Understanding the general theory of topological vector spaces.
Prerequisite(s)
MBY0023 General Topology and MBY0022 Methods of Functional Analysis
Corequisite(s)
None
Special Requisite(s)
Proficiency in English, enough to be able to follow graduate texts in Mathematics.
Instructor(s)
Professor Mert ÇAĞLAR
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
-H. Jarchow, Locally Convex Spaces, B.G. Teubner, Stuttgart, 1981.
-G. Köthe, Topological Vector Spaces I, II, Springer-Verlag, Berlin-Heidelberg-New York,1969, 1979.
-H.H. Schaefer, Topological Vector Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1971.
Course Schedules
Week
Contents
Learning Methods
1. Week
Introduction to topological vector spaces
Lecture and homework
2. Week
Locally-convex topological vector spaces
Lecture and homework
3. Week
Inductive and projective limits I
Lecture and homework
4. Week
Inductive and projective limits II
Lecture and homework
5. Week
Fréchet spaces I
Lecture and homework
6. Week
Fréchet spaces II
Lecture and homework
7. Week
Montel and Schwartz spaces
Lecture and homework
8. Week
Midterm Exam
Midterm Exam
9. Week
Nuclear spaces
Lecture and homework
10. Week
Bases in Fréchet spaces I
Lecture and homework
11. Week
Bases in Fréchet spaces II
Lecture and homework
12. Week
Köthe sequence spaces I
Lecture and homework
13. Week
Köthe sequence spaces II
Lecture and homework
14. Week
Linear topological invariants
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 ability to develop new mathematical ideas and methods by using high-level mental processes such as creative and critical thinking, problem solving and decision-making.
PO-2
Follow the current developments in the field of mathematics, and make the critical analysis, synthesis and evaluation of new and complex ideas.
PO-3
Understand the interdisciplinary interaction related to Mathematics and play a role in an effective manner in environments that require with the resolution of problems encountered in this process.
PO-4
Defend original views on the discussion of the issues in the field of mathematics with experts and communicate to show competence in oral and written.
PO-5
Do research with high-level national and international scientific working groups, and acquire the responsibility to contribute to the literature by publishing original works in respected scientific journals.
PO-6
Use computer software to solve problems effectively by following the developments in information and communication technologies.
PO-7
Contribute to the solution of social, scientific, cultural and ethical problems encountered issues related to the field and support the development of these values.
PO-8
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-9
Establish and discuss in written, oral and visual communication at an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Understanding the basic properties of topological vector spaces.
LO-2
Understanding the structure of locally-convex topological vector spaces.
LO-3
Understanding and analyzing inductive and projective limits.
LO-4
Understanding and analyzing the structure of Frechet, Montel, Schwartz, and nuclear spaces.
LO-5
Understanding and analyzing bases in Frechet spaces, Köthe sequence spaces, and linear topological invariants.
