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An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Developing, with many examples, the elementary theory of elliptic curves, this book goes on to the subject of modular forms and the first connections with elliptic curves.

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Explores developments in the theory of planar quasiconformal mappings with a focus on the interactions with partial differential equations and nonlinear analysis. This book presents a modern approach to the classical theory and features applications across a spectrum of mathematics such as dynamical systems and singular integral operators.

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Describes the developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics - the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem.

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This book contains the lectures presented at a conference held at Princeton University in May 1991 in honor of Elias M. Stein's sixtieth birthday. The lectures deal with Fourier analysis and its applications. The contributors to the volume are W. Beckner, A. Boggess, J. Bourgain, A. Carbery, M. Christ, R. R. Coifman, S. Dobyinsky, C. Fefferman, R.

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The Neumann problem is probably the most important and natural example of a non-elliptic boundary value problem, arising as it does from the Cauchy-Riemann equations. It has been known for some time how to prove solvability and regularity by the use of L2 methods. In this monograph the authors apply recent methods involving the Heisenberg group

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Euler systems are special collections of cohomology classes attached to p-adic Galois representations. This book presents a development of the theory of Euler systems. It reviews and develops the necessary facts from Galois cohomology and then introduces Euler systems, states the main theorems, and develops examples and applications.

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Mathematical No/ex, 27 Originally published in 1981. 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 presenting them in durable paper

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The description for this book, Existence Theorems in Partial Differential Equations. (AM-23), will be forthcoming.

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Using the statistical techniques discussed, a sound simulation model can be built and adequately tested before implementation.

The book also shows how simulation results can be generalized by discussing in full the growing emphasis on simulation metamodeling.

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Deals with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. This book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G).

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Combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. This book provides introduction to linear algebra, a branch of mathematics that studies vectors and vector spaces.

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Applies model theoretic methods to the study of certain finite permutation groups, the automorphism groups of structures for a fixed finite language with a bounded number of orbits on 4-tuples. This book treats the general case by developing analogs of the model theoretic methods of geometric stability theory.

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Surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. This work considers every proposed fix, each with its distinctive philosophical advantages and drawbacks.

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In classical dynamics the action of a one-parameter group-time- on the phase space is one of the principal objects of study. Ergodic theory concerns itself with the case when the phase space is a measure spaces. The purpose of this chapter is to give an outline of the basic theorems in the theory of solvmanifolds.