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What can I do if I had a mandatory module, e.g. Stochastik 1, already in my bachelor?

You can attand an equivalent course during your master. The lecturer of the mandatory course decides which courses are equivalent and you need an equivalence form signed by her.

In the case of Stochastik 1 you could do the following: 1) show that you attanded an equivalent Stochastik 1 course during your bachelor 2) attend e.g. Stochastics 2 and count it as your Stochastik 1 grade in the master program.

What kind of courses can be recognised for the Überfachlicher Wahlbereich (ÜWP) and can external courses be recognised?

In the ÜWP all modules can be recognised that are identified as ÜWP and are in module catalogues of other programs of HU or institutions that participate in the Statistics Masters program. Also, other external courses, such as language courses taken abroad, can often be recognised. You then need to provide proof of how many ECTS were achieved.