-R. Engelking, General Topology, Taylor & Francis, 1977.
-James R. Munkres, Topology, 2nd Edition, Prentice Hall, Inc., Upper Saddle River, NJ, 2000.
Course Schedules
Week
Contents
Learning Methods
1. Week
Topological spaces
Lecture and homework
2. Week
Neighborhoods, bases, ans sub-bases
Lecture and homework
3. Week
Continuous functions
Lecture and homework
4. Week
Homeomorphisms
Lecture and homework
5. Week
Product and quotient spaces
Lecture and homework
6. Week
Separation axioms
Lecture and homework
7. Week
Normal spaces and extensions of functions
Lecture and homework
8. Week
Urysohn's Lemma and Tietze's Extension Theorem
Lecture and homework
9. Week
Compactness
Lecture and homework
10. Week
Compactness
Lecture and homework
11. Week
Local compactness
Lecture and homework
12. Week
Lindelöf spaces
Lecture and homework
13. Week
Connectedness
Lecture and homework
14. Week
Path-connectedness
Lecture and homework
15. Week
Final Exam Week
Final Exam
16. Week
Final Exam Week
Final Exam
17. Week
Final Exam Week
Final Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Homework / Term Projects / Presentations
1
50
Final Exam
1
50
Program Outcomes
PO-1
Have scientific research in mathematics and computer science in the level of theoretical and practical knowledge.
PO-2
On the basis of undergraduate level qualifications, develop and deepen the same or a different areas of information at the level of expertise, and analyze and interpret by using statistical methods
PO-3
Develop new strategic approaches for the solution of complex problems encountered in applications related to the field and unforeseen and take responsibility for the solution.
PO-4
Evaluate critically skills acquired in the field of information in the level of expertise and assess the learning guides.
PO-5
Transfer current developments in the field and their work to the groups inside and outside the area supporting with quantitative and qualitative datas as written, verbal and visual by a systematic way.
PO-6
Use information and communication technologies with computer software in advanced level.
PO-7
Develop efficient algorithms by modeling problems faced in the field and solve such problems by using actual programming languages.
PO-8
Respect to social, scientific, cultural and ethical values at the stages of data collection related to the field, interpretation, and implementation.
PO-9
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-10
Establish and discuss in written, oral and visual communication in an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Understanding the basic properties of topological spaces.
LO-2
Understanding the concepts of neighborhood, base, and sub-base.
LO-3
Understanding and analyzing the properties of continuous functions.
LO-4
Understanding and analyzing product and qoutient spaces, separation axioms, and normal spaces, and solving problems involving these.
LO-5
Understanding and analyzing Urysohn's Lemma and Tietze's Extension Theorem; understanding and analyzing compactness, local compactness and connectedness, and solving problems involving these.
