This course provides an overview of key advances in continuous optimization and statistical analysis for machine learning. We review recent learning formulations and models as well as their guarantees
The course provides an introduction to scientific computing. Several numerical methods are presented for the computer solution of mathematical problems arising in different applications. The software MATLAB is used to solve the problems and verify the theo ...
The students will learn key numerical techniques for solving standard mathematical problems in science and engineering. The underlying mathematical theory and properties are discussed. ...
The aim of the course is to review mathematical concepts learned during the bachelor cycle and apply them to concrete problems commonly found in Engineering, and Materials Science in particular. ...
We will give an overview of the field of Artificial Life (Alife). We study questions such as emergence of complexity, self-reproduction, evolution, both through concrete models and through mathematical results. We will describe some of the most influential ...
This course presents the problem of static optimization, with and without (equality and inequality) constraints, both from the theoretical (optimality conditions) and methodological (algorithms) point of view. Economics and financial applications are provi ...
In this lecture series some important objects of random geometry are introduced and studied. In particular, the relation between the Gaussian free field and random walks / Brownian motions is explored. This provides a toolbox of techniques for studying mat ...
This course is in the form of a reading course / working group. We will focus on some mathematical aspects of the theory of neural networks, including universal approximation theorems, connections to ODEs and PDEs, optimiza-tion algorithms for NN training ...