Computer Algebra Systems

Table of Contents

1 General Information

Spezialvorlesung Symbolisches Rechnen: Computeralgebrasysteme.
Dr. Johannes Middeke
jmiddeke (AT)

2 Summary

This course provides an introduction into working with computer algebra systems from a users perspective. We will discuss the popular systems Maple, Mathematica, and Sage.

In particular, for each system we will concentrate on

  • the user interface,
  • entering and manipulating basic expressions,
  • common use case (solving equations, computing derivatives, computing integrals, etc),
  • extended examples from various areas of mathematics,
  • basic programming (repetition, control flow),
  • extending the system with our own functions.

We will not cover the mathematical theory behind computer algebra. For this, please refer to Prof. Winkler's course or the general curriculum at RISC.

3 Time and Room

The time for the lecture is going to determined together with the students.

4 Materials

This section will contain course material such as the Maple worksheets and Mathematica notebooks presented during the lectures. It will be frequently updated.

5 Format

The course is held as a lecture. All classes will be taught in English.

6 Prerequisites

We do not require any special knowledge in (computer) mathematics or any previous experience with programming.

7 Grading

Students can obtain a grade in this course

  • either by giving a presentation about a computer algebra system of their choice (other than the ones already covered in the lecture)
  • or by taking a written exam.

A presentation should give a general introduction to the chosen computer algebra system and provide a comparison to the system discussed in the lecture. In particular, the student should explain the main focus of the system, its limitations (if any) and the facilities for programming. The exam will contain questions about basic expression manipulation and programming section. It will be a closed book exam. Its date will be fixed after consultation with the students.

8 Access to Computer Algebra Systems

We will set up a temporary accounts for students on the RISC computers. There the students will have access to the latest versions of Maple, Mathematica, and Sage, as well as a couple of other computer algebra systems. Details will be given in class.

Alternatively, student licences for Mathematica are available for 25€/year from the JKU IT services. See Software for Students.

Sage is free software. For instructions on how to install it please refer to the Sage download and installation guide. Additionally, it is possible to use online Sage services in a browser as, for instance, SageMathCell or SageMathCloud.