Understanding the basic concepts of Hilbert spaces and the basic theory of special operators on Hilbert spaces.
Prerequisite(s)
-
Corequisite(s)
-
Special Requisite(s)
The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Lokenath Debnath, Piotr Mikusinski, "Introduction to Hilbert Spaces with Applications", Third Edition, 2005.
Other Sources
1- E. Kreyszig, Introductory Functional Analysis.
2- John B. Conway, A Course in Functional Analysis.
3- Kubrusly C.S.- Elements of Operator Theory, Birkhauser, 2001.
Course Schedules
Week
Contents
Learning Methods
1. Week
Inner Product Spaces
Lecture and Homework
2. Week
Hilbert Spaces
Lecture and Homework
3. Week
Orthonormal Sets
Lecture and Homework
4. Week
Fourier Series
Lecture and Homework
5. Week
Linear Functionals
Lecture and Homework
6. Week
The Riesz Representation Theorem
Lecture and Homework
7. Week
Dual Spaces
Lecture and Homework
8. Week
Linear Operators on Hilbert Spaces
Lecture and Homework
9. Week
The Adjoint of an Operator
Lecture and Homework
10. Week
Projections
Lecture and Homework
11. Week
Self-adjoint Operators
Lecture and Homework
12. Week
Compact Operators
Lecture and Homework
13. Week
Compact Operators on Hilbert Spaces
Lecture and Homework
14. Week
Unitary Operators
Lecture and Homework
15. Week
16. Week
17. Week
Assessments
Evaluation tools
Quantity
Weight(%)
Homework / Term Projects / Presentations
1
50
Final Exam
1
50
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
I. Understanding the basic properties of Hilbert spaces.
LO-2
II. Understanding the properties of the Riesz representation theorem.
LO-3
III. Understanding the concepts of the adjoint of an operator.
LO-4
IV. Understanding the basic properties of compact operators on Hilbert spaces.
