MT502 Topological Vector Spaces

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code MT502
Name Topological Vector Spaces
Semester . Semester
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 Goal

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