MATH419 MEASURE THEORY
| Course Code: | 2360419 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 6.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
This course is intended to serve as a classical introduction to abstract measure theory and integration. The subject is essential for students who plan to continue in any area of analysis, differential equations or probability theory, and also very useful for students who plan to continue in many other areas such as geometric group theory or model theory.
Course Content
Measurable spaces and functions. Measures. Integration with respect to a measure. Integrable functions. L_p spaces. Modes of convergence. Generation of measures. Product measures. Decomposition of measures.
Course Learning Outcomes
At the end of the course, students are expected to:
- prove results about measurable spaces, sigma algebras and measurable functions,
- employ the monotone convergence theorem, Fatou lemma and Lebesgue dominated convergence theorem to prove results,
- use Minkowski and Hölder inequalities to deduce results in L_p spaces,
- understand and differentiate between various modes of convergence,
- use extension theorems to prove existence of measures,
- employ Tonelli’s and Fubini’s theorems in calculations and proofs.
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 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 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 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 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