Syllabus ( MATH 206 )
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Basic information
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| Course title: |
Topology |
| Course code: |
MATH 206 |
| Lecturer: |
Assoc. Prof. Dr. Ayşe SÖNMEZ
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| ECTS credits: |
6 |
| GTU credits: |
3 (3+0+0) |
| Year, Semester: |
2, Spring |
| Level of course: |
First Cycle (Undergraduate) |
| Type of course: |
Compulsory
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| Language of instruction: |
English
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| Mode of delivery: |
Face to face
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| Pre- and co-requisites: |
None |
| Professional practice: |
No |
| Purpose of the course: |
To teach the fundamental concepts of Topology |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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Define fundamental concepts of topology
Contribution to Program Outcomes
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Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
Method of assessment
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Written exam
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Use countibility and separation axioms
Contribution to Program Outcomes
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Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
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Exhibiting professional and ethical responsibility.
Method of assessment
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Written exam
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Explain the basic information about the concept of compactness
Contribution to Program Outcomes
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Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
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Ability to work in interdisciplinary research teams effectively.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
Method of assessment
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Written exam
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Contents
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| Week 1: |
Preliminaries (The Basics of Set Theory, Functions) |
| Week 2: |
Preliminaries (Infinite Sets) |
| Week 3: |
Topological Spaces |
| Week 4: |
The Euclidean Topology |
| Week 5: |
Limit Points |
| Week 6: |
Homeomorphisms |
| Week 7: |
Continuous Mappings |
| Week 8: |
General Review |
| Week 9: |
Metric Spaces |
| Week 10: |
Completeness |
| Week 11: |
Compactness |
| Week 12: |
The Heine-Borel Theorem |
| Week 13: |
Finite Products |
| Week 14: |
Tychonoff's Theorem for finite products, Products and connectedness |
| Week 15*: |
- |
| Week 16*: |
Final exam |
| Textbooks and materials: |
Topology Without Tears, Sidney A. Morris |
| Recommended readings: |
An Introduction to Set Theory and Topology, Ronald C. Freiwald |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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| Method of assessment |
Week number |
Weight (%) |
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| Mid-terms: |
8 |
40 |
| Other in-term studies: |
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0 |
| Project: |
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0 |
| Homework: |
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0 |
| Quiz: |
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0 |
| Final exam: |
16 |
60 |
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Total weight: |
(%) |
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Workload
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| Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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| Courses (Face-to-face teaching): |
3 |
14 |
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| Own studies outside class: |
4 |
14 |
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| Practice, Recitation: |
0 |
0 |
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| Homework: |
0 |
0 |
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| Term project: |
0 |
0 |
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| Term project presentation: |
0 |
0 |
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| Quiz: |
0 |
0 |
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| Own study for mid-term exam: |
20 |
1 |
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| Mid-term: |
2 |
1 |
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| Personal studies for final exam: |
25 |
1 |
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| Final exam: |
2 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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