In metric spaces a distance is defined between each pair of points. In topological spaces, distances are replaced by only a certain notion of nearness. This abstract setting sheds new light upon basic questions: What is continuity? When should we consider two spaces to be equal?
This course provides an introduction to probability theory - the mathematical study of randomness. The aim is to get to know the basic mathematical framework of probability theory, and to learn to think and argue in this framework.
This is an introductory course on Gaussian fields and processes - or more shortly, on Gaussian magic. By discussing both the general theory and concrete examples, we will try to understand where and how Gaussian processes appear, and how to study them.
This is an introductory course to the concentration of measure phenomenon - random functions that depend on many random variables tend to be often close to constant functions.