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Information
| Code | MT549 |
| Name | Presentations of Groups II |
| Term | 2024-2025 Academic Year |
| 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. GONCA AYIK |
Course Goal / Objective
The aim of this course is to teach further results of group presentations to the students.
Course Content
In this course presentations of certain subgroups, presentations of certain group extensions, Relation modules, finite p-groups, The nilpotent Quotient algorithm and Golod-Shafarevich Theorem are descibed.
Course Precondition
Take a basic algebra course
Resources
Miscellaneous Articles
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes Alternating group, Braid groups and von Dyck group. |
| LO02 | Recognizes triangle groups and free products. |
| LO03 | Recognizes HNN extensions and Schur multiplicator. |
| LO04 | Recognizes presentations of group extensions. |
| LO05 | Recognizes Relation modules. |
| LO06 | Recognizes finite p-groups. |
| LO07 | Recognizes the Nilpotent Quotient Algorithm. |
| LO08 | Recognizes the Golod-Shafarevich theorem. |
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. | 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 | |
| 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. | 5 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Sets up original problems in her field and offers different solution techniques | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | It 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. | 4 |
| 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. | 3 |
| 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. | 5 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Alternating groups and Braid groups | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Von Dyck groups. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Triangle groups and free products | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 4 | HNN extensions . | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 5 | Schur multiplicator | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Group extensions. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım |
| 7 | Presentations of group extensions. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Lecture, problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Relation modules, G-module | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | The augmentation ideal, derivations. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Free differential calculus. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 12 | An algorithm for N/N' | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Finite p-groups. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Nilpotent Quotient Algorithm | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Golod-Shafarevich theorem | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 16 | Term Exams | Lecture, problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Lecture, problem solving | 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 | ||