| Course Type | Elective Course |
|---|
| Course Level | Bachelor's Degree |
|---|
| Year of Study | - |
|---|
| Semester | - |
|---|
| ECTS | 4 |
|---|
| Name of Lecturer(s) |
- |
| Learning Outcomes |
At the end of this course, the students;
- Know the concept of set; can explain the concepts of finite set, countable set.
- Know the concepts of opean set, closed set.
- Know the concepts of metric space.
- Know the concept of convergence in metric spaces.
- Know the basic concepts of normed spaces.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | EMT103-EMT104-EMT203 |
|---|
| Course Description | The course content includes the following topics: the concept of a set, finite sets, countable sets, supremum and infimum concepts, definition of the metric, norm, open and closed set, closure of a set, boundary, neighborhoods and accommodation points in metric spaces, sequences and convergence, continuity, cauchy sequences, completeness. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Concept of a set, finite sets, countable sets |
|
2nd Week |
Sup and inf concepts, related examples |
|
3rd Week |
Introduction to metric spaces-description and properties |
|
4th Week |
Examples related to metric spaces |
|
5th Week |
Open and closed sets in metric spaces-topology concept |
|
6th Week |
Inner point, outer point |
|
7th Week |
Accumulation points, closing point, neighbourhoods |
|
8th Week |
Midterm |
|
9th Week |
Neighbourhoods and convergence in metric spaces |
|
10th Week |
Convergence in metric spaces |
|
11th Week |
Normed spaces-definition and examples |
|
12th Week |
Basic properties of normed spaces |
|
13th Week |
Introduction to inner product spaces |
|
14th Week |
Basic properties of inner product spaces-examples |
|
15th Week |
General review |
|
| Recommended or Required Reading | Mustafa Bayraktar- Fonksiyonel Analiz-Analiz
Öner Çakar, Fonksiyonel Analize Giriş
Seyit Ahmet Kılıç-Musa Erdem, Metrik Uzaylar ve Topoloji |
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
40 |
| Quiz |
2 |
10 |
| Total(%) |
|
50 |
| Contribution of In-term Studies to Overall Grade(%) |
|
50 |
| Contribution of Final Examination to Overall Grade(%) |
|
50 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
2 |
2 |
| Preparation for Quiz |
2 |
3 |
6 |
| Individual or group work |
13 |
3 |
39 |
| Preparation for Final exam |
1 |
20 |
20 |
| Course hours |
13 |
3 |
39 |
| Preparation for Midterm exam |
1 |
12 |
12 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
2 |
2 |
| Homework |
|
|
|
| Total Work Load | 120 |
| Total Work Load / 30 (h) | 4 |
| ECTS Credit of the Course | 4 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
