Computer Algebra for Concrete Mathematics
Summersemester 2019
Carsten.Schneider@risc.jku.at
| First lecture: |
Thursday |
5.3.2019 12:00 - 13:30 room:
HS12 |
In this lecture basic skills and techniques will be elaborated which are relevant
to simplify formulas related to enumeration, in particular, to carry out the average and worst case complexity analysis of algorithms.
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.
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).
Requirements: Basic knowledge from analysis and linear algebra.
Exercises
Meetings: Tuesday 11:00 - 11:45, room HS12, start: March 12
Exercise instructor: Silviu Radu (SilviuDOTRaduATriscDOTjkuDOTat)
The exercises will be stated in the lectures in form of "homeworks" and will be discussed one (or more) weeks later in the exercise class. Further details will be discussed in the lecture and exercise class.
Starting from March 26, the posed exercises will be collected in Exercises.pdf. (For HW51-HW53 see also HW51To53.nb and HW51To53.pdf.)
Some calculations using RISC packages from the combinatorics group can be found in the Mathematica notebook CADiscreteMath.nb (for a pdf version see CADiscreteMath.pdf).