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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
  • B.Sc. Business Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • M.Sc. Business 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).


Recommended Reading

  • Ziegler, G.M., Lectures on Polytopes (Graduate Texts in Mathematics), Springer, 1995
  • Barvinok, A., A Course in Convexity, Graduate Studies in Mathematics, Volume: 54, Amer. Math. Soc, 2002



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. 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.