This entry is from Winter semester 2016/17 and might be obsolete. You can find a current equivalent here.

# Probability Theory (dt. Wahrscheinlichkeitstheorie)

 Level, degree of commitment Specialization module, compulsory elective module 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): Written or oral examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises. 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. 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

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen und in den Aufbaumodulen Maß- und Integrationstheorie und Elementare Stochastik vermittelt werden

## Applicability

Module imported from M.Sc. Business Mathematics.

It can be attended at FB12 in study program(s)

• B.Sc. Mathematics
• M.Sc. Data Science
• M.Sc. Computer Science
• M.Sc. Mathematics
• LAaG Mathematics

When studying M.Sc. Computer Science, this module can be attended in the study area Minor subject Mathematics.

• 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