Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
YMB0026		Olasılık ve Ölçü Teorisi	3/0/0	DE	Turkish	8

Course Goals	The aim of Probability and Measure Theory is to apply knowledge of measurement theory obtained by Lebesgue measure and Lebesgue integral to probability theory.
Prerequisite(s)	None
Corequisite(s)	None
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. Selçuk Türer
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	-Resitation and Oral Presentation
Principle Sources	-Williams, D.: Probability with Martingales, Cambridge University Press, Cambridge, 1991.
Other Sources	-

Course Schedules
Week	Contents	Learning Methods
1. Week	Measure Spaces	Resitation and Oral Presentation
2. Week	Measure Spaces	Resitation and Oral Presentation
3. Week	Events	Resitation and Oral Presentation
4. Week	Random Variables	Resitation and Oral Presentation
5. Week	Independence	Resitation and Oral Presentation
6. Week	Independence	Resitation and Oral Presentation
7. Week	Integration	Resitation and Oral Presentation
8. Week	Integration	Resitation and Oral Presentation
9. Week	Midterm	Midterm
10. Week	Expectation	Resitation and Oral Presentation
11. Week	Expectation	Resitation and Oral Presentation
12. Week	Conditional Expectation	Resitation and Oral Presentation
13. Week	Martingales	Resitation and Oral Presentation
14. Week	Martingales	Resitation and Oral Presentation
15. Week
16. Week
17. Week

Assessments
Evaluation tools	Quantity	Weight(%)
Midterm(s)	1	40
Final Exam	1	60

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 Understand why a more sophisticated theory of integration and measure is needed; LO-2 Show that certain functions are measurable; LO-3 Construct the Lebesgue integral; LO-4 Understand properties of the Lebesgue integral; LO-5 Develop probabilistic concepts (random variables, expectation and Martingales) within the framework of measure theory.

Course Assessment Matrix:

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10