Proficiency in English, enough to be able to follow graduate texts in Mathematics.
Instructor(s)
Assist. Prof. Dr. Uğur Gönüllü
Course Assistant(s)
None
Schedule
Will be announced in the forthcoming term.
Office Hour(s)
Assoc. Prof. Dr. Mert ÇAĞLAR, AK/3-A-03/05.
Teaching Methods and Techniques
-Lecture and homeworks.
Principle Sources
-R. Meise & D. Vogt, Introduction to Functional Analysis, Translated by M.S. Ramanujan, Clarendon Press, Oxford, 1997.
Other Sources
-John B. Conway, A Course in Functional Analysis, 2nd ed., Springer-Verlag, New York, 1990.
-W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill Book Co., New York, 1987.
-T. Terzioğlu, Fonksiyonel Analizin Yöntemleri, Matematik Vakfı, Istanbul, 1998.
Course Schedules
Week
Contents
Learning Methods
1. Week
Review of metric spaces
Lecture and homework
2. Week
Normed spaces
Lecture and homework
3. Week
Dual spaces
Lecture and homework
4. Week
Hahn-Banach Theorem I
Lecture and homework
5. Week
Hahn-Banach Theorem II
Lecture and homework
6. Week
Second dual and reflexivity
Lecture and homework
7. Week
Baire's Theorem and its consequences I
Lecture and homework
8. Week
Midterm Exam
Midterm Exam
9. Week
Baire's Theorem and its consequences II
Lecture and homework
10. Week
Dual operators
Lecture and homework
11. Week
Projections
Lecture and homework
12. Week
Hilbert spaces
Lecture and homework
13. Week
Spaces of continuous and integrable functions I
Lecture and homework
14. Week
Spaces of continuous and integrable functions II
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(%)
Midterm(s)
1
30
Homework / Term Projects / Presentations
7
30
Final Exam
1
40
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 metric and normed spaces.
LO-2
Understanding and analyzing dual spaces and the Hahn-Banach Theorem.
LO-3
Understanding and analyzing Baire's Theorem and its consequences, and solving problems involving these.
LO-4
Understanding and analyzing Hilbert spaces, and solving problems involving these.
LO-5
Understanding and analyzing the spaces of continuous and integrable functions, and solving problems involving these.
