Currently offered projects

Projects for Winter 2025

  • Mathematical Magic ()
    Description:

    The purpose of this project is to understand existing magical tricks based on mathematics, experiment with them, explain them, and, very important, come up with new ones, as variations of existing ones. There are magic tricks based only on linear algebra, others need some group theory or more advanced algebra.

    Goal:

    In the project, several magic tricks based on mathematics shall be explored, presented and explained. Moreover, new ones shall be found and experimented with.

    The outcome could be as follows:

    The project report should contain some general mathematical background. The core could be that for each magical trick, precise instructions for the magician are given, and, separately, a full mathematical explanation should be included. Another nice output would be two videos for each magic trick: one showing it, one explaining it.

    Literature:

    E. Behrends, Mathematik und Zaubern - ein Einstieg für Mathematiker. Springer, Spektrum, 2017 One finds many resources (also in French and English) on the internet.

    supervisor: Gabor Wiese

  • Kakeya Needle Problem: Numerical Constructions and Experimental Investigations ()
    Description:

    This project focuses on implementing and visualising discrete versions of Kakeya (Besicovitch) sets, exploring their geometric properties, estimating their area and fractal dimensions, and optionally investigating finite-field variants.

    More details here

    supervisor: Thomas Lamby

  • The Fibonacci Word Fractal: Construction and Geometric Properties ()
    Description:

    This project aims at constructing the Fibonacci word fractal computationally, producing visualisations and animations, and estimating its fractal dimension and the geometry of its boundary. As an extension, students may also investigate Fibonacci tilings.

    More details here

    supervisor: Thomas Lamby

  • Gaps between Pythagorean triples ()

    supervisor: Mike Daas

  • Plank problem ()

    supervisor: Alexey Balitskiy

  • Sections of the cube ()

    supervisor: Szabi Buzogány, Wai Yeung Lam

  • Muffin or Chihuahua? ()
    Description:

    Nowadays, deep learning models can solve difficult tasks that would normally require a lot of time for human beings. In this project, we will study the basics of neural networks and implement a model capable of distinguishing between a muffin and a chihuahua.

    More details here

    supervisor: Francesca Pistolato, Luís Maia

  • Mathematical Modeling of Voting Systems ()
    Description:

    Study the basics about Theory of Voting. After that, focus on two apportionment method for allocating seats in a parliament and study their characteristics and differences. In the next step, both methods will be implemented computationally. Finally, simulations will be used to compare their proportionality and to explore how outcomes change under different voting system characteristics (varying number of seats, legal thresholds, comparing two-party versus multi-party systems,...)

    More details here

    supervisor: Francesca Pistolato, Luís Maia

  • Simulation of Gaussian Random Functions ()

    supervisor: Felix Benning, Francesca Pistolato, Luís Maia