TÜRKÇE
ENGLISH
Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (MASTER) (WITH THESIS) | |
| Code | MT526 |
| Name | Topological Groups |
| Term | 2022-2023 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 | Belirsiz |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
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 |
|---|
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 |
|
| 17 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |