Inhalt

[ 201COMAAKOV18 ] VL Algorithmic Combinatorics

Versionsauswahl
(*) Unfortunately this information is not available in english.
Workload Education level Study areas Responsible person Hours per week Coordinating university
3 ECTS B2 - Bachelor's programme 2. year Mathematics Carsten Schneider 2 hpw Johannes Kepler University Linz
Detailed information
Original study plan Bachelor's programme Technical Mathematics 2025W
Learning Outcomes
Competences
The students are familiar with basic skills and techniques that are relevant to simplify formulas related, e.g., to enumeration problems and the analysis of algorithms. In particular, the participant gets acquainted to computer algebra algorithms and to apply them to non-trivial examples.
Skills Knowledge
  • Manipulating formal power series with classical and algorithmic tools [K2,K5];
  • Algorithmic treatment of hypergeometric sequences and the understanding of the basic algorithms [K2,K4,K5] (summation, recurrence solving);
  • Understanding of the basic properties of C-finite sequences [K2] and the most relevant algorithms (rational representation, closure properties, recurrence solving) [K3,K4,K5];
  • Applying closure properties to holonomic functions/sequences and understanding of the underlying algorithmic toolbox [K2,K3,K5];
  • Understanding of basic aspects in asymptotics [K2,K3];
Formal power series and Laurent series with operations such as inversion, composition and formal limits, poynomial summation, Gosper's algorithm, Petkovsek's algorithm, asymptotics.
Criteria for evaluation Oral or written exam at the end of the semester.
Methods Blackboard- or Zoom-presentation (depending on pandemic situation); usage of computer algebra tools.
Language (*)Deutsch - but could be English, provided there is general agreement.
Study material "The Concrete Tetrahedron" by M. Kauers and P. Paule, also other books.
Changing subject? No
Corresponding lecture (*)ist gemeinsam mit 201UCMAAKOU18: UE Algorithmische Kombinatorik (1,5 ECTS) äquivalent zu
TM1PEKVINFO: KV Informationssysteme (3 ECTS) +
[ Lehrveranstaltung aus dem Wahlfach h. Symbolisches Rechnen (1,5 ECTS) oder
Lehrveranstaltung aus dem Wahlfach i. Logik (1,5 ECTS) oder
Lehrveranstaltung aus dem Wahlfach j. Algebra und Diskrete Mathematik (1,5 ECTS) ]
On-site course
Maximum number of participants -
Assignment procedure Direct assignment