# Discrete Geometry (dt. Diskrete Geometrie)

 Level, degree of commitment Advanced module, depends on importing study program Forms of teaching and learning,workload Lecture (3 SWS), recitation class (1 SWS) or lecture (2 SWS), seminar (2 SWS), 180 hours (60 h attendance, 120 h private study) Credit points,formal requirements 6 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination (individual examination) Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics. Origin B.Sc. Mathematics Duration,frequency One semester, irregular Person in charge of the module's outline Prof. Dr. Volkmar Welker

## Contents

Basic sets of convex geometry (e.g. Helly, Radon, separation sets). Simple transformations of convex sets (e.g. polarity, duality). Definition and basic properties of polytopes. Interrelationships with optimization. Side structure of polytopes.

## Qualification Goals

Students will

• understand basic principles of discrete geometry,
• grasp phenomena of geometry in spaces of any dimension using the objects of discrete geometry,
• recognize the geometric background of linear and convex optimization.
• have practiced mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, reasoning),
• have improved oral communication skills in exercises 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.

## Applicability

The module can be attended at FB12 in study program(s)

• B.Sc. Data Science
• B.Sc. Mathematics
• M.Sc. Computer Science
• M.Sc. Mathematics
• LAaG Mathematics
• BA Minor Mathematics

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

The module can also be used in other study programs (export module).