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 ...
In this course, various aspects of probability theory are considered. The first part covers the main theorems in the field (law of large numbers, central limit theorem), while the second part focuses on the theory of martingales and concentration inequalit ...
This course introduces students to continuous, nonlinear optimization. We study the theory of optimization with continuous variables (with full proofs), and we analyze and implement important algorithms to solve constrained and unconstrained problems. ...
This course serves as an introduction to classical differential geometry, which studies the geometric properties of curves and surfaces in the Euclidean space. ...
The course aims to introduce the basic concepts and results of integer optimization with special emphasis on algorithmic problems on lattices that have proved to be important in theoretical computer science and cryptography during the past 30 years. ...
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 ...
Ce cours couvre les fondements des systèmes numériques. Sur la base d'algèbre Booléenne et de circuits combinatoires et séquentiels incluant les machines d'états finis, les methodes d'analyse et de synthèse de système logiques sont étudiées et appliquées. ...
Machine learning and data analysis are becoming increasingly central in sciences including physics. In this course, fundamental principles and methods of machine learning will be introduced and practised. ...
Welcome to the introductory course in digital design and computer architecture. In this course, we will embark on a journey into the world of digital systems, exploring the fundamental principles and concepts that underpin modern computing technology. ...