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 |
MAT6003 | Advanced Topology I | Spring | 3 | 0 | 3 | 8 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
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” as 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 |
Convergens, nets, filters, subnets, ultra filters in topological spaces, Tychonoff theorem, Locally compact spaces, Compactification, Compactness in metric space, Components, Completely disconnected spaces, arcwise connected spaces. |
Week | Subject | Related Preparation |
2) | Convergens in topological spaces | |
3) | Nets in topological spaces | |
4) | Nets in topological spaces | |
5) | Filters in topological spaces | |
6) | Filters in topological spaces | |
7) | Subnets, ultra filters in topological spaces | |
8) | Subnets, ultra filters in topological spaces | |
9) | Tychonoff theorem | |
10) | Tychonoff theorem | |
11) | Locally compact spaces | |
12) | Compactification | |
13) | Compactness in metric space | |
14) | Completely disconnected spaces, arcwise connected spaces |
Course Notes / Textbooks: | )Prof. Dr. Gülhan ASLIM, “ Genel Topoloji”, Ege Üni. Fen Fakültesi Yayınları, (1998) 2)Munkres, J. P., “ Topology a First Course”, Prentice Hall. Inc., (1975). 3)Kuratowski, C., “ Topologie I.", Wydawnictwo naukewe Warsawa, (1958). 4)Kelley, John. L., “General Topology”, Springer-Verlag , (1955). 5)Willard, S. “General Topology”, Addision-Wesley Publishing Company, 1970 6)Engelking,R.,"General Topology",Heldermann Verlag Berlin,1989. |
References: |
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 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Study Hours Out of Class | 14 | 5 | 70 |
Presentations / Seminar | 1 | 20 | 20 |
Midterms | 1 | 33 | 33 |
Final | 1 | 35 | 35 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |