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Five papers by distinguished American and European mathematicians describe some current trends in mathematics in the perspective of the recent past and in terms of expectations for the future. Among the subjects discussed are algebraic groups, quadratic forms, topological aspects of global analysis, variants of the index theorem, and partial differential equations.

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This collection brings together papers by mathematicians exploring the research frontiers of topology. The book covers a wide range of topological specialities.

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Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras, this book introduces a class of non-associative algebras related to exceptional algebraic groups and their associated buildings.

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Book 22 in the Princeton Mathematical Series. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presentin

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Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.

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Offers an examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry. This book focuses on the spectral rigidity problem.

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The description for this book, Ramification Theoretic Methods in Algebraic Geometry (AM-43), will be forthcoming.

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In a series of three papers published in 1930 and 1931, Paley and Zygmund 44 studied a variety of problems concerning series of independent random functions and raised the question of the uniform convergence a.s. of the random Fourier series.

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Addressing the topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. It includes fixed point theorems and applications to functional equations and optimization theory.

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This book presents many of the main developments of the past two decades in the study of real submanifolds in complex space, providing crucial background material for researchers and advanced graduate students.

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This volume answers the question, what does maths have to do with real life Up to 50 maths concepts are presented here, with multiple examples of how each concept is applied to tasks in everyday life, such as work and sport. It meets the National Mathematics Teachers Association standards.

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We shall study a notion of capacity for compact subsets of complex projective space. Our principal motivation for this comes from a theorem of Sibony and Wong 8 , Let K be a compact circled subset of the unit sphere in C2.

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Throughout the book, an approach to errors as opportunities for learning and inquiry will be developed and employed both as a means to create the kinds of instructional experiences advocated for school mathematics reform, and as a heuristic to invite reflections about school mathematics as well as mathematics as a discipline.

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Throughout the book, an approach to errors as opportunities for learning and inquiry will be developed and employed both as a means to create the kinds of instructional experiences advocated for school mathematics reform, and as a heuristic to invite reflections about school mathematics as well as mathematics as a discipline.

(Hardback)

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Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make

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Gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity.