Syllabus ( MATH 571 )
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Basic information
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Course title: |
General Topology |
Course code: |
MATH 571 |
Lecturer: |
Assoc. Prof. Dr. Ayşe SÖNMEZ
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ECTS credits: |
7.5 |
GTU credits: |
3 (3+0+0) |
Year, Semester: |
1/2, Fall and Spring |
Level of course: |
Second Cycle (Master's) |
Type of course: |
Area Elective
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Language of instruction: |
Turkish
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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 give the infrastructure in the field of topology for researchers who want to specialize in the field of mathematics, develop abstract thinking by means of sets and analysis. |
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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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Development of abstract thinking skills
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
Method of assessment
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Written exam
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Homework assignment
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Explain the basic concepts of Topology
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
Method of assessment
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Written exam
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Make use of topology in many areas of mathematics
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
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Work effectively in multi-disciplinary research teams
Method of assessment
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Written exam
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Homework assignment
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Contents
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Week 1: |
Fundamental concepts in topological spaces |
Week 2: |
Methods of generating topologies |
Week 3: |
Continuous functions |
Week 4: |
Closed and open functions, homeomorphisms |
Week 5: |
Axioms of separation |
Week 6: |
Compact spaces, locally compact spaces |
Week 7: |
Sequentially compactness. |
Week 8: |
Countably compactness. Midterm Exam. |
Week 9: |
Euclid space of real numbers |
Week 10: |
Metric spaces |
Week 11: |
Continuous functions in metric spaces |
Week 12: |
Totally bounded and complete metric spaces |
Week 13: |
Metrization |
Week 14: |
Paracompact Spaces. Connected Spaces. |
Week 15*: |
- |
Week 16*: |
Final Exam. |
Textbooks and materials: |
Stephen Willard, “General Topology” Ryszard Engelking, “General Topology”
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Recommended readings: |
G.J.O. Jameson, “Topology and Normed Spaces” |
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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: |
3,5,7,9,11,13 |
10 |
Quiz: |
- |
0 |
Final exam: |
16 |
50 |
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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: |
7 |
6 |
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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: |
3 |
1 |
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Personal studies for final exam: |
20 |
1 |
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Final exam: |
3 |
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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