[ 921PECOCACV20 ] VL Computer Algebra for Concrete Mathematics

Workload Education level Study areas Responsible person Hours per week Coordinating university
3 ECTS M1 - Master's programme 1. year Computer Science Carsten Schneider 2 hpw Johannes Kepler University Linz
Detailed information
Original study plan Master's programme Computer Science 2021W
Objectives In this lecture basic skills and techniques will be elaborated which are relevant to simplify formulas related to enumeration. Special emphasis is put on tools that support the student for the analysis of algorithms (best case, worst case and average case). In particular, the participant gets acquainted to apply these computer algebra tools to non-trivial examples.
Subject The content of the lecture can be summarized by the following key words:

  • algorithmic treatment of formal power series;
  • c-finite and holonomic functions/sequences;
  • recurrence solving;
  • basic aspects of asymptotics;
  • symbolic summation.

A major emphasis of the lecture is to present the basic notions, to develop the basic ideas of the underlying algorithms and to put computer algebra into action for concrete examples.

Criteria for evaluation Oral exam.
Methods Blackboard presentation combined with Mathematica sessions where the introduced computer algebra tools are applied to non-trivial problems combing from combinatorics and the analysis of algorithms.
Language English
Study material Detailed lecture notes will be provided. In addition, many of the topics discussed in the lecture can be found in the book "Concrete Mathematics - A Foundation for Computer Science" by R.L.Graham, D.E.Knuth und O.Patashnik (Addison-Wesley, 1994) and "The Concrete Tetrahedron" by Manuel Kauers and Peter Paule (Springer Wien, 2011).
Changing subject? No
Corresponding lecture TM1WHVOANKO: VO Analytische Kombinatorik (3 ECTS)
Earlier variants They also cover the requirements of the curriculum (from - to)
201SYMRCACV12: VL Computer Algebra for Concrete Mathematics (2012W-2020S)
On-site course
Maximum number of participants -
Assignment procedure Direct assignment