This self-contained volume offers an expanded version of lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. Several surprising phenomena appear when studying Sobolev spaces on manifolds, according to the author. Questions that are elementary for Euclidean space become challenging and give rise to sophisticated mathematics, where the geometry of the manifold plays a central role.
This self-contained volume offers an expanded version of lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifol...
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n times n matrices exhibit universal behavior as n > infinity? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. ...
Written by a leading specialist in the area of atmosphere/ocean science (AOS), these lecture notes present an introduction to this important topic. The goals of the lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied...
Written by a leading specialist in the area of atmosphere/ocean science (AOS), these lecture notes present an introduction to this important topic. Th...
Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book has served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references.
Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book has served as an introduction to various su...
This volume contains notes of the lectures given at the Courant Institute and a DMV-Seminar at Oberwolfach. The focus is on the work of the authors on semilinear wave equations with critical Sobolev exponents and on wave maps in two space dimensions. Background material and references have been added to make the notes self-contained. The book is suitable for use in a graduate-level course on the topic. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
This volume contains notes of the lectures given at the Courant Institute and a DMV-Seminar at Oberwolfach. The focus is on the work of the authors on...
Supersymmetry has been studied by theoretical physicists since the early 1970s. This book presents a cogent and self-contained exposition of the foundations of supersymmetry for the mathematically-minded reader. It is suitable for graduate students and mathematicians interested in the mathematical theory of supersymmetry.
Supersymmetry has been studied by theoretical physicists since the early 1970s. This book presents a cogent and self-contained exposition of the found...
The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. This book presents various mathematical aspects of the nonlinear Schrodinger equation. It studies both problems of local nature and problems of global nature.
The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear o...
This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences, USA. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation.
This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences,...
Algebraic curves have many special properties that make their study particularly rewarding. As a result, curves provide a natural introduction to algebraic geometry. In this book, the authors also bring out certain aspects of curves and emphasize connections with algebra. This text covers the essential topics in the geometry of algebraic curves, such as line and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups. The authors make a point of using concrete examples and explicit methods to ensure that the style is clear and...
Algebraic curves have many special properties that make their study particularly rewarding. As a result, curves provide a natural introduction to alge...
Presents an introduction to the field of dynamical systems, in particular, to the special class of Hamiltonian systems. This book keeps the requirements of mathematical techniques minimal but gives detailed proofs and many examples and illustrations from p
Presents an introduction to the field of dynamical systems, in particular, to the special class of Hamiltonian systems. This book keeps the requiremen...
