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Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-know Yamabe type.

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This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial different

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Offers an introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. This book traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter.

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The description for this book, Calculus on Heisenberg Manifolds. (AM-119), will be forthcoming.

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In a follow up to his "Ferman's Last Theorem", the author shows readers how to maximize or minimize chance, depending on the circumstance, analyzing luck from a statistician's perspective.

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The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, that is it escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems.

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This book presents a classification of all (complex) irreducible representations of a reductive group with connected centre, over a finite field. To achieve this, the author uses etale intersection cohomology, and detailed information on representations of Weyl groups.

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Provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. This title delves into arguments originating in Nori's work that have been further developed by others.

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Presenting mathematics in the context of social issues makes it relevant and helps students learn how to apply math skills appropriately. Working through the activities will motivate them and help them grow as mathematicians and as citizens.

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Brings together a number of lectures given between 1993 and 1999 as part of a series hosted by the Federal University of Pernambuco, in which researchers came to Recife, Brazil, to lecture on classical or celestial mechanics. This work is aimed at graduate students and researchers interested in Hamiltonian dynamics and celestial mechanics.

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In this book, the author introduces classical logic alongside constructive, relevant, comparative, and other nonclassical logics. It begins with brief introductions to informal set theory and general topology, and avoids advanced algebra; thus it is self-contained and suitable for readers with little background in mathematics.

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Relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. This book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings.

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What did it mean to be reasonable in the Age of Reason This title demonstrates how this view profoundly shaped the internal development of probability theory and defined its applications.

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The theory of games, first given a rigorous formulation by von Neumann in 1928, is a subfield of mathematics and economics that models situations in which individuals compete and cooperate with each other. This book assembles the fundamental contributions in this field. It is useful for researchers in game theory and for students.

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In the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go further to study the classification over an arbitrary field. An isomorphism theorem proved here determines the auto

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