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Information
| Code | MT502 |
| Name | Topological Vector Spaces |
| Term | 2024-2025 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. DİLEK KAHYALAR |
| Course Instructor |
1 |
Course Goal / Objective
To define Frechet and Köthe sequence spaces and to teach general properties.
Course Content
Topological vector spaces, Frechet spaces and Köthe sequence spaces
Course Precondition
NONE
Resources
Lecture Notes
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the concept of topological vector space and gives examples. |
| LO02 | Defines locally convex topological vector spaces |
| LO03 | Knows the concept of base for Frechet spaces |
| LO04 | Knows Kothe sequnce spaces and their general properties. |
| LO05 | Knows some linear topological invariants |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 5 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 5 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | 5 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Some informations about metric and normed spaces | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Topological vector spaces and properties 1 | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Topological vector spaces and properties | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Bounded and totally bounded sets | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Finite dimensional vector spaces | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | locally convex topological spaces | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Frechet spaces 1 | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Exam | Ölçme Yöntemleri: Ödev |
| 9 | Frechet spaces | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Montel and Schwartz spaces | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Bases of Frechet spaces 1 | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Bases of Frechet spaces | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Kothe sequence spaces 1 | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Kothe sequence spaces | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Linear topological invariants | Prepare the releated topics | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Term Exam | Öğretim Yöntemleri: Anlatım, Tartışma |
| 17 | Term Exams | Term Exam | Ölçme Yöntemleri: Ödev |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||