1. Differential geometry, global analysis, and topology
    - Analysis and Geometry on manifolds: J.M. Sullivan, TU
    - Differential Geometry: K. Polthier, FU

2. Algebra and number theory, algebraic and arithmetic geometry
    - Commutative Algebra: W. Kleinert, HU
    - Algebraic Geometry: R.N. Kloosterman, HU

3. Probability theory and financial mathematics
    - Stochastic processes I: Discrete time: M. Reiss, HU

4. Discrete mathematics and discrete geometry
    - Geometry: J.M. Sullivan, TU

5. Linear, nonlinear, and combinatorial optimization
    - Linear and integer programming: M. Grötschel, TU

6. Numerical analysis, scientific computing, and visualization
    - Numerical methods for ODEs and numerical linear algebra: C. Schütte, FU

7. Applied analysis, mathematical physics, and dynamical systems
    - None

* Additional courses:
    - Functional analysis: J. Sprekels, HU
    - Topology: G.M. Ziegler, TU