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This entry is from Winter semester 2021/22 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

The module 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. 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).

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


Recommended Reading

  • Depending on topic



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2021/22. 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:

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.