Modul

Leistungsnachweis in der semesterbegleitenden Übung plus mündliche Prüfung im Umfang von 20 min

The aim of the course is to give a gentle introduction to group theory from a computational point of view. The students will learn not only the mathematical theory, but also how to think in terms of the computational feasibility. As a result students will develop computational understanding for questions within group theory.

After successful participation students can

• understand the difference between construction and definition by property
• understand how scaling of the computational problems influences the choice of algorithms and data structures
• choose the correct algorithms and data structures balancing speed and storage to obtain computational feasibilty
• exploit the structure of permutation groups to quickly find (some or all) elements satisfying requested properties.
• understand the basics of the theory of automata and their role for computation in finitely presented groups
• use string-rewriting algorithms to potentially solve the word problem in (some) finitely presented groups.

Keine

1. Group actions, orbits, stabilizers, Schreier vectors
2. Permutation groups, bases, Stabilizer chains, Schreier-Sims algorithm.
3. Broad overview of transitive groups, primitive groups
4. Finitely presented groups, their homomorphisms, quotients
5. Formal languages, and rewriting systems
6. Knuth-Bendix completion
7. Automata for problems in finitely presented groups
8. Coset enumeration, subgroups and their presentation

Grundkenntnisse in der Gruppentheorie und in der Programmierung werden dringend empfohlen.

Gesamter Arbeitsaufwand: 240 Stunden

Präsenzzeit: 90 Stunden

• Lehrveranstaltung einschließlich studienbegleitender Modulprüfung

Selbststudium: 150 Stunden

• Vertiefung der Studieninhalte durch häusliche Nachbearbeitung des Vorlesungsinhaltes
• Bearbeitung von Übungsaufgaben
• Vertiefung der Studieninhalte anhand geeigneter Literatur und Internetrecherche
• Vorbereitung auf die studienbegleitende Modulprüfung