| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Advanced Differential Geometry | MAT520 | 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. Fatih HEZENCİ |
| Instructors | |
| Assistants | |
| Goals | Teaching high level of mathematics to graduate degree students. |
| Course Content | Symmetric bilinear forms Scalar products Isometries Levi-Civita connection Levi-Civita connection Parallel shift Geodesics Exponential transformation, Curvature, Sectional curvature midterm Semi-Riemannian surfaces Roof fields Some differential operators Ricci and scalar curvation Semi-Riemannian product manifolds |
| Learning Outcomes |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Symmetric bilinear forms | |
| 2. Week | Scalar products | |
| 3. Week | Isometries | |
| 4. Week | Levi-Civita connection | |
| 5. Week | Parallel shift | |
| 6. Week | Geodesics | |
| 7. Week | Exponential transformation, Curvature, Sectional curvature | |
| 8. Week | Midterm | |
| 9. Week | Semi-Riemannian surfaces | |
| 10. Week | Roof fields | |
| 11. Week | Some differential operators | |
| 12. Week | Ricci and scalar curvation | |
| 13. Week | Semi-Riemannian product manifolds | |
| 14. Week | Local isometries |
| Semi-Riemannian Geometry, O’Neill, B., Academic Pres, 1983. |
| Differentiable Manifold, Yozo, M., Marcel Dekle,Inc.1972. |
| Yüksek Diferensiyel Geometriye Giriş, H. Hilmi Hacısalihoğlu, Fırat Ünv. Fen Fakültesi Yayınları No.2, 1980. |
| Program Requirements | Contribution Level | Measurement Method |
|---|---|---|
| PY1 | 5 | 60 |
| PY2 | 4 | 60 |
| PY3 | 2 | 60 |
| PY4 | 4 | 60 |
| PY5 | 3 | 60 |
| PY6 | 2 | 60 |
| PY7 | 1 | 60 |
| PY8 | 3 | 60 |
| PY9 | 4 | 60 |
| PY10 | 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 |
| Research | 14 | 2 | 28 |
| Midterm 1 | 1 | 2 | 2 |
| Midterm 2 | 1 | 2 | 2 |
| Homework 1 | 14 | 3 | 42 |
| Homework 2 | 14 | 2 | 28 |
| Quiz 1 | 1 | 2 | 2 |
| Quiz 2 | 1 | 2 | 2 |
| Final | 1 | 2 | 2 |
| Practice | 6 | 6 | 36 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 200 | ||
| ECTS Credit of the Course | 8.0 | ||
