BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6004 | Advanced Topology II | Spring | 3 | 0 | 3 | 8 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Basic information
| Language of instruction: | Turkish |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Assoc. Prof. ATABEY KAYGUN |
| Recommended Optional Program Components: | None |
| Course Objectives: | The aim of the courses is to provide developing of “General Topology” courses as in graduate level. |
Learning Outcomes
|
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. |
Course Content
| 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. |
Weekly Detailed Course Contents
| 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 |
Sources
| Course Notes / Textbooks: | 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: |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Presentation | 1 | % 20 |
| Midterms | 1 | % 30 |
| Final | 1 | % 50 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 14 | 6 | 84 |
| Presentations / Seminar | 1 | 30 | 30 |
| Midterms | 1 | 22 | 22 |
| Final | 1 | 22 | 22 |
| Total Workload | 200 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |