Information on the lecture Probability Theory (SS 2025)

Lecture: Tue, Thu, 10-12 a.m., HS Weismann-Haus, Albertstr. 21a

Exercise: 2 hours, date to be determined

Written exam: date to be announced

Language: english

Current

Content

The problem of axiomatizing probability theory was solved by Kolmogorov in 1933: a probability is a measure of the set of all possible outcomes of a random experiment. From this starting point, the entire modern theory of probability develops with numerous references to current applications.

The lecture is a systematic introduction to this field based on measure theory and includes, among other things, the central limit theorem in the Lindeberg-Feller version, conditional expectations and regular versions, martingales and martingale convergence theorems, the strong law of large numbers and the ergodic theorem as well as Brownian motion.

Exercise groups

There will be an exercise group to discuss the solutions of the weekly exercises. The time for these meetings will be found in accordance with the participants. The exercise group meets for the first time in the second week of the semester.

Exercise sheets

There will be weekly exercise sheets that have to be handed in. The exact date for this is decided depending on the time of the exercise groups. The first exercise sheet is issued in the first week of the semester.

Previous knowledge

Literature

Will be announced in the lecture.

Usability

Wahlmodul im Optionsbereich (2HfB21)
Wahlpflichtmodul Mathematik (BSc21)
Mathematische Vertiefung (MEd18, MEH21)
Angewandte Mathematik (MSc14)
Wahlmodul (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)

Consultation hour

Lecturer consultation hours: Tuesday, 4 p.m. (or by arrangement)
Consultation hour assistant: Tuesday, 2 p.m. (or by arrangement)