**Computer Algebra for Concrete Mathematics**

### Summer Semester 2020

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

*First lecture: * |
Thuesday |
3.3.2020 12:00 - 13:30 ** room:
**HS6 |

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.

The e-Lectures for
- March 17, 2020
- March 24, 2020
- March 31, 2020
- April 21, 2020
- April 28, 2020
- May 05, 2020
- May 12, 2020
- May 19, 2020
- May 26, 2020
- June 9, 2020
- June 16, 2020
- June 23, 2020
- June 30, 2020

can be found here: LectureNotes.pdf.

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 (marked in a special form so that you can find them easily).
## Exercises

*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 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.

The posed exercises are collected in Exercises.pdf.