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, depends on importing study program 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. Subject, Origin Mathematics, 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.

• 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.