Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
DMB0012		C* Algebras	3/0/0	DE	Turkish	8

Course Goals	Understanding the basic concepts of C* algebras.
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.)
Instructor(s)	Assist. Prof. Dr. Uğur Gönüllü
Course Assistant(s)
Schedule	Day, hours, XXX Campus, classroom number.
Office Hour(s)	Instructor name, day, hours, XXX Campus, office number.
Teaching Methods and Techniques	Lecture and Homework
Principle Sources	Murphy G.J. C*-Algebras and Operator Theory, Academic Press Inc, 1990.
Other Sources	1- Arveson W. An Invitation to C*-Algebras, Springer-Verlag, 1976. 2- Dixmier J. C*-Algebras, North-Holland Mathematical Library, 1977.

Course Schedules
Week	Contents	Learning Methods
1. Week	Banach Algebras	Lecture and Homework
2. Week	The Spectrum and the Spectral Radius	Lecture and Homework
3. Week	The Gelfand Representation	Lecture and Homework
4. Week	C*-Algebras	Lecture and Homework
5. Week	Positive Elements of C*-Algebras	Lecture and Homework
6. Week	Operators and Sesquilinear Forms	Lecture and Homework
7. Week	Compact Hilbert Space Operators	Lecture and Homework
8. Week	The Spectral Theorem	Lecture and Homework
9. Week	Ideals in C*-Algebras	Lecture and Homework
10. Week	Positive Linear Functionals	Lecture and Homework
11. Week	The Gelfand-Naimark Representation	Lecture and Homework
12. Week	Von Neumann Algebras	Lecture and Homework
13. Week	The Double Commutant Theorem	Lecture and Homework
14. Week	Abelian Yon Neumann Algebras	Lecture and Homework
15. Week
16. Week
17. Week

Assessments
Evaluation tools	Quantity	Weight(%)
Midterm(s)	1	20
Homework / Term Projects / Presentations	5	60
Final Exam	1	20

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 C* algebras and Banach algebras. LO-2 II. Understanding the concepts of the Spectrum and the Spectral radius. LO-3 III. Understanding the properties of the Gelfand-Naimark representation. LO-4 IV. Understanding the basic properties of positive linear functionals.

Course Assessment Matrix:

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9