MATH424 GALOIS THEORY OF COVERINGS AND LINEAR DIFFERENTIAL EQUATIONS
| Course Code: | 2360424 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (0.00 - 0.00) |
| ECTS Credit: | 6.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
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.
Course Content
Basics of topological spaces, fundamental groups covering spaces, topological Galois Theory, functions on surfaces, differential equations, regular singular points and differential equations of Fuchsian type