04-10-0600-vu Selected Topics in Logic: Algorithmic group theory

Instructors: Prof. Dr. rer. nat. Pascal Schweitzer; M.Sc. Thomas Schneider

Event type: Lecture & Exercise

Org-unit: Dept. 04 - Mathematics

Displayed in timetable as: 04-10-0600

Subject:

Crediting for:

Hours per week: 6

Language of instruction: Englisch

Min. | Max. participants: - | -

Digital Teaching:
The course is entirely digital.
The lecture will consist of videos available online.
The exercises will be help via video conference.

Course Contents:
Various ways to encode groups in a computer.

Algorithms for the computation of elementary properties and objects within group such element order, order of groups, suitable generating systems. The focus lies on algorithms for permutation groups.

Literature:
Lecture Notes.
Seress, Ákos. Permutation group algorithms. Vol. 152. Cambridge University Press, 2003.
Holt, Derek F., Bettina Eick, and Eamonn A. O'Brien. Handbook of computational group theory. CRC Press, 2005.

Official Course Description:
Upon successful completion of the module, students will be able to

• explain the theoretical basics of handling of groups,
  
• explain the operation of efficient algorithms which are used for calculation in groups and the limits of computability in this context,
  
• use computer algebra systems for handling groups,  
  
• to clarify the limits of computability and efficiency of algorithms when dealing with algebraic objects at concrete problems.
  
• Know different ways of encoding groups in the computer.  
  
• Design algorithms for calculating elementary properties and objects in groups such as order of elements, order of group and favorable generating systems.
  

Online Offerings:
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