The core offering of the BMS Phase I Program consists of 18 one-semester Basic Courses, each offered at least once per year. The Basic Courses include a two-semester sequence in each of the seven Research/Teaching Areas, plus four additional Basic Courses in other fields. 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 give a broad coverage 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 of lectures and, in addition, has a tutorial session for two hours per week devoted to problem solving. Students need to pass a final exam (oral or written) at the end of each semester course; the exam is designed to verify that the students have mastered the contents of the course at an active working level.

Each BMS Basic Course has well-defined contents, as listed below, specifying the knowledge and skills that any student pursuing advanced work in the corresponding area should have.

Teaching area 1: Differential geometry, global analysis, and mathematical physics

Teaching Area 2: Algebraic and arithmic geometry, number theory

Teaching Area 3: Probability, statistics and financial mathematics

Teaching Area 4: Discrete mathematics and combinatorial optimization

Teaching Area 5: Geometry, topology, and visualization

Teaching Area 6: Numerical analysis and scientific computing

Teaching Area 7: Applied analysis and differential equations

Additional basic courses