Böcker i Courant Lecture Notes-serien

The second of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics. The book provides a varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved.

The first of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics who have a basic understanding of matrix algebra. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise.

Offers a concise and self-contained introduction to recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. The authors present key concepts that they believe are the core of these methods.

Based on a course on advanced topics in differential equations given at the Courant Institute of Mathematical Sciences, this book describes aspects of mathematical modeling, analysis, computer simulation, and visualization in the mathematical sciences and engineering that involve singular perturbations.

Features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles - orthogonal, unitary, and symplectic. This book presents a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights.

Based on a course entitled 'Wigner measures and semiclassical limits of nonlinear Schrodinger equations,' this book applies the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quantum mechanics.

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.

Introduces the notion of topological degree and develops its basic properties. This book uses these properties in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz's global bifurcation theorem. It is suitable as a graduate level textbook and a supplementary course text.

Offers lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. This volume includes a brief introduction to differential and Riemannian geometry. It deals with the general theory of Sobolev spaces for compact manifolds, and also presents special types of Sobolev inequalities under constraints.