This course serves as an introduction to classical differential geometry, which studies the geometric properties of curves and surfaces in the Euclidean space. ...
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 ...
P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Ze ...
The student will learn state-of-the-art algorithms for solving differential equations. The analysis and implementation of these algorithms will be discussed in some detail. ...
Biological macromolecules such as DNA, RNA, proteins and cytoskeletal filaments are polymers. As such, they share a set of properties that are common to any polymer, which are the focus of this course. Details about the protein folding problem will be cove ...
A first graduate course in algorithms, this course assumes minimal background, but moves rapidly. The objective is to learn the main techniques of algorithm analysis and design, while building a repertory of basic algorithmic solutions to problems in many ...
The course introduces the paradigm of quantum computating in an axiomatic way. We introduce the notions of quantum bits, gates, and circuits. We introduce themost important quantum algorithms. We also touch upon error-correcting codes. This course is indep ...