Detailed information 
Original study plan 
Master's programme Computer Science 2021S 
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 nontrivial examples.

Subject 
The content of the lecture can be summarized by the following key words:
 algorithmic treatment of formal power series;
 cfinite 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 nontrivial 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 (AddisonWesley, 1994) and
"The Concrete Tetrahedron" by Manuel Kauers and Peter Paule (Springer Wien, 2011).

Changing subject? 
No 
Corresponding lecture 
^{(*)}201SYMRCACV12: VL Computer Algebra for Concrete Mathematics (3 ECTS)
