MATH502 SPECTRAL THEORY OF LINEAR OPERATORS
| Course Code: | 2360502 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Assist.Prof.Dr BURAK KAYA |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the student is expected to have learned the basics of spectral theory of Hilbert spaces and Banach algebras.
Course Content
Compact operators, compact operators in Hilbert Spaces, Banach Algebras, The spectral theorem for normal operators, unbounded operators between Hilbert spaces, the spectral theorem for unbounded self-adjoint operators, self-adjoint operators, self-adjoint extensions.
Course Learning Outcomes
A student that satisfactorily passes this course will be able to apply the techniques of spectral theory to problems in analysis and topology whenever a suitable Hilbert space or Banach algebra arises.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution