Probability theory plays a central role throughout applied mathematics and has become increasingly important in many areas of pure mathematics as well. This course provides a rigorous introduction to the foundations of modern probability theory and prepares students for further courses in probability, stochastic processes, and mathematical statistics.
Topics include: probability spaces, random variables, and independence, modes of convergence and zero–one laws, laws of large numbers and the central limit theorem, characteristic functions and weak convergence, conditional expectation, stable laws and large deviations, Brownian motion and the invariance principle.
Prerequisites:
This course builds on EWS (introductory probability) and Analysis III (measure theory). Some basic complex analysis will be used, pre-knowledge is not strictly required, but helpful.
Module: B.A. Modul 4: Wahlpflichtmodul - Zwei mittlere Vorlesungen jeweils aus dem Gebiet der Analysis und
der Algebra/Geometrie (Variante 2)
B.Sc. Modul 9a: Gebiet A (mündliche Prüfung)
B.Sc. Modul 9a: Gebiet Analysis (aktive Teilnahme)
B.Sc. Modul 9b: zwei mittlere Vorlesungen aus Gebiet B und C (Variante 2)
M.Ed. Modul 3: Fachwissenschaftliche Vertiefung
M.Sc. Modul 1 aus dem Gebiet Analysis
M.Sc. Modul 2 aus dem Gebiet Analysis
M.Sc. Modul 3 aus dem Gebiet Analysis
M.Sc. Modul 5: Spezialvorlesung
- Kursleiter/in: Tanja Schiffmann
- Kursleiter/in: Christoph Thäle
- Kursleiter/in: Jeroen Van Haastert