We have updated the information concerning the state exam, see the dedicated webpage State exam (MSc Physics) and State exam (MSc Mathematics). In particular, the list of topics for the state exam should be now more specific and also more consistent with the topics covered by the compulsory lectures.
If you are looking for a decent New Year’s resolution, you should consider something like “I will write a fantastic thesis. I am looking forward to the state exam — I will enjoy it.” :-)