At the end of the semester a successful student will
- Describe a given covering space and its Galois group (in reasonable cases)
- Describe the covering space of a given space together a specified Galois group (in reasonable cases)
- Determine topological invariants of covering spaces such as Euler number.
- Describe the relation between the rings and fields of (continuous or analytic) functions on the base and the total space of a covering space of surfaces.
- Determine and explain solutions of 2nd order linear ODEs near regular singular points.