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This entry is from Winter semester 2018/19 and might be obsolete. No current equivalent could be found.

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

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

Contents

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.

Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen und im Aufbaumodul Diskrete Mathematik vermittelt werden, sowie ggf. je nach Schwerpunktsetzung eines der Aufbaumodule Elementare Stochastik oder Algebra.


Applicability

Module imported from M.Sc. 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 Reinen Mathematics zugeordnet ist.


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 Winter semester 2018/19. 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.