| Course Description |
|
| Course Name |
: |
Measure Theory |
|
| Course Code |
: |
MT 432 |
|
| Course Type |
: |
Optional |
|
| Level of Course |
: |
First Cycle |
|
| Year of Study |
: |
4 |
|
| Course Semester |
: |
Spring (16 Weeks) |
|
| ECTS |
: |
5 |
|
| Name of Lecturer(s) |
: |
|
|
| Learning Outcomes of the Course |
: |
Identifies measurable sets.
Understands measurable functions.
Defines measurements.
Understands the Lebesgue integral.
Understands the difference between Lebesgue and Riemann integrals.
Defines the Lebesgue spaces.
Improves the ability of abstract thinking.
|
|
| Mode of Delivery |
: |
Face-to-Face |
|
| Prerequisites and Co-Prerequisites |
: |
None |
|
| Recommended Optional Programme Components |
: |
None |
|
| Aim(s) of Course |
: |
The aim of this course is to introduce the Lebesgue integral within the Riemann integral which the students are already familiar with. |
|
| Course Contents |
: |
Measurable sets, measurable functions, measurement, integrable functions, Lebesgue integral |
|
| Language of Instruction |
: |
Turkish |
|
| Work Place |
: |
Faculty of Science Classrooms |
|
|
Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Measurable sets and measurable functions. |
Review of the relevant pages from sources |
Lecture and discussion |
|
2 |
Properties of measurable functions. |
Review of the relevant pages from sources |
Lecture and discussion |
|
3 |
Measurable sets and functions, problem solving |
Review of the relevant pages from sources |
Lecture and discussion |
|
4 |
Examples of measurements and measurement. |
Review of the relevant pages from sources |
Lecture and discussion |
|
5 |
Solving problems on measurement. |
Review of the relevant pages from sources |
Lecture and discussion |
|
6 |
Definition and properties of integrals. |
Review of the relevant pages from sources |
Lecture and discussion |
|
7 |
Solving integral problems |
Review of the relevant pages from sources |
Lecture and discussion |
|
8 |
Mid-term exam |
Topics discussed in the lecture notes and sources again |
Written Exam |
|
9 |
Integrable functions and Lebesgue integral. |
Review of the relevant pages from sources |
Lecture and discussion |
|
10 |
Comparison of the Lebesgue and Riemann integral. |
Review of the relevant pages from sources |
Lecture and discussion |
|
11 |
Integrable functions, problem solving |
Review of the relevant pages from sources |
Lecture and discussion |
|
12 |
Lebesgue spaces. |
Review of the relevant pages from sources |
Lecture and discussion |
|
13 |
Properties of Lebesgue spaces |
Review of the relevant pages from sources |
Lecture and discussion |
|
14 |
Lp spaces |
Review of the relevant pages from sources |
Lecture and discussion |
|
15 |
Problem solving. |
Review of the relevant pages from sources |
Lecture and discussion |
|
16/17 |
Final exam |
Topics discussed in the lecture notes and sources again |
Written Exam |
|
|
| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
5 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
5 |
|
3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
1 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
2 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
2 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
3 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
4 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
3 |
|
9 |
Knows at least one computer programming language |
3 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
0 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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