Students entering Phase I of the BMS are expected to have a bachelor degree, Vordiplom, or equivalent. (Thus, in particular, Berlin mathematics students in their "Hauptstudium" can apply for membership in BMS. For students who are further advanced, part of the Phase I course requirements may be waived.)
For entering Phase II, students are expected to have a master or Diplom degree, or to pass the BMS Qualifying Exams. (In particular, they thus satisfy the regular admission requirements of the Berlin universities' PhD programs.)