Fachbereich 10 Institut für Mathematik Vorlesungsankündigung für das SS 18 Prof. Dr. Wolfram Koepf

# Computer Algebra I und II

 Veranstaltung SWS Tag Zeit Ort/Raum Dozenten Beginn Vorlesung 2 2 Dienstag Donnerstag 9-11 Uhr 9-11 Uhr HPS / R. 2404 Wolfram Koepf 10.04.18 Übung 2 Freitag 9-11 Uhr HPS / R. 2421 / PC-Pool Daniel Tcheutia 13.04.18

Geeignet für: Bachelor Mathematik, Lehramt Gymnasium, Bachelor Physik, Bachelor und Master Informatik.

Abstract:
This lecture will be presented in English language and covers in the first half of the semester the topic "Computer Algebra I" and in the second half the topic "Computer Algebra II". Those who want to cover only one of these parts should contact the lecturer to get informed about the ending and starting times.

Computer Algebra I:
Computer algebra deals with algebraic algorithms which are available in computer algebra systems like DERIVE, Maple or Mathematica and also in scientific calculators like the TI 89 and others. In future every high school teacher must be aware that he has to deal with computer algebra in his work. Also in many business branches computer algebra plays a more and more important role. Therefore this lecture is recommended to every Mathematics student, but also to students of Physics. The lecture is compulsory for Bachelor Mathematics (Modul BM 6), obligatory for Anwendungsgebiet Computational Mathematics in the Bachelor Computer Science as well as compulsory for Lehramt Mathematik L3 (Modul MAL 3-5). Finally the lecture can be used in the module "Vertiefung in Mathematik/Elektrotechnik" for the Master Computer Science.

The lecture contains basic algorithms and their backgrounds. In the excercises we work with Mathematica. Here the internal features are used as well as the embedded programming language which we use to implement algebraic algorithms.

Topics:
1. Capabilities of General Purpose Systems
2. Programming in Computer Algebra Systems
3. Number Systems and Arithmetics of Integers and Polynomials

Computer Algebra II covers applications from Discrete Mathematics and Analysis:

4. Simplification and Normal Forms
5. Taylor Polynomials and power series
6. Algorithmic summation
7. Algorithmic integration

The last chapter is only covered if time permits. The Exercises are delivered in the PC pool. We will use the computer algebra system Mathematica in the Exercises.

 Literatur: Koepf, Computeralgebra. Eine algorithmisch orientierte Einführung. Springer, 2006 Voraussetzungen: Hörer der Vorlesung Grundlagen der Algebra und Computeralgebra, aber auch interessierte Bachelor-, Diplom- bzw. Gymnasialstudenten sowie Studenten des Bachelor-Studiengangs Informatik mit Vertiefung Computational Mathematics und des Masterstudiengangs Informatik. Bemerkung Die Vorlesung wird so gestaltet, dass auch Interessenten, die die Vorlesung Grundlagen der Algebra und Computeralgebra nicht gehört haben, teilnehmen können. Lehramtsstudenten L3 können jede der beiden Veranstaltungen Computeralgebra I und II  für das Modul MAL 3-5 verwenden. Leistungsnachweis: Regelmäßige Teilnahme an den Übungen, 50% korrekt bearbeitete Aufgaben und mündliche Prüfung oder Klausur.