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 ...
The most important clinical diagnostic and therapeutic applications of light will be described. In addition, this course will address the principles governing the interactions between light and biological tissues, their optical properties and basic concept ...
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. ...
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. ...
We cover the theory and applications of sparse stochastic processes (SSP). SSP are solutions of differential equations driven by non-Gaussian innovations. They admit a parsimonious representation in a wavelet basis and are relevant to coding, compressed se ...
The course focuses on mathematical models based on PDEs with random parameters, and presents numerical techniques for forward uncertainty propagation, inverse uncertainty analysis in a Bayesian framework and optimal control under uncertainty. ...
Probabilistic proof system (eg PCPs and IPs) have had a tremendous impact on the theoretical computer science, and have also found practical uses. They underlie delegation of computation protocols and hardness of approximation. This course covers the found ...
This course offers an introduction to numerical methods for the solution of mathematical problems as: solution of systems of linear and non-linear equations, functions approximation, integration and differentiation and solution of differential equations. ...