| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Advanced Topology II | MAT508 | 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. İzzettin DEMİR |
| Instructors |
Merve İLKHAN KARA |
| 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 | Metric Spaces and metrizable spaces, Metrization, Complete metric spaces, Connected topological spaces, Local connected spaces, Path connected spaces, Continuity, completely unconnected spaces, Peano spaces, Homotopy relation and fundamental group, Uniform spaces, Complete uniform spaces, Function spaces, Stone-Weierstrass approximation theorems |
| Learning Outcomes |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Metric Spaces and metrizable Spaces | |
| 2. Week | Metrization | |
| 3. Week | Complete Metric Spaces | |
| 4. Week | Connected Topological Spaces | |
| 5. Week | Local Connected Spaces | |
| 6. Week | Path Connected Spaces | |
| 7. Week | Continuity ,Completely Unconnected Spaces | |
| 8. Week | Midterm | |
| 9. Week | Peano Spaces | |
| 10. Week | Homotopy Relation and Fundamental Group | |
| 11. Week | Uniform Spaces | |
| 12. Week | Complete Uniform Spaces | |
| 13. Week | Function Spaces | |
| 14. Week | Stone-Weierstrass approximate theorems |
| 1.General Topology, Stephen Willard, Addison-Wesley Publishing Company, 1970. |
| 2.Topology, James Dudundji, Wm.C.Brown Publishers, Iowa, 1989. |
| Program Requirements | Contribution Level | Measurement Method |
|---|---|---|
| PY1 | 4 | 60 |
| PY2 | 4 | 60 |
| PY3 | 4 | 60 |
| PY4 | 1 | 60 |
| PY5 | 5 | 60 |
| PY6 | 1 | 60 |
| PY7 | 4 | 60 |
| PY8 | 4 | 60 |
| PY9 | 2 | 60 |
| PY10 | 3 | 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 | 3 | 42 |
| Other Activities | 14 | 1 | 14 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 14 | 3 | 42 |
| Homework 2 | 14 | 2 | 28 |
| Final | 1 | 2 | 2 |
| Practice | 6 | 2 | 12 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 198 | ||
| ECTS Credit of the Course | 8.0 | ||
