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 |
MAT5006 | Topology | 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 this lesson is to give the fundamental concepts of general topology and the methods of proof. Also, the other aim is to give information about metric and topological properties of mathematical concepts in metric spaces that are important for the mathematics science. |
The students who have succeeded in this course; 1) He/She defines the basic concepts of metric space, 2) He/She decides whether arbitrary functions are metrics or not, 3) He/She adapts knowledge of functions theory and analysis to metric space, 4) He/She proves and interprets the basic theorems in metric space, 5) He/She defines basic concepts of topology which are the bases of theoretical courses, 6) He/She decides whether structure on an arbitrary set are topology or not, 7) He/She adapts knowledge of functions theory and analysis to topologic space, 8) He/She proves and interprets the fundamental theorems by using properties of topologic space, 9) He/She solves problem by using topology, 10) He/She develops the culture of mathematic by gaining abstract thinking ability. |
1 Metric spaces, submetric spaces, isometries 2 Open and closed disks, spheres, diameters 3 Topology of metric spaces 4 Sequences and continuity in metric spaces 5 Topological structure and open sets in topological spaces closed sets and properties of the family of closed subsets in topological spaces, neighborhoods of a point and fundamental systems of neighborhoods 6 Bases and subbases of a topology 7 Systems of open neighborhoods 8 Equality of topologies and comparison of topologies 9 Contact and limit points of a set in the topologic space 10 Interior point and interior of a set, closure point and closure of a set 11 The frontier of a subset, dense, nowhere dense, somewhere dense subsets of topological spaces 12 Continuity of functions in a topological space and homeomorphisms 13 Sequences in the topological space and limit of a sequence, T2 14 Subspaces, finite products of topological spaces |
Week | Subject | Related Preparation | |
1) | Metric spaces, submetric spaces, isometries | ||
2) | Open and closed disks, spheres, diameters | ||
3) | Topology of metric spaces | ||
4) | Sequences and continuity in metric spaces | ||
5) | Topological structure and open sets in topological spaces closed sets and properties of the family of closed subsets in topological spaces, neighborhoods of a point and fundamental systems of neighborhoods | ||
6) | Bases and subbases of a topology | ||
7) | Systems of open neighborhoods | ||
8) | Equality of topologies and comparison of topologies | ||
9) | Equality of topologies and comparison of topologies | ||
10) | Contact and limit points of a set in the topologic space | ||
11) | Interior point and interior of a set, closure point and closure of a set | ||
12) | The frontier of a subset, dense, nowhere dense, somewhere dense subsets of topological spaces | ||
13) | Continuity of functions in a topological space and homeomorphisms | ||
14) | Sequences in the topological space and limit of a sequence, T2 Subspaces, finite products of topological spaces |
Course Notes: | 1. Gürkanlı A. Turan, Genel Topoloji, Samsun, 1993. |
References: | 1. Lipschutz, S., General Topology, Schaum Publishing Co., 1965 2. Özdamar, E., Görgülü A., Alp, A., Genel topoloji, Uludağ Üni. Yayınları, 1999. 3. Aslım, G., Genel topoloji, İzmir, Ege Üniversitesi, 1988 |
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 | 1 | % 20 |
Presentation | % 0 | |
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 | 5 | 70 |
Presentations / Seminar | 0 | 0 | 0 |
Project | 0 | 0 | 0 |
Homework Assignments | 1 | 20 | 20 |
Quizzes | 0 | 0 | 0 |
Preliminary Jury | 0 | ||
Midterms | 1 | 30 | 30 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 38 | 38 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |