The core offering of the BMS Phase I Program consists of Basic Courses, which are offered at least once a year. The Basic Courses include a two-semester or three-semester sequence in each of the eight Research Training Areas, plus one Additional Course in another field. These courses, whose content is fixed, are state-of-the-art introductions to knowledge and research in the respective areas, stressing interdisciplinary and transdisciplinary connections and applications, modern trends and current questions. Their aim is to provide solid foundations in the field, geared towards ambitious students headed into mathematical research.
The topics of the Basic Courses cover a broad range of both pure and applied mathematics, but they also reflect the particular strengths and interests of mathematics in Berlin.
Each BMS Basic Course meets for four hours per week for lectures plus an additional two hours per week for a tutorial session devoted to problem solving. Students are required to pass a final exam (oral or written) at the end of each semester course; the exam is designed to demonstrate the student's mastery of the contents of the course at a level that is appropriate for active research.
Each BMS Basic Course has well-defined contents, as listed in each of the Research Training Areas, specifying the knowledge and skills that any student pursuing advanced work in the corresponding area should have.
RTA 1: Differential geometry, global analysis, and mathematical physics
RTA 2: Algebraic and arithmetic geometry, number theory
RTA 3: Stochastics and mathematical finance
RTA 4: Discrete mathematics and optimization
RTA 5: Geometry, topology, and visualization
RTA 6: Numerical analysis and scientific computing
RTA 7: Applied analysis and differential equations
RTA 8: Mathematics of data science