MATH782 DESCRİPTİVE SET THEORY
| Course Code: | 2360782 |
| 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 and Spring Semesters. |
Course Objectives
At the end of the course, students are expected to have learned the basic theory of Polish spaces and standard Borel spaces at a level that will allow them to build upon further research related material.
Course Content
Topological preliminaries. Polish spaces, compact metric spaces, zero-dimensional spaces and Baire category methods. Measurable spaces and standard Borel spaces. Borel hierarchy, Borel sets and their regularity properties, and the Borel isomorphism theorem. Projective sets, analytic and coanalytic sets, and their regularity properties. Separation theorems. Polish groups. Selected topics: Borel determinacy, various uniformization theorems, theory of Borel equivalence relations etc.
Course Learning Outcomes
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