Search results for ""mp-amm american mathematical""

The Mathematical Olympiad examinations, covering the USA Mathematical Olympiad (USAMO) and the International Mathematical Olympiad (IMO), have been published annually since 1976. This is the fourth volume in that series. The IMO is a world mathematics competition for high school students that takes place each year in a different country.

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Provides teachers with over 100 projects ready to assign to students in single and multivariable calculus. The authors have designed these projects with one goal in mind: to get students to think for themselves. Each project is a multistep, take-home problem, allowing students to work both individually and in groups.

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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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Contains a collection of mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof, and assumes only a modest background in linear algebra. The topics include Hamming codes, the matrix-tree theorem, the Lovász bound on the Shannon capacity, and a counterexample to Borsuk's conjecture.

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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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Describes the relation between classical and quantum mechanics. This book contains a discussion of problems related to group representation theory and to scattering theory. It intends to give a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.

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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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Addresses the major issues of graduate school, including choosing a program, passing the qualifying exams, finding an advisor, writing a thesis, and getting that first job. This book also contains a description of the basic elements of a mathematical education, as well as a glossary and appendices on the structure of a typical department.

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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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The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book presents an introduction to various facets of the theory.

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Model categories have become a standard tool in algebraic topology and homological algebra and, increasingly, in other fields where homotopy theoretic ideas are becoming important, such as algebraic $K$-theory and algebraic geometry. Suitable for graduate level, this title intends to obtain a deeper understanding of Quillen's model categories.

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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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Introduces $p$-adic numbers from the point of view of number theory, topology, and analysis. Covering several topics from real analysis and elementary topology, this book includes totally disconnected spaces and Cantor sets, points of discontinuity of maps and the Baire Category Theorem, and surjectivity of isometries of compact metric spaces.

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Recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results. This book collects these results, both old and new, and organises them into a natural foundation for all aspects of dynamical systems theory.

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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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Presents an introduction to various topics in harmonic analysis. This book discusses Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem).

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Dedicated to the memory of Russian mathematician, V A Rokhlin (1919-1984), this is a collection of research papers written by his former students and followers. It includes topics such as: topology, real algebraic geometry, dynamics, geometry of Riemannian manifolds, theory of Teichmuller spaces, and measure theory.

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An introductory survey of elliptic curves, modular forms, and $L$-functions. The main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory.

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Covers classical modular forms. This book is suitable to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations.

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Provides a useful exposition of results on the structure of semisimple algebraic groups over an arbitrary algebraically closed field. After the fundamental work of Borel and Chevalley in the 1950s and 1960s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups.

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The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects.

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Examines in some depth two important classes of point processes, determinantal processes and 'Gaussian zeros', i.e., zeros of random analytic functions with Gaussian coefficients. This title presents a primer on modern techniques on the interface of probability and analysis.

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This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or Analysis-I (beginning graduates). It is intended for students who completed a course in AP Calculus, possibly followed by a routine course in multivariable calculus and a computational course in linear algebra.

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Focuses on probabilistic foundations of the Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), this book presents four different proofs of the Feynman-Kac formula.

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Based on lectures presented by Popa at the NSF-CBMS Regional Conference held in Eugene, Oregon, in August 1993, this title offers a unified and self-contained presentation of the results presented in Popa's earlier papers.

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There is a tradition in Russia that holds that mathematics can be both challenging and fun. One fine outgrowth of that tradition is the magazine, ""Kvant"", which has been enjoyed by many of the best students since its founding in 1970. This book presents a collection of articles from ""Kvant"".

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Includes expositions of key developments in commutative and non-commutative algebra, algebraic $K$-theory, infinite group theory, and applications of algebra to topology. This book contains articles that are based on lectures given at a conference at Columbia University honoring the 65th birthday of Hyman Bass.

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Presents a systematic and unified study of geometric nonlinear functional analysis. This book presents a study of uniformly continuous and Lipschitz functions between Banach spaces, which leads naturally also to the classification of Banach spaces and of their important subsets (mainly spheres) in the uniform and Lipschitz categories.

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Features the Poincare Conjecture, a hundred-year-old problem that has apparently been solved by Grigory Perelman of St Petersburg, Russia. This book also contains chapters on Venn diagrams and primality testing.

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