### Timetable

### Description

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Analysis I-II, Topology I, Vector analysis I, Measure and integral

Vector analysis II, Probability II.

The course gives a firm theoretical ground for Probability and introduces some of its classical results

Recommended time/stage of studies for completion: 1. year

Term/teaching period when the course will be offered: varying

Measure theoretic foundations of probability, independence, laws of large numbers, characteristic functions and the central limit theorm, Gaussian measures, recurrence/transience of random walks

Lecture notes; D. Williams: "Probability with martingales", R. Durrett: "Probability: theory and examples"

Lectures and exercise classes, possibly other methods like reading assignments+discussion

Exam and excercises, Course will be graded with grades 1-5

Exam, other methods will be described later