**Outline:**

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

Individual and statistical descriptions

The Pólya urn process

The Ehrenfest–Brillouin model

Applications to statistical physics

Applications to stylized models in economics and finance

The Ewens sampling formula

The Zipf–Simon–Yule process

Computer-based sessions on Monte Carlo will complement the theoretical material

simulations of the processes and models introduced in the course.