| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT4068 | Topology | Fall | 3 | 0 | 3 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Dr. Öğr. Üyesi TUĞCAN DEMİR |
| Course Objectives: | To teach math majors about convergence, continuity and connectedness in the set of real numbers, in metric spaces and abstract topological spaces in depth. |
|
The students who have succeeded in this course; A student who finished this class successfully will have learned the basic concepts of convergence, continuity and connectedness and their manifestations in different types of topological spaces. |
| Metric Spaces, Metric Topology, Equivalent Metrics, Subspaces, Interior, Exterior and Boundary Points, Dense sets, Continuous Maps, Homeomorphisms, Connectedness, Path-Connectedness, Separation Axioms, Compactness, Local Compactness and Paracompactness, Sequential Compactness, Product of Topologies, Quotient Spaces |
| Week | Subject | Related Preparation | |
| 1) | A review of topics and examples from real analysis. | ||
| 2) | A review of topics and examples from real analysis. | ||
| 3) | Metric spaces and analysis over metric spaces. | ||
| 4) | Metric spaces and analysis over metric spaces. | ||
| 5) | Topological spaces. Open and closed sets. Convergence and neighborhoods. Nets and filters. | ||
| 6) | Examples of topological spaces. | ||
| 7) | Coverings and compactness. | ||
| 8) | Continuous functions. Topology on function spaces. Compact-open topology. | ||
| 9) | Tychonoff's Theorem. | ||
| 10) | Hausdorff spaces and separation axioms. | ||
| 11) | Urysohn and Tietze Extension Theorems. | ||
| 12) | Borsuk-Ulam Theorem. Ham and Cheese Sandwich Theorem. | ||
| 13) | Combinatorial topology. Simplicial and CW complexes. | ||
| 14) | Classification of orientable surfaces. | ||
| Course Notes: | Instructor's own lecture notes. J Dugundji. Topology. Boston: Allyn and Bacon, 1966. M A Armstrong. Basic Topology. Springer, 1983. |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 0 | % 0 |
| Laboratory | 0 | % 0 |
| Application | 0 | % 0 |
| Field Work | 0 | % 0 |
| Special Course Internship (Work Placement) | 0 | % 0 |
| Quizzes | 3 | % 10 |
| Homework Assignments | 0 | % 0 |
| Presentation | 0 | % 0 |
| Project | 0 | % 0 |
| Seminar | 0 | % 0 |
| Midterms | 2 | % 50 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 40 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 3 | 3 | 9 |
| Preliminary Jury | 0 | ||
| Midterms | 2 | 10 | 20 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 12 | 12 |
| Total Workload | 125 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |