German original

# 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,workload Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study) Credit points,formal requirements 9 CP Translation missing. German original: Studienleistung: Erreichen von mindestens 50 Prozent der Punkte aus den wöchentlich zu bearbeitenden Übungsaufgaben. Prüfungsleistung: Klausur oder mündliche Prüfung 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

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.

• 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.