This entry is from Winter semester 2018/19 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 LAaG Mathematics, this module can be attended in the study area Advanced Modules.

Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Angewandten Mathematics zugeordnet ist.

• 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