Q: What can I as a mathematician profit from writing a Master's thesis?
A: The Master's thesis is somewhat substantially different from coursework in Phase I. During doing your Master's thesis, you will enter research, read and digest current research papers and possibly do new mathematics, instead of writing homeworks and studying for exams. You can experience if you like working together with your supervisor, and if you feel like doing the same kind of work (on a higher level) for 3 years in your PhD.
Q: But BMS is a fast-track PhD program. Am I obliged to do a Master's thesis?
A: No, officially it is enough to do the Qualifying Exam, but it is very highly recommended to obtain a Master's degree. Apart from the BMS Phase II scholarship, which is available for a very limited number of students, every other PhD scholarship or position requires the holder to have a Master's degree in Mathematics. More than 75% of the Phase II students has external funding, and it is even not guaranteed that the current number of new BMS Phase II scholarships will be awarded from autumn 2017. Many PhD students in Germany hold a position that is paid according to TVL-13, which requires a Masters degree. However, the external funding sources in Berlin will be available for sure. There are PhD students at TU and FU who do not have a Master's degree, but the BMS does not recommend this. For example, should you decide to discontinue your PhD, your Masters degree will be recognized all over the world, while the BMS Qualifying Exam of course is not (unfortunately). Also, in some countries, PhD does not count as an official qualification. If you are from one of these countries, definitely do a Master's!
Q: OK, I want to do a Master's thesis, and I will apply for external funding with my supervisor. Do I have to do the BMS qualifying exam?
A: Yes, if you want to stay a member of BMS for Phase II. This will give you the opportunity to get funding from the BMS for one conference every year, and to participate soft-skills seminars offered by the BMS. According to the new BMS study regulations from 2015, you don't have to do the qualifying exam from 3 subjects. You may do only one exam of a BMS basic course outside your field of concentration, and the rest of your QE can be about the material of your Master's thesis, it can even have the form of a Master's defence. This may even be a bit before you submit your thesis, according to how you agree with the examiners. As a TU student, you can also obtain 20 credits for the BMS Fridays after completing your qualifying exam. As an FU student, 15 credits. As a HU student, you can also obtain 15 credits, but it depends on the decision of Prof. Schüth.
Q: So do I have to obtain new mathematical results in my Master's thesis, or is it satisfactory to summarize several articles or books?
A: It depends on your field. In fields such as Numerics, Applied Analysis, Functional Analysis, Mathematical Physics, Discrete Mathematics, Stochastics or Optimization, you will probably have to generalize a problem contained in some paper or book. Therefore you will probably obtain new results, but you are not expected to be very creative and develop new methods for proofs. In fields where the understanding of the current literature requires much more time, e.g. Algebraic Geometry, Arithmetic Geometry or Number Theory, your thesis will more likely be understanding and integrating several articles or books, without working out problems individually. Still, this will take in average more time than in other fields.
Q: How much time do I need for writing my Master's thesis in Berlin?
A: It depends on your field, topic, advisor and personal schedule. In most of the cases, 6 months should be enough for the whole process, for reading the necessary literature and writing the thesis. This does not mean that you have to work on it each day, but you shouldn't do too many courses and take too many holidays during this period. In Algebra and related fields, 6 months may be too little, it can be useful to start a bit earlier than registering your thesis at the university.