| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Singular Semi-Riemann Geometry I | MAT636 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Res. Assist. Burcu FEDAKAR |
| Instructors | |
| Assistants | |
| Goals | Knows the basic definitions and theorems about semi-Riemannian gometry. |
| Course Content | Manifold theory: differentiable manifolds, tangent vectors, derivative transformation, curves, vector fields, 1-forms, Tensors: basic tensor algebra, tensor fields, tensor derivative, symmetric bilinear forms, scalar multiplication, Semi-Riemannian manifolds: isometries, parallel translation, geodesics, exponential transformation, curvatures, Semi-Riemann product manifolds, local isometries, Semi-Riemann submanifolds: tangents and normals, reduced conjecture, geodesics on submanifolds, total geodesic submanifolds, semi-Riemann hypersurfaces. |
| Learning Outcomes |
- Students will learn theoretical concepts in mathematics. - Students will learn how to read academical journals. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Manifold theory: differentiable manifolds. | |
| 2. Week | Tangent vectors, derivative transformation, curves. | |
| 3. Week | Vector fields, 1-forms. | |
| 4. Week | Tensors: elementary tensor algebra, tensor fields, tensor derivatives. | |
| 5. Week | Symmetric bilinear forms, scalar multiplication. | |
| 6. Week | Semi-Riemannian manifolds: isometries. | |
| 7. Week | Parallel translation, geodesics, exponential transformation, curvatures. | |
| 8. Week | Midterm | |
| 9. Week | Semi-Riemann product manifolds. | |
| 10. Week | Local isometries. | |
| 11. Week | Semi-Riemann submanifolds. | |
| 12. Week | Geodesics on submanifolds. | |
| 13. Week | Total geodesic submanifolds. | |
| 14. Week | Semi-Riemann hypersurfaces. |
| Semi-Riemannian Geometry With Applications to Relativity, Barrett O'Neill, Academic Press, 1983. |
| Program Requirements | Contribution Level | DK1 | DK2 | Measurement Method |
|---|---|---|---|---|
| PY1 | 5 | 5 | 5 | 40 |
| PY2 | 5 | 5 | 5 | 40 |
| PY3 | 4 | 4 | 4 | 60 |
| PY4 | 5 | 5 | 5 | 60 |
| PY5 | 5 | 5 | 5 | 40 |
| PY6 | 5 | 5 | 5 | 60 |
| PY7 | 5 | 5 | 5 | 40 |
| PY8 | 4 | 4 | 4 | 60 |
| PY9 | 5 | 5 | 5 | 60 |
| PY10 | 4 | 4 | 4 | 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 | 1 | 3 | 3 |
| 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 | 12 | 72 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 197 | ||
| ECTS Credit of the Course | 8.0 | ||
