratic forms, it presents Minkowski's classical theory.

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Places Lebesgue's early work on integration theory within in proper historical context by relating it to the developments during the nineteenth century that motivated it and gave it significance and also to the contributions made in this field by Lebesgue's contemporaries.

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Offers a focused point of view on the differential geometry of curves and surfaces. This monograph treats the Gauss - Bonnet theorem and discusses the Euler characteristic. It also covers Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature.

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Based on CBMS lectures given at Texas Christian University, this book describes some of the interplay between string dualities and topology and operator algebras. It shows how several seemingly disparate subjects are closely linked with one another. It gives readers an overview of some areas of research.

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The papers in this volume were written by members of the seminar on representation theory at Moscow University, which has been running continuously since 1961. Among the topics included are representation theory of ""large"" groups and dual objects for certain real reductive Lie groups.

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Derives from lectures presented at the 2001 John H Barrett Memorial Lectures at the University of Tennessee, Knoxville. This work is suitable for graduate students as well as the many groups of researchers working in advanced computations, including engineering and computer scientists.

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There have been many wonderful developments in the theory of minimal surfaces and geometric measure theory. This book covers variational geometry. It focuses on Plateau's Problem, which is concerned with surfaces that model the behavior of soap films.

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A guide to the basics of modern algebraic geometry.

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