The theme of this course is the allocation of n objects (or elements) into g categories (or classes), discussed from several viewpoints. This approach can be traced back at least to the early work of 24-year-old Ludwig Boltzmann in his first attempt to derive Maxwell’s velocity distribution for a perfect gas in probabilistic terms. We shall start with descriptions of the world as facts (taking place or not), and events as propositions (true or not) about facts (taking place or not). Not everything in the world is known, and a set of possibilities remains. For this reason, events can be probabilized and probability theory plays a fundamental, but often underestimated, role in our scientific theories. Indeed, it turns out that many important problems in statistical physics and some problems in economics and finance can be formulated and solved using these methods.

Syllabus: The following topics will be addressed