Zusammenhang zwischen Fraktaler Dimension und Konvergenzgeschwindigkeit der Spektralreihe bei rationalen Fraktalen
(this roughly translates to "The connection between fractal dimension and convergence speed of the spectral series for rational fractals")
This is the topic of my diploma thesis. Interestingly the topic has been given to me by a professor in the CS department, although it doesnt sound like this – but there is stuff like finite automatons and regular languages in it :-)
It is a mathemathics thesis though...
At the end of the last week the stuff I already wrote for the thesis suddenly shrank. I had cited some things from a book. It was a highly complicated way to be able to compute P^n quickly when P is a matrix (n matrix multiplications are expensive, especially when they appear in a limes for n->infinity...). It involved stuff like characteristic polynomials, partial fraction expansion, comparing coefficients, wild index shuffling and had some quite annoying prerequisites.
Last Friday I visited my supervising mathematics professor and he had a look into that stuff. He wanted to understand what actually happens there. After five minutes he found it: The theoretical base for this is the Jordan decomposition of matrices. And poof: If you write this down by means of the linear algebra suddenly the whole stuff suddenly becomes shorter, easier to understand and – that is the best thing about it – more general. :-)
However, the GIMPs new path tool suffers heavily because of this thesis...