Teaching Programming for Mathematical Scientists

TL;DR

This paper reviews the integration of programming, computer algebra, and numerical computation in mathematics education, discussing their evolution towards AI applications and sharing practical course design insights.

Contribution

It provides a reflective analysis of course designs combining programming and mathematics, highlighting their relevance to AI in mathematics education.

Findings

Programming enhances understanding of mathematical concepts.

Course experiences inform AI integration strategies.

Theoretical insights support practical teaching approaches.

Abstract

Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics courses. These activities are, in some important ways, natural precursors to the use of Artificial Intelligence in Mathematics Education. This paper reflects on some of our course designs and experiences and is therefore a mix of theory and practice. Underlying both is a clear recognition of the value of computer programming for mathematics education. We use this theory and practice to suggest good techniques for and to raise questions about the use of AI in Mathematics Education.