Please find attached a method to visualize finite groups:

- Visualization of finite groups in 2 dimensions.
- A poster of 30 groups visualized with the method above. (97MB)

Here we use the exp function to visualize each element of the finite group:

- Visualization of the elements of the finite group C3
- Visualization of the elements of the finite group C4
- Visualization of the elements of the finite group KleinFourGroup
- Visualization of the elements of the finite group C5
- Visualization of the elements of the finite group C6
- Visualization of the elements of the finite group S3
- Visualization of the elements of the finite group C7
- Visualization of the elements of the finite group C8
- Visualization of the elements of the finite group C2xC4
- Visualization of the elements of the finite group C2xC2xC2
- Visualization of the elements of the finite group D4
- Visualization of the elements of the finite group Quaternions
- Visualization of the elements of the finite group C9
- Visualization of the elements of the finite group C3xC3
- Visualization of the elements of the finite group C10
- Visualization of the elements of the finite group D5
- Visualization of the elements of the finite group C11
- Visualization of the elements of the finite group C12
- Visualization of the elements of the finite group C6xC2
- Visualization of the elements of the finite group D6
- Visualization of the elements of the finite group A4
- Visualization of the elements of the finite group C3_C4
- Visualization of the elements of the finite group C13
- Visualization of the elements of the finite group C14
- Visualization of the elements of the finite group D7
- Visualization of the elements of the finite group C15
- Visualization of the elements of the finite group C16
- Visualization of the elements of the finite group D8
- Visualization of the elements of the finite group Q16
- Visualization of the elements of the finite group SD16
- Visualization of the elements of the finite group M4_2
- Visualization of the elements of the finite group C4oD4
- Visualization of the elements of the finite group C8xC2
- Visualization of the elements of the finite group C17
- Visualization of the elements of the finite group D9
- Visualization of the elements of the finite group D10
- Visualization of the elements of the finite group D11
- Visualization of the elements of the finite group D12
- Visualization of the elements of the finite group S4

Here we use the exp function to visualize each element of the finite group where each group is in a printable pdf file:

- Visualization of the elements of the finite group C3 (pdf)
- Visualization of the elements of the finite group C4 (pdf)
- Visualization of the elements of the finite group KleinFourGroup (pdf)
- Visualization of the elements of the finite group C5 (pdf)
- Visualization of the elements of the finite group C6 (pdf)
- Visualization of the elements of the finite group S3 (pdf)
- Visualization of the elements of the finite group C7 (pdf)
- Visualization of the elements of the finite group C8 (pdf)
- Visualization of the elements of the finite group C2xC4 (pdf)
- Visualization of the elements of the finite group C2xC2xC2 (pdf)
- Visualization of the elements of the finite group D4 (pdf)
- Visualization of the elements of the finite group Quaternions (pdf)
- Visualization of the elements of the finite group C9 (pdf)
- Visualization of the elements of the finite group C3xC3 (pdf)
- Visualization of the elements of the finite group C10 (pdf)
- Visualization of the elements of the finite group D5 (pdf)
- Visualization of the elements of the finite group C11 (pdf)
- Visualization of the elements of the finite group C12 (pdf)
- Visualization of the elements of the finite group C6xC2 (pdf)
- Visualization of the elements of the finite group D6 (pdf)
- Visualization of the elements of the finite group A4 (pdf)
- Visualization of the elements of the finite group C3_C4 (pdf)
- Visualization of the elements of the finite group C13 (pdf)
- Visualization of the elements of the finite group C14 (pdf)
- Visualization of the elements of the finite group D7 (pdf)
- Visualization of the elements of the finite group C15 (pdf)
- Visualization of the elements of the finite group C16 (pdf)
- Visualization of the elements of the finite group D8 (pdf)
- Visualization of the elements of the finite group Q16 (pdf)
- Visualization of the elements of the finite group SD16 (pdf)
- Visualization of the elements of the finite group M4_2 (pdf)
- Visualization of the elements of the finite group C4oD4 (pdf)
- Visualization of the elements of the finite group C8xC2 (pdf)
- Visualization of the elements of the finite group C17 (pdf)
- Visualization of the elements of the finite group D9 (pdf)
- Visualization of the elements of the finite group D10 (pdf)
- Visualization of the elements of the finite group D11 (pdf)
- Visualization of the elements of the finite group D12 (pdf)
- Visualization of the elements of the finite group S4 (pdf)

If you are interested in Galois-Theory, here you can find my diploma, where I compute the Galois groups of some polynomials.

If you are interested in some unfinished ideas, I try to collect those in a notebook.

I am mostly interested in positive definite kernels for structured data, especially over the natural numbers and applications thereof (in measuring the consonance of two musical notes and in generating an infinite number of formulas for the circle number pi).

In Some inequalities which are equivalent to the Riemann hypothesis I prove that there exists an infinite number of inequalities similar to the Lagarias inequality, which are equivalent to the Riemann hypothesis.

In Railway networks with Timetables an abstract mathematical model of a railway network with timetables is suggested.

I presented a fast algorithm for the problem "inverse shortest paths in directed acyclic graphs" at the conference KLAIM 2023 in Kaiserslautern with source-code as a Jupyter-Notebook in Python.

In The Mason-Stothers theorem for natural numbers a proof based on the proof by Serge Lang in "Algebra" is given for natural numbers.

Please find attached an image of a fractal I stumbled upon which is based on lexicographic sorting of the prime factorization.

In my spare time I did some algorithmic composition as a hobby, culminating in a participation on the AI song contest 2023.

The method I used to generate this piece for piano, is a combination of Long Short-Term Memory method combined with the positive definite kernel I stumbled upon to measure musical note consonance. The code can be found here.