Information on the lecture Probability Theory (SS 2025)

Lecturer: Prof. Dr. Angelika Rohde

Assistant: Dr. Johannes Brutsche

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

Exercise: 2 hours, Mo 8-10 a.m., SR 404, Ernst-Zermelo-Straße 1

Written exam: 22nd September 2025, 10-12 a.m.

Language: english

Current

• On Monday 28th of April, the exercise class is replaced by an additional lecture (in room 404).
• The final exam will be written on the 22nd September 2025 from 10-12 a.m. Further information will follow.

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. This exercise group is taking place on Monday 8-10 a.m. in SR 404 in the Institute of Mathematics, Ernst-Zermelo-Straße 1.

Lecture notes

• Lecture notes (Tuesday, April 29)
  
  Profound knowledge on measure theory as taught in Analysis III is taken for granted. Here are the lecture notes of Peter Pfaffelhuber's bridging course on measure theory (MSc Data and Technology).
  
  

Exercise sheets

There will be weekly exercise sheets that have to be handed in. They will be issued on Thursdays, starting in the first week of the semester.

Please hand in your exercise sheet using the yellow mailbox 3.09 in the basement of the Institute of Mathematics.

You are allowed to hand in your solutions in groups of two.

Literature

• Achim Klenke, Probability Theory: A comprehensive course, 3rd ed. 2020, Springer
• Heinz Bauer, Probability theory, 1996, de Gruyter

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)