Probability Theory

Prerequisites:

Fundamental Algebra and Analysis II

Course description: 

This course is an introduction to the mathematical theory of probability. It aims to help students familiarize themselves with the language and reasoning of modern probability, appreciate its way of thinking and its connections with other subjects in mathematics and science. We will work with some measure theory, but emphasis will be placed on correctly understanding the languages/concepts, and developing the ability to identify and use well known theorems in possibly sophisticated situations.

Detailed topics include:

1. Probability space, events, etc.;

2. Discrete and continuous random variables, distribution and density functions;

3. Independence, conditioning, etc.;

4. Limit theorems – laws of large numbers, central limit theorem, (Cramer's theorem of) large deviations;

5. Markov chains;

6. Further selected topics (depending on the instructor).