Title: Computer Algebra: A Tool of Today for the Mathematics of Yesterday

Author: Franz Lichtenberger* (franz.lichtenberger@scch.at)

Affiliation: Research Institute for Symbolic Computation, Hagenberg, Austria

Abstract: There is no doubt that teaching mathematics, especially for students in the classical engineering disciplines, can substantially be enhanced by the uses of computer algebra systems. From my experience in teaching math to software engineering students I have learned that this kind of traditional, calculus-based mathematics and the tools of today are inappropriate. More than that: I believe that extensive use of these tools deteriorates their ability to use a more formal, abstract, axiomatic kind of mathematics, which is essential for software engineers. As an example I will show what kind of mathematics is needed to define the notion of "abstract data type" in a precise way, which is central in programming. Since software and thus software engineering will gain even more importance in everyday life and in economy, math education of the future should adapt to these new needs. I will also give my views on what kind of tools should be developed for tomorrows mathematics, based on the computer algebra systems of today.