What was the question?
This mentorship program had the format of a reading course. We read great part of the book Dynamics, Statistics and Projective Geometry of Galois Fields by V. Arnold.
What motivated me?
I wanted to engage in something that had to do with number theory and that the students could understand and explore. I was trying to pick something that had experimentation in it.
What did the students do?
Luckily for us, the students knew how to program quite well. Thus, they could make very big experiments regarding the matrices that are studied in the book. Then we used these to find patterns and make conjectures. It was a very experimentation based project.
Special moments I remember 🙂
At some point we noticed a pattern related to certain matrices. We tested it many times, but we could never come up with a proof of it. This was very rewarding, because we found something by experimentation that we were not expecting and that we could treat as a problem/conjecture to chase. It was even more surprising we did not find a proof!
Outcomes of the work
The students presented the experiments in their final project. They discussed the predictions we could not prove.
Malors 