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 ...
We discuss a set of topics that are important for the understanding of modern data science but that are typically not taught in an introductory ML course. In particular we discuss fundamental ideas and techniques that come from probability, information the ...
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 ...
Students will learn the principles of mechanics to enable a better understanding of physical phenomena, such as the kinematics and dyamics of point masses and solid bodies. Students will acquire the capacity to quantitatively analyze these effects with the ...
This course serves as an introduction to classical differential geometry, which studies the geometric properties of curves and surfaces in the Euclidean space. ...