This entry is from Winter semester 2022/23 and might be obsolete. You can find a current equivalent here.

# Probabilistic Combinatorics (dt. Probabilistische Kombinatorik)

 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): 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. Duration,frequency One semester, irregular Person in charge of the module's outline Prof. Dr. Volkmar Welker

## Contents

Positive probability to prove existence

1st and 2nd moment method

Erdös-Renyi model

Threshold functions

Lovasz Local Lemma

correlation inequalities

## Qualification Goals

Students can

• derive basic properties of combinatorial structures with the help of probabilistic methods,
• recognize combinatorial structures in different contexts and analyze them with the help of probabilistic methods.

They deepen

• the practice of mathematical methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof methods),
• in the recitation classes, their oral communication skills through discussion and free speech in front of an audience.

## Prerequisites

None. The competences taught in the following modules are recommended: either Elementary Stochastics [Bachelor Module] or Elementary Stochastics [Lehramt Module], Discrete Mathematics.

## Applicability

Module imported from M.Sc. Business Mathematics.

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

• B.Sc. Mathematics
• B.Sc. Business Mathematics
• M.Sc. Data Science
• M.Sc. Mathematics
• M.Sc. Business Mathematics

When studying M.Sc. Data Science, this module can be attended in the study area Advanced and Specialization Modules in Mathematics.

The module is assigned to the focus area Analytics. Further information on eligibility can be found in the description of the study area.