16 November 2020

Research-based teaching in experimental mathematics


Closer integrating research in teaching is a focus area for the University of Copenhagen. It is now being tested at the Department of Mathematical Sciences in the field of Experimental Mathematics.

The textbook in Experimental Mathematics and Søren Eilers
The textbook in Experimental Mathematics and Søren Eilers

Master's students have for a number of years been able to take the course "Experimental Mathematics (XM)", which this year started on 16/11 2020. The course is taught and developed by Søren Eilers, who also wrote the textbook. This year, some extra vitamins are added to XM, as Søren has received a share of UCPH's funds for experiments with research integration in teaching.

UCPH’s ambition is that all students must have the opportunity to get in touch with research during their education, and that research integration must be clearly present in all programs.

It is not so easy when it comes to teaching pure mathematics. As a consequence of the pyramidal structure of pure mathematics, the distance to the research front here is very great, and it is traditionally only at the thesis writing that the students can hope to study open-ended questions.

However, it has since the inception of the course Experimental Mathematics been a central ambition to give the course participants the opportunity in project work to study open questions in pure mathematics using computer-based experimentation.

A project catalogue has been produced from which the participants have chosen projects, and it has often proved possible for the participants to generate new insights experimentally. However, as such projects only extend over a few weeks, it has been necessary to complete them before this insight could be made the subject of publication.

This leaves an untapped potential for research integration at the highest level, which is now sought to be realized by partly providing more time for the students to immerse themselves in the issues, and partly by creating a framework for actual publications with students as co-authors.

The grant from the University of Copenhagen makes it possible to hire an additional part-time lecturer to further develop the project catalogue and to be in charge of preparing two actual articles together with former students on the course.

Next year, the pilot project will lead to a new bachelor's course "Introduction to Experimental Mathematics", co-taught with the existing master's course. This creates a clear profile for experimental bachelor projects in the education in mathematics. In parallel, the possibility of making the master's course part of the new education in Quantum Science is being considered.

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