|Level, degree of commitment in original study programme||Advanced module, compulsory elective module|
|Forms of teaching and learning,
|Lecture (4 SWS), recitation class (2 SWS), |
270 hours (90 h attendance, 180 h private study)
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
|German,The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Business Mathematics.|
|Original study programme||M.Sc. Wirtschaftsmathematik / Mathematische Vertiefungs- und Praxismodule|
|One semester, |
each winter semester
|Person in charge of the module's outline||Prof. Dr. Hajo Holzmann|
The basic concepts of probability theory, based on measure and integration theory, are discussed, in particular
- General probability spaces, random variables
- Independence, laws of large numbers
- weak convergence, characteristic functions and central limit theorem
- conditional expectations, conditional distributions, martingales
- stochastic processes, in particular Brownian motion
The students shall
- learn the basics of probability theory in a mathematically rigorous way, based on measure theory,
- practice mathematical methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof methods),
- improve their oral communication skills in the recitation classes by practicing free speech in front of an audience and during discussion.
None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Measure and Integration Theory, either Elementary Stochastics [Bachelor Module] or Elementary Stochastics [Lehramt Module].
- Bauer, H., „Wahrscheinlichkeitstheorie“, de Gruyter 2004.
- Billingsley, P., „Probability and Measure“, John Wiley & Sons 1995
- Durrett, R., „Probability Theory and Examples“, Wadsworth & Brooks 1991
- Klenke, A., „Wahrscheinlichkeitstheorie“, Springer 2008
This page describes a module according to the latest valid module guide in Wintersemester 2022/23. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:
- WiSe 2016/17 (no corresponding element)
- SoSe 2018 (no corresponding element)
- WiSe 2018/19
- WiSe 2019/20
- WiSe 2020/21
- SoSe 2021
- WiSe 2021/22
- WiSe 2022/23
The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.
The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.