Mentors: Anna Schilling, Florent Schaffhauser 

Team members: Sywon Jin

Description: The second topic we considered was the prove assistant LEAN. We got to know the Lean programming language, which is also used to formulate and check mathematical proofs. Hereby we solved several exercises from a seminar on Lean.

Mentor: Anna Schilling, Florent Schaffhauser

Description: This week it was all about different aspects of symmetry: the Rubik's Cube and group theory on the one hand side, and aperiodic tilings on the other hand side. 

The Rubiks Cube can be described using group theory, especially with the symmetric group. To do this, we first looked at groups in general and then specifically at the symmetric group $S_n$. We also had to figure out how to uniquely describe a cube mathematically. We were then able to devote ourselves to the proof of the “solvability theorem”, which clearly characterizes how you can tell from a twisted cube whether it is solvable.
 

In the second part of the internship we looked at aperiodic tilings, especially the Penrose tiling with kites and darts and the Einstein tile. Here we found out how the tiling is created and why it is aperiodic.

Mentor: Anna Schilling 

Team members: Thomas Bergunder

Description: This week it was all about the Rubik's Cube, which can be beautifully described using group theory. To do this, we first looked at groups in general and then specifically at the symmetric group $S_n$. We also had to figure out how to uniquely describe a cube mathematically. We were then able to devote ourselves to the proof of the “solvability theorem”, which clearly characterizes how you can tell from a twisted cube whether it is solvable.
At the end of the week we had a look at the game "Dobble" and found out how the structure of the game is connected to projective geometry.

Mentor: Anna Schilling 

Team members: Victoria Weidmann (Graf-Eberhard-Gymnasium Bad Urach)

Description: This week it was all about the Rubik's Cube, which can be beautifully described using group theory. To do this, we first looked at groups in general and then specifically at the symmetric group $S_n$. We also had to figure out how to uniquely describe a cube mathematically. We were then able to devote ourselves to the proof of the “solvability theorem”, which clearly characterizes how you can tell from a twisted cube whether it is solvable.
For the game SET, we looked at the mathematical description and how many cards there can be without a set.

Mentor: Anna Schilling

Team members: Sophie Rehberger (Englisches Institut Heidelberg), Sophie Rupp (Englisches Institut Heidelberg)

Description: During the one week of internship, we worked on the games “Dobble” and “SET” and analyzed their structures. We learned about projective geometry, which is closely linked to the game Dobble, and created our own game. We learned how the game SET can be described mathematically and we found out the maximum number of cards there can be without a set.

Mentors: Anna Schilling, Diaaeldin Taha
Team members: Paul Martin
Description: In this two-week internship, we learned about the mathematics of random walks in the hyperbolic plane and simulated these dynamical systems.
Online app: link

Mentors: Anna Schilling, Diaaeldin Taha
Team members: Max Dörich (DBG Eppelheim), Lukas Kühlwein (DBG Eppelheim)
Details: This project aimed to introduce the interns to the mathematics of games of chance and skill using computer explorations. During the first week, we studied the game SET using algebra, geometry, combinatorics, and computer simulations. During the second week, we learned about the Sprague–Grundy theorem, and how to write programs that play famous impartial games perfectly.
GitHub: link