| 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 |
| MAT6004 | Advanced Topology II | Fall | 3 | 0 | 3 | 8 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | Tr |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Assoc. Prof. ATABEY KAYGUN |
| Course Objectives: | The aim of the courses is to provide developing of “General Topology” courses as in graduate level. |
|
The students who have succeeded in this course; 1 Be able to understand the importance of mathematics and especially some extensions in topology 2 To improve the ability to get results by arguments to find the solutions of the problems 3 Be able to comment events in a different point of view 4 Be able to improve mathematical sense. |
| Baire’s Category Theorem, Completeness and compactness, Function spaces, Point open topology, Compact open topology, Ascoli’s theorem, The concepts of locally finite, Paracompactness, Lightly compact spaces and duality. |
| Week | Subject | Related Preparation | |
| 1) | Complete spaces | ||
| 2) | Baire’s Category Theorem. Completeness and compactness | ||
| 3) | Completeness and compactness | ||
| 4) | contraction transformations | ||
| 5) | Completeness and Baire spaces | ||
| 6) | Function spaces | ||
| 7) | Point open topology | ||
| 8) | Toplogy of Uniform continuity | ||
| 9) | Ascoli theorem | ||
| 10) | Uniform spaces | ||
| 11) | Uniform spaces | ||
| 12) | Local finiteness, paracompactness | ||
| 13) | Local finiteness, paracompactness | ||
| 14) | Lightly compakt spaces and its duals | ||
| Course Notes: | Prof. Dr. Gulhan ASLIM, “ Genel Topoloji”, Ege Uni. Fen Fakultesi Yayinlari, (1998) Lipschutz, S., “ General Topology”, Schaum. Pub. Co. New york, (1964). Munkres, J. P., “ Topology a First Course”, Prentice Hall. Inc., (1975). Willard, S. “General Topology”, Addision-Wesley Publishing Company, 1970. Engelking, R. "General Topology" Heldermann Verlag, Berlin 1989. |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | % 0 | |
| Presentation | 1 | % 20 |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 1 | % 30 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 50 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| 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 | 6 | 84 |
| Presentations / Seminar | 1 | 30 | 30 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 1 | 22 | 22 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 22 | 22 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |