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Information
| Code | MT554 |
| Name | Computational Group Theory II |
| Term | 2024-2025 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 | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GONCA AYIK |
| Course Instructor |
1 |
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 and The nilpotent Quotient algorithm are descibed.
Course Precondition
NONE
Resources
Miscellaneous Articles
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows some special group structures. |
| LO02 | Recognizes finite p-groups. |
| LO03 | Recognizes the Nilpotent Quotient Algorithm. |
| LO04 | Recognizes some special group structures. |
| LO05 | Comprehends group extensions. |
| LO06 | Comprehends HNN extension. |
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. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 4 |
| 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 | 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. | 4 |
| 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. | 5 |
| 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 | Some special group constructions | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 2 | Some special group constructions 1 | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Some special group constructions 2 | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Some special group 3 constructions | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | HNN extensions . | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Group extensions 1 | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Group extensions 2 | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Lecture, problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Group extensions 3 | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Relation modules, G-module 1 | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Relation modules, G-module 2 | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | The augmentation ideal, derivations 1 | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | The augmentation ideal, derivations 2 | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Free differential calculus 1 | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Free differential calculus 2 | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 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 | ||