**Computer Algebra for Concrete Mathematics**

### Summer Semester 2021

#### Carsten.Schneider@risc.jku.at

*First lecture: * |
Thuesday |
9.3.2021 12:00 - 13:30 ** we start via Zoom ** |

The Zoom-link can be found on the moodle page.
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 books
- "Concrete Mathematics - A Foundation for Computer Science" by R.L.Graham, D.E.Knuth und O.Patashnik (Addison-Wesley, 1994)
- "The Concrete Tetrahedron" by Manuel Kauers and Peter Paule (Springer Wien, 2011).

Requirements: Basic knowledge from analysis and linear algebra.

The lecture notes will be enhanced step wise and will be found here: LectureNotes.pdf; a supplementing Mathematica notebook can be found here. In addition, the lecture will be recorded (at least as long as we are in the zoom-modus). The movies can be found on the moodle pages

https://moodle.jku.at/jku/course/view.php?id=14886#section-1

In case that some content is unclear, feel free to contact me. I will try to
answer all your questions, and will incorporate the answers also into the lecture
notes.
## Exercises

The exercises will be stated in the lectures in form of "homeworks".
*Unfortunately, there will be no physical exercise classes. Whenever you are ready
(preferable the week after the lecture),
send your worked out examples via Email to Silviu Radu. He will look at them and
will send you his feedback.*

Exercise instructor: Silviu Radu (SilviuDOTRaduATriscDOTjkuDOTat)

The posed exercises are collected in Exercises.pdf.