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Information
| Code | MT567 |
| Name | Topics in Group Theory I |
| Term | 2024-2025 Academic Year |
| Term | Fall |
| 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 | Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ |
| Course Instructor |
1 |
Course Goal / Objective
To teach the properties of some simple linear groups, some free group structures, torsion groups and Character groups.
Course Content
Simple groups, simple linear groups, free groups, free abelian groups, torsion groups, Character groups.
Course Precondition
Pre-requisites None
Resources
Hungerford T. W. : Algebra
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understand finite fields. |
| LO02 | Understands the concept of simple group. |
| LO03 | Prove some of the properties of some simple linear group structures. |
| LO04 | Understand the definition of free group. |
| LO05 | Understand free abelian groups. |
| LO06 | Understand finitely generated free abelian groups. |
| LO07 | Understand the Nielsen-Schreier theorem and its results. |
| LO08 | Understand the Kurosh theorem and its results. |
| LO09 | Understand the Van Kampen theorem and its results. |
| LO10 | Understand the expansion of HNN. |
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 | 4 |
| 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. | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics | 3 |
| 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. | 3 |
| 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. | |
| 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. | 3 |
| 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. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Finite field structure and examples. | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 2 | Investigated of some simple linear groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 3 | PSL (2, K) and PSL(m, K) groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 4 | Free groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 5 | Free abelian groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 6 | Finitely generated free abelian groups. | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 7 | Torsion groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Ölçme Yöntemleri: Ödev |
|
| 9 | Subgroups of Q | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 10 | Character groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 11 | Nielsen-Schreier theorem and its applications | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 12 | Kurosh Theorem and its applications | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 13 | Van Kampen theorem and its applications | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 14 | HNN expansions | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 15 | HNN expansions 2 | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
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 | ||