MATH779 SET THEORY
| Course Code: | 2360779 |
| 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 learn
- various combinatorial set-theoretic principles and their consequences,
- basics of forcing, which is the main tool to show independence results, and
- various independence results and how such independence results are connected to other branches of mathematics.
Course Content
Review of ordinals, cardinals, transfinite induction and recursion. Basics of infinitary combinatorics, Suslin s hypothesis and trees, the diamond principle,Martin s axiom and their consequences. Models of set theory, relative consistency, absoluteness and reflection. Gödel s constructible universe and the axiom of constructibility. Forcing and its general theory, the forcing theorems. The relative consistency of CH, CH and other applications of forcing.
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