Rapor Tarihi: 13.04.2026 03:07
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Topology II | MAT310 | Turkish | Compulsory | 6. Semester | 2 + 2 | 3.0 | 6.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Doç. Dr. İzzettin DEMİR |
| Instructor(s) | |
| Goals | The objective of this course is to introduce students to the fundamental structures of metric spaces, deeply examine countability axioms (first and second countable spaces) and separability, and provide an understanding of separation axioms in topological spaces to develop advanced topological analysis skills. |
| Course Content | Definition and fundamental properties of metric spaces; metric topology; first countable spaces and local bases; second countable spaces and countable bases; separable spaces and countable dense subsets; separation axioms in topological spaces (T_0, T_1, T_2, regular, and normal spaces) and the hierarchical relationships among these spaces. |
| # | Öğrenme Kazanımı |
| 1 | Define the concept of a metric space and analyze the topological structure induced by a metric. |
| 2 | Determine the fundamental properties of first and second countable spaces to evaluate the structural differences between them. |
| 3 | Comprehend the concept of a separable space and prove the relationships between countability properties and separability. |
| 4 | Classify topological spaces according to separation axioms ($T_0, T_1, T_2$, regular, and normal spaces) and examine their properties. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Metric spaces | Preparation, After Class Study, Research, Interview |
| 2. Week | Metric spaces | Preparation, After Class Study, Research, Interview |
| 3. Week | Metric spaces | Preparation, After Class Study, Research, Interview |
| 4. Week | Metric spaces | Preparation, After Class Study, Research, Interview |
| 5. Week | First Countable Spaces | Preparation, After Class Study, Research, Interview |
| 6. Week | First Countable Spaces | Preparation, After Class Study, Research, Interview |
| 7. Week | Second Countable Spaces | Preparation, After Class Study, Research, Interview |
| 8. Week | Second Countable Spaces | Preparation, After Class Study, Research, Interview |
| 9. Week | Second Countable Spaces | Preparation, After Class Study, Research, Interview |
| 10. Week | Separable spaces | Preparation, After Class Study, Research, Interview |
| 11. Week | Seperation Axioms | Preparation, After Class Study, Research, Interview |
| 12. Week | Seperation Axioms | Preparation, After Class Study, Research, Interview |
| 13. Week | Seperation Axioms | Preparation, After Class Study, Research, Interview |
| 14. Week | Seperation Axioms | Preparation, After Class Study, Research, Interview |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Possesses theoretical and applied knowledge of the fundamental areas of mathematics (Analysis and Function Theory, Algebra and Number Theory, Geometry, Applied Mathematics, Topology and Foundations of Mathematics, and Mathematical Logic). | ✔ | |||||
| 2 | Explains the historical development of mathematical concepts, their relationship with other branches of science, and their application areas. | ✔ | |||||
| 3 | Defines mathematical problems, selects appropriate methods, and solves them using analytical/numerical techniques. | ✔ | |||||
| 4 | Constructs mathematical expressions with logical integrity and reaches conclusions using proof methods. | ✔ | |||||
| 5 | Formulates and interprets real-life problems by performing mathematical modeling. | ✔ | |||||
| 6 | Effectively uses information technologies and mathematical software in data analysis and computation processes. | ✔ | |||||
| 7 | Takes responsibility in individual or team work; plans and executes projects. | ✔ | |||||
| 8 | Follows current developments in their field; improves themselves with a lifelong learning awareness. | ✔ | |||||
| 9 | Expresses mathematical ideas verbally and in writing clearly and in accordance with academic rules. | ✔ | |||||
| 10 | Acts in accordance with professional and academic ethical values; acts with a sense of social responsibility. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 |
|---|---|---|---|---|
| PY1 | 4 | 4 | 4 | 4 |
| PY2 | 4 | 4 | 4 | 4 |
| PY3 | 4 | 4 | 4 | 4 |
| PY4 | 5 | 5 | 5 | 5 |
| PY5 | 3 | 3 | 3 | 3 |
| PY6 | 1 | 1 | 1 | 1 |
| PY7 | 3 | 3 | 3 | 3 |
| PY8 | 3 | 3 | 3 | 3 |
| PY9 | 4 | 4 | 4 | 4 |
| PY10 | 2 | 2 | 2 | 2 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 4 | 56 |
|
Ders Dışı |
Homework | 14 | 2 | 28 |
| Research | 14 | 2 | 28 | |
| Interview | 14 | 2 | 28 | |
|
Sınavlar |
Midterm | 1 | 2 | 2 |
| Total Workload | 142 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 6.0 | ||
