| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Algebric Topology | MAT550 | 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. ZAKİR DENİZ |
| Instructors | |
| Assistants | |
| Goals | The aim of this course is to introduce the basic ideas of algebraic topology by studying the fundamental group and the homology groups of a topological space and giving some applications. |
| Course Content | Basic algebra review (needed througout). The fundamental group: paths and path connectedness. The fundamental group: defintions and verification of some properties. The fundamental group: examples and computations. The fundamental group: applications such as Brouwer’s fixed point theorem. Simplicial complexes: geometric and abstract simplicial complexes, triangulations. Simplicial approximation theorem. The fundamental group of spheres. Simplicial homology: defintinitions and examples. Topological invariants and homotopy. Topological invariants and homology. Euler and Betti numbers. |
| Learning Outcomes |
- The students gain primary informations about the mathematics |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | General description and history of algebraic topology. | |
| 2. Week | Basic algebra review (needed througout). | |
| 3. Week | The fundamental group: paths and path connectedness. | |
| 4. Week | The fundamental group: defintions and verification of some properties. | |
| 5. Week | The fundamental group: examples and computations. | |
| 6. Week | Topological Spaces | |
| 7. Week | Retrakt | |
| 8. Week | midterm | |
| 9. Week | Retrakt | |
| 10. Week | Simplisiyal complexs | |
| 11. Week | Simplisiyal complexs | |
| 12. Week | Poliedr | |
| 13. Week | Manifolds | |
| 14. Week | Manifolds |
| 2.Massey W.S., Homology and Cohomology Theory. New York-Bassel, 1978 |
| 1.Hu Sze Tsen, Homotopy Theory, Academic Pres, New York and London, 1959 |
| Program Requirements | Contribution Level | DK1 | Measurement Method |
|---|---|---|---|
| PY1 | 2 | 2 | 60 |
| PY2 | 3 | 3 | 60 |
| PY3 | 2 | 2 | 60 |
| PY4 | 2 | 2 | - |
| PY5 | 2 | 2 | 60 |
| PY6 | 2 | 2 | 60 |
| PY7 | 2 | 2 | 60 |
| PY8 | 2 | 2 | 60 |
| PY9 | 2 | 2 | 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 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 14 | 1 | 14 |
| Homework 2 | 14 | 1 | 14 |
| Quiz 1 | 4 | 4 | 16 |
| Quiz 2 | 4 | 4 | 16 |
| Final | 1 | 2 | 2 |
| Practice | 15 | 2 | 30 |
| Practice End-Of-Term | 15 | 2 | 30 |
| Classroom Activities | 15 | 2 | 30 |
| Total Workload | 196 | ||
| ECTS Credit of the Course | 8.0 | ||
