Metric and topological spaces

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?

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Probability

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.

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Gaussian processes

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.

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Concentration of measures

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.

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