This course serves as an introduction to classical differential geometry, which studies the geometric properties of curves and surfaces in the Euclidean space. ...
This is an introductory course on Elliptic Partial Differential Equations. The course will cover the theory of both classical and generalized (weak) solutions of elliptic PDEs. ...
Statistics lies at the foundation of data science, providing a unifying theoretical and methodological backbone for the diverse tasks enountered in this emerging field. This course rigorously develops the key notions and methods of statistics, with an emph ...
We develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemannian geometry (with a focus dictated by computational con ...
The goal of this course is to give an introduction to the theory of distributions and cover the fundamental results of Sobolev spaces including fractional spaces that appear in the interpolation theory. Those notions are central to the study of partial dif ...
The main theme in Diopahntine approximation is to approximate a real number by a rational number with a certain denominator bound. The course covers the case of one real number, that is classical and well understood, and proceeds to simultaneous Diophantin ...