| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Differentiable Manifolds II | MAT523 | 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 | Teaching the fundamental knowledge of the subject related Topological manifolds, differentiable manifolds and submanifolds. |
| Course Content | Tensor fields in manifolds and associated geometric structures,Riemannian Metrics,Affine and Riemannian connections,Curvature |
| 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 | Tensor fields in manifolds and associated geometric structures | |
| 2. Week | Tensor fields in manifolds and associated geometric structures | |
| 3. Week | Tensor fields in manifolds and associated geometric structures | |
| 4. Week | Riemannian Metrics | |
| 5. Week | Riemannian Metrics | |
| 6. Week | Riemannian Metrics | |
| 7. Week | Affine and Riemannian connections | |
| 8. Week | Midterm | |
| 9. Week | Differentiable manifolds and submanifolds | |
| 10. Week | Affine and Riemannian connections | |
| 11. Week | Curvature | |
| 12. Week | Curvature | |
| 13. Week | Curvature | |
| 14. Week | Curvature |
| Hacısalihoğlu, H.Hilmi. Diferensiyel Geometri, Ankara Üniversitesi Fen Fakültesi, Matematik Bölümü.,2000. |
| Sabuncuoğlu, Arif. Diferensiyel Geometri, Nobel Yayınları, Ankara, 2001 |
| Gray, A. Modern Differential Geometry, CRC Press LLC, 1998. |
| Oprea, J. Differential Geometry and Aplication, Prentice-Hall, Inc, 1997 |
| do Carmo, M. p., Riemannian Geometry, Birkhauser, Boston, 1993. |
| Program Requirements | Contribution Level | DK1 | Measurement Method |
|---|---|---|---|
| PY1 | 5 | 5 | 40,60 |
| PY2 | 5 | 5 | 60 |
| PY3 | 2 | 2 | 60 |
| PY4 | 1 | 1 | 60 |
| PY5 | 4 | 4 | 60 |
| PY6 | 3 | 3 | 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 | ||
