| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Differentiable Manifolds | MAT511 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Assoc. Prof. Dr. Merve İLKHAN KARA |
| Instructors | |
| Assistants | |
| Goals | Ensuring high level of knowledge related to the topics in the content of the course, giving the ability of using this konwledge in discussion and research environments to students. |
| Course Content | Fundamental definitions in R^n, Differentiable manifolds, Tangent space, Vector fields, Differentiable functions, Covariant derivative, Lie bracket, Submanifolds, Immersions, Submersions, Embeddings, Standard connection of R^n, HypersurfaceS, Shape operator, Gauss map, Curvatures, Riemannian metric and Riemannian connection, Riemannian curvature tensor. |
| Learning Outcomes |
- Student’s ability of commenting and thinking truely will improve and the students will get basic information about mathematics. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Fundamental definitions in R^n | |
| 2. Week | Differentiable manifolds | |
| 3. Week | Tangent space, Vector fields | |
| 4. Week | Differentiable functions | |
| 5. Week | Covariant derivative | |
| 6. Week | Lie bracket | |
| 7. Week | Submanifolds | |
| 8. Week | Midterm | |
| 9. Week | Immersions, Submersions | |
| 10. Week | Embeddings | |
| 11. Week | Standard connection of R^n | |
| 12. Week | Hypersurfaces | |
| 13. Week | Shape operator, Gauss map | |
| 14. Week | Curvatures, Riemannian metric and Riemannian connection |
| Program Requirements | Contribution Level | DK1 | Measurement Method |
|---|---|---|---|
| PY1 | 5 | 5 | 60 |
| PY2 | 5 | 5 | 60 |
| PY3 | 2 | 2 | 60 |
| PY4 | 2 | 2 | 60 |
| PY5 | 3 | 3 | 60 |
| PY6 | 1 | 1 | 60 |
| PY7 | 4 | 4 | 60 |
| PY8 | 1 | 1 | 60 |
| PY9 | 3 | 3 | 60 |
| PY10 | 2 | 2 | 60 |
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Course Hours | 14 | 3 | 42 |
| Preparation, After Class Study | 14 | 1 | 14 |
| Research | 14 | 1 | 14 |
| Other Activities | 14 | 1 | 14 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 7 | 3 | 21 |
| Homework 2 | 7 | 3.5 | 24.5 |
| Final | 1 | 2.5 | 2.5 |
| Practice | 14 | 1 | 14 |
| Practice End-Of-Term | 14 | 2 | 28 |
| Classroom Activities | 14 | 2 | 28 |
| Total Workload | 204 | ||
| ECTS Credit of the Course | 8.0 | ||
