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This entry is from Winter semester 2019/20 and might be obsolete. You can find a current equivalent here.
Probability Theory
(dt. Wahrscheinlichkeitstheorie)
Level, degree of commitment | Specialization module, depends on importing study program |
Forms of teaching and learning, workload |
Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study) |
Credit points, formal requirements |
9 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination |
Language, Grading |
German,The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Business Mathematics. |
Origin | M.Sc. Business Mathematics, M.Sc. Business Mathematics |
Duration, frequency |
One semester, each winter semester |
Person in charge of the module's outline | Prof. Dr. Hajo Holzmann |
Contents
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
Qualification Goals
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.
Prerequisites
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].
Applicability
The module can be attended at FB12 in study program(s)
- B.Sc. Mathematics
- B.Sc. Business Mathematics
- M.Sc. Data Science
- M.Sc. Computer Science
- M.Sc. Mathematics
- M.Sc. Business Mathematics
- LAaG Mathematics
When studying M.Sc. Business Mathematics, this module can be attended in the study area Specialization and Practical Modules in Mathematics.
The module can also be used in other study programs (export module).
Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Angewandten Mathematics zugeordnet ist.
Recommended Reading
- 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
Please note:
This page describes a module according to the latest valid module guide in Winter semester 2019/20. 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:
- Winter 2016/17
- Summer 2018
- Winter 2018/19
- Winter 2019/20
- Winter 2020/21
- Summer 2021
- Winter 2021/22
- Winter 2022/23
- Winter 2023/24
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.