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Information
| Code | MT526 |
| Name | Topological Groups |
| Semester | . Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Belirsiz |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ |
Course Goal
to give the concept of topological groups and investigate the actions of a topological group on a topological space, in particular to investigate representations of topological groups.
Course Content
Definition of topological group and some examples, global and local properties of topological groups, actions of topological groups on a topolocial space, continuous real valued functions on a topological groups, Haar integration and representation of topological groups
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Can explain the concept of topological group |
| LO02 | Know global and local properties of topological groups |
| LO03 | Investigate the action of a topological group on a topological space |
| LO04 | Know the structure of the continuous real valued functions on the topological groups |
| LO05 | Know the existence of Haar integral on a compact group and its consequences |
| LO06 | Know some knowledge about the representation of compact groups |
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. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | |
| 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. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | |
| 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. | |
| 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. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definition of topological group and neighbourhood system of the identity | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 2 | Subgroups, normal subgroups and factor groups | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 3 | Subgroups, normal subgroups and factor groups | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 4 | topological homomorphisms and topological isomorphisms | Read the relevant sections in the textbook and solving problems | |
| 5 | Direct product of topological groups | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 6 | Connected and totally disconnected topological groups | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 7 | Local properties of topological groups and local isomorphisms | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | local properties of topological groups and local isomorphisms | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 10 | Topological transformation groups | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 11 | Topological transformation groups | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 12 | Continuous real valued functions on topological groups | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 13 | Haar integration on compact topological groups | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 14 | Schur lemma | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 15 | Peter-Weyl theorem | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
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| 17 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |