Computer Algebra I

Adapted to: Bachelor Modul B6 / B8, Lehramt Modul MAL 3-5, Bachelor Physik, Bachelor und Master Informatik.

Abstract:
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 TI89 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 the application field 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 exercises 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:

• Capabilities of General Purpose Systems
• Programming in Computer Algebra Systems
  
• Arithmetic of  Integers and Polynomials
  
• Factorization of Polynomials