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Combinatorics (Large Specialization Module)
(dt. Kombinatorik (Großes Vertiefungsmodul))

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
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
One semester,
Person in charge of the module's outline Prof. Dr. Volkmar Welker


Basic combinatorial structures (e.g. set systems, graphs, etc.) are introduced and their central properties are derived. The competence for a deeper analysis of the structures is imparted by means of extreme, probabilistic, geometric or algebraic methods.

Qualification Goals

Students can

  • derive basic properties of combinatorial structures,
  • recognize and analyze combinatorial structures in different contexts,
  • apply methods from other areas of mathematics to the analysis of combinatorial structures.

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.


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 [Bachelor Module] or Elementary Stochastics [Lehramt Module] or Algebra [Bachelor Module] or Algebra [Lehramt Module]. In addition, depending on the focus, the competences that are taught in one of the modules Elementary Stochastics or Algebra are recommended.

Recommended Reading

  • N. Alon, J. Spencer, The probabilistic method, Wiley, 2008.
  • I. Anderson, Combinatorics of finite sets, Dover, 2011.
  • S. Jukna, Extremal combinatorics, Springer, 2011.
  • B. Sturmfels, E. Miller, Combinatorial commutative algebra, Springer, 2005.

Please note:

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