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Combinatorics (Small Specialization Module)
(dt. Kombinatorik (kleines Vertiefungsmodul))

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (3 SWS), recitation class (1 SWS) oder lecture (2 SWS), seminar (2 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements
6 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises or presentation with written assignment.
Examination type: Written or oral examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency
One semester,
irregular
Person in charge of the module's outline Prof. Dr. Volkmar Welker

Contents

Special combinatorial structures and their mathematical context are investigated. Specialized methods for the investigation of structures are developed and applied. The possible conclusions about the mathematical context in which the structures occur are worked out.


Qualification Goals

Students

  • are able to analyze specific combinatorial structures,
  • apply methods tailored to special combinatorial structures,
  • to recognize and investigate combinatorial structures in the context of other mathematical disciplines.

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 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, Discrete Mathematics, either Elementary Stochastics or Algebra. In addition, depending on the focus, the competences that are taught in one of the modules Elementary Stochastics or Algebra are recommended.


Recommended Reading

  • A. Björner, F. Brenti, Combinatorics of Coxeter groups, Springer, 2005.
  • B. Bollobas, Random graphs, Cambridge, 2001.
  • M. de Longueville, A course in topological combinatorics, Springer, 2012.



Please note:

This page describes a module according to the latest valid module guide in Sommersemester 2021. 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.