This entry is from Summer semester 2021 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): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination 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

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.

## 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 B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

The module is assigned to Pure Mathematics. Further information on eligibility can be found in the description of the study area.

• 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.