HU: Partial Differential Equations, Mielke, 2019 (Shah Faisal)Research area I: Differential geometry, global analysis, and mathematical physics
Analysis and geometry on manifolds
Riemannian Geometry
Symplectic Geometry and Topology
Research area II: Algebraic and arithmetic geometry, number theory
Commutative Algebra
See many qualifying exam reports available about courses in Algebraic Geometry and Number Theory from FU and HU.
Research area III: Stochastics and mathematical finance
Stochastic Processes I: discrete time
Stochastic Processes III: continuous-time
Research area IV: Discrete mathematics and optimization
There are some qualifying exam reports available about courses in Combinatorics, all of them written before 2012. It would be great if you could add more reports about your own experience!
Research area V: Geometry, topology, and visualization
See many qualifying exam reports available about courses in Classical Geometries, Discrete Geometry I-II, Discrete Topology and Topology at FU and TU.
Research area VI: Numerical analysis and scientific computing
Numerical Methods for PDEs
Research area VII: Applied Analysis and Differential Equations
Functional Analysis
TU: Functional Analysis, Carstensen, 2018 (editing in progress)
Dynamical systems
Differential Equations
Research area VIII: Mathematics of data science