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

The theory of Lie groups involves many areas of mathematics: algebra, differential geometry, algebraic geometry, analysis, and differential equations. This work outlines the prerequisites to get the reader started, and then chooses a path through this theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces.

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Presents a collection of 180 mathematical puzzles and elementary problems that great mathematicians have posed, discussed, and solved. This book intends to show that famous mathematicians have all communicated brilliant ideas, methodological approaches, and absolute genius in mathematical thoughts by using recreational mathematics as a framework.

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Contains everything that is needed to run a successful mathematical circle for a full year. The materials, distributed among 29 weekly lessons, include detailed lectures and discussions, sets of problems with solutions, and contests and games. In addition, the book shares some of the know-how of running a mathematical circle.

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Perhaps the most famous example of how ideas from modern physics have revolutionized mathematics is the way string theory has led to an overhaul of enumerative geometry, an area of mathematics that started in the eighteen hundreds. The book begins with an insightful introduction to enumerative geometry.

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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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The goal of this text is to teach the subject and lead readers to where the vast literature - in the subject specifically and in its many applications - becomes accessible. The choice of material was made from among the fundamentals of what may be called the ""classical'' theory of operator algebras.

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Deals with the topic of geometric configurations of points and lines. This book presents the history of the topic, with its surges and declines since its beginning in 1876. It covers the advances in the field since the revival of interest in geometric configurations.

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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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Diophantine analysis, an area of number theory that helps to discover hidden treasures and truths within the numbers by exploring rational numbers, comprises two different but interconnected domains - diophantine approximation and diophantine equations. This book presents the fundamental ideas and theorems from diophantine approximation.

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Presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open. The hypotheses range from geometry and topology to combinatorics to algebra and number theory.

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Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. This book contains an account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces.

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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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Explores the mathematical ideas involved in creating and analyzing maps. This book presents the famous problem of mapping the earth. Through the visual context of maps and mapmaking, it shows students how contemporary mathematics can help them to understand and explain the world.

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Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the self-similarity phenomenon in group theory and shows its relationship with dynamical systems.

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Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. This book offers a modern perspective on cones and ordered vector spaces.

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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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Convexity is a simple idea that manifests itself in a surprising variety of places. This work demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. It demonstrates the power of a few simple unifying principles in a variety of pure and applied problems.

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Contains sections on Automorphic representations and L-functions as well as Arithmetical algebraic geometry and L-functions.

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Offers a self-contained presentation of classical methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. This book is suitable for students and mature scientists interested in nonlinear wave phenomena.

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The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organising and simplifying the proof.

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Filtering and prediction is about observing moving objects when the observations are corrupted by random errors. This title includes chapters that deal with discrete probability spaces, random variables, conditioning, Markov chains, and filtering of discrete Markov chains. It also discusses filtering and prediction of stationary sequences.

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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 name Bourbaki is known to every mathematician. This book presents accounts of the origins of Bourbaki, their meetings, their seminars, and the members themselves. It also discusses the lasting influence that Bourbaki has had on mathematics, through both the Elements and the Seminaires.

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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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Focuses on ergodic theory, combinatorics, and number theory. This book discusses a variety of topics, ranging from developments in additive prime number theory to expository articles on individual mathematical topics such as the law of large numbers and the Lucas-Lehmer test for Mersenne primes.

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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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Describes billiards and their relation with differential geometry, classical mechanics, and geometrical optics. This book covers such topics as variational principles of billiard motion, and symplectic geometry of rays of light and integral geometry. It is suitable for students interested in ergodic theory and geometry.

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Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds. This book unifies Riemannian geometry with modern complex analysis, as well as with algebra and number theory.

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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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Deals with the theory of Toeplitz forms. This work also focuses on applications, in particular to the calculus of probability and mathematical statistics. It intends to elucidate the principal ideas of this chapter of modern analysis and to help the interested student of mathematical statistics to acquire a working knowledge of the subject.

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Mathematics has been called the science of order. This book intends to provide examples - and proofs - of the complexity law: discrete systems are either simple or they exhibit advanced pseudorandomness and a priori probabilities often exist even when there is no intrinsic symmetry.

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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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Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. A sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. This book covers the theory of sheaves and their cohomology.

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A textbook for pre-service elementary school teachers and for current teachers who are taking professional development courses. Wu provides a comprehensive treatment of all the standard topics about numbers in the school mathematics curriculum: whole numbers, fractions, and rational numbers.

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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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