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 |
| MAT6003 | Advanced Topology I | Fall 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” as 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
| 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. |
Weekly Detailed Course Contents
| 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 |
Sources
| 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: |
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 | 5 | 70 |
| Presentations / Seminar | 1 | 20 | 20 |
| Midterms | 1 | 33 | 33 |
| Final | 1 | 35 | 35 |
| 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 | |
| 1) | Ability to assimilate mathematic related concepts and associate these concepts with each other. | 4 |
| 2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | 4 |
| 3) | Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. | 4 |
| 4) | Ability to make individual and team work on issues related to working and social life. | 4 |
| 5) | Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. | 4 |
| 6) | Ability to use mathematical knowledge in technology. | |
| 7) | To apply mathematical principles to real world problems. | 4 |
| 8) | Ability to use the approaches and knowledge of other disciplines in Mathematics. | 4 |
| 9) | Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. | 5 |
| 10) | To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. | 4 |
| 11) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | 4 |
| 12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. | 4 |