| Course Description |
|
| Course Name |
: |
Functional Analysis I |
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| Course Code |
: |
MT 463 |
|
| Course Type |
: |
Optional |
|
| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
4 |
|
| Course Semester |
: |
Fall (16 Weeks) |
|
| ECTS |
: |
5 |
|
| Name of Lecturer(s) |
: |
|
|
| Learning Outcomes of the Course |
: |
Knows convergence in metric spaces, the Cauchy sequence and the concept of completeness.
Understands the relationship between vector spaces and normed spaces.
Realizes that every normed space is a metric space.
Illustrates the concepts of convergence and continuity in normed spaces.
Relates fundamental analysis details to the concepts of normed space.
Understands the importance of the norm of a linear transformation.
Describes and illustrates a Banach space.
Has a comprehensive and systematic understanding of the basic problems in analysis.
|
|
| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
|
| Recommended Optional Programme Components |
: |
None |
|
| Aim(s) of Course |
: |
Understanding the relationships between metric spaces, vector spaces and normed spaces and understanding Banach spaces. |
|
| Course Contents |
: |
Metric spaces, normed spaces, Banach spaces. |
|
| Language of Instruction |
: |
Turkish |
|
| Work Place |
: |
Faculty of Science Annex Classrooms |
|
|
Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Review of general metric spaces, definitions and examples |
Review of the relevant pages from sources |
Lecture and discussion |
|
2 |
Metric spaces, convergence, continuity, and the relationships between them. |
Review of the relevant pages from sources |
Lecture and discussion |
|
3 |
Problem solving |
Review of the relevant pages from sources |
Lecture and discussion |
|
4 |
Cauchy sequences and complete metric spaces |
Review of the relevant pages from sources |
Lecture and discussion |
|
5 |
Some specific examples of complete metric space |
Review of the relevant pages from sources |
Lecture and discussion |
|
6 |
Problem solving |
Review of the relevant pages from sources |
Lecture and discussion |
|
7 |
Review of the basic concepts related to vector spaces |
Review of the relevant pages from sources |
Lecture and discussion |
|
8 |
Mid-term exam |
Topics discussed in the lecture notes and sources again |
Exam |
|
9 |
Some specific examples of linear spaces |
Review of the relevant pages from sources |
Lecture and discussion |
|
10 |
Summary of basic concepts of linear transformations |
Review of the relevant pages from sources |
Lecture and discussion |
|
11 |
normed spaces and examples of normed spaces |
Review of the relevant pages from sources |
Lecture and discussion |
|
12 |
The relationship between metric spaces and normed spaces |
Review of the relevant pages from sources |
Lecture and discussion |
|
13 |
Convergence in normed spaces and the norm of a linear transformations |
Review of the relevant pages from sources |
Lecture and discussion |
|
14 |
Banach Spaces and examples |
Review of the relevant pages from sources |
Lecture and discussion |
|
15 |
Finite-dimensional normed spaces |
Review of the relevant pages from sources |
Lecture and discussion |
|
16/17 |
Final exam |
Topics discussed in the lecture notes and sources again |
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 |
1 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
1 |
|
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 |
5 |
|
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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