MT563 Topological Algebraic Structures

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

Information
Goal, Content & Resources
Course Learning Outcomes
Relation with Program Learning Outcome
Week Plan
Student Workload - ECTS

Information

Code MT563
Name Topological Algebraic Structures
Semester . Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 6 ECTS
National Credit 3 National Credit
Teaching Language Türkçe
Level Doktora Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. ALİ ARSLAN ÖZKURT


Course Goal

Investigate Topological Algebraic Structures

Course Content

Topological Groups and properties uniform continuity on topological groups, topological rings, Topological vector spaces and locally convex topological vector spaces

Course Precondition

No

Resources

The Structure of Compact Groups, Karl H. Hofmann, Sidney A. Morris

Notes

Topological Groups, L. S. Pontryagin


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Comprehends the concept of Topological Groups
LO02 Knows the properties of topological groups
LO03 Comprehends the concept of uniform continuity onTopological Groups
LO04 Comprehends the concept of Topological Rings
LO05 Comprehends the concept of Topological Vector spaces
LO06 Knows the properties of locally convex topological vector spaces


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Knows the results of previous research in a special field of mathematics 5
PLO02 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. 3
PLO03 Bilgi - Kuramsal, Olgusal Establishes new mathematical models with the help of the knowledge gained in the field of specialization.
PLO04 Bilgi - Kuramsal, Olgusal Has basic knowledge in all areas of mathematics
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 4
PLO07 Bilgi - Kuramsal, Olgusal Sets up original problems in her field and offers different solution techniques 3
PLO08 Bilgi - Kuramsal, Olgusal It carries out original and qualified scientific studies on the subject related to its field. 3
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 foreign language knowledge 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 It presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders.
PLO13 Yetkinlikler - Öğrenme Yetkinliği Adheres to the ethical rules required by its scientific title 5


Week Plan

Week Topic Preparation Methods
1 Introduction of Topological Groups Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
2 Seperation Properties of Topological groups Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
3 Subgroups of Topological groups Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
4 Quotient of topological Groups Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
5 Products of topological Groups Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
6 Uniform Continuity on Topological Groups Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
7 Topological rings Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
8 Mid-Term Exam Topics discussed in the lecture notes and sources again Ölçme Yöntemleri:
Ödev
9 Subrings of Topological rings Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
10 Topological Division rings continue Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
11 topological Modules Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
12 Topological Vector spaces Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
13 Topological Vector spaces continue Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
14 locally convex topological vector spaces Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
15 locally convex topological vector spaces continue Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
16 Term Exams Topics discussed in the lecture notes and sources again Ölçme Yöntemleri:
Ödev, Performans Değerlendirmesi
17 Term Exams Topics discussed in the lecture notes and sources again Ölçme Yöntemleri:
Ödev, Performans Değerlendirmesi


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