Magic squares and beyond
(Prof. Dr. Anke Pohl)
Magic squares are quite famous objects. These square matrices consist of pairwise different positive integers such that the sum of the numbers in each row, column, and in both main diagonals always equals the same number. Magic squares can be obtained by solving linear systems of equations (over the integers).
The goal of this project is to generalize or modify observations about magic squares. This can be done, for example, by placing additional conditions on the numbers (e.g. only using square numbers) or trying to complete cubes instead of squares, or not solving over integers, but other rings. There are no limits to your imagination. Some suggestions can be found here:
Numberphile's youtube series
Basic knowledge from analysis and linear algebra is recommended for completing this project. Depending on which direction you choose, you may need in-depth knowledge of other areas. The project should take at least four weeks to complete as a group, and includes both a written paper and a presentation.