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Information
| Code | MT519 |
| Name | Introduction to Group Presentations |
| 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 | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. LEYLA BUGAY |
Course Goal / Objective
The aim of this course is to teach the definition of free group and its elementary properties, existence and further properties of F(X), Schreier's Method and its certain properties, Nielsen's method and certain properties, certain group presentations to the students.
Course Content
In this course the definition of free groups and elementary properties, existence and further properties of F(X), Schreier's Method and its certain properties, Nielsen's method and certain properties, certain group presentations are descibed.
Course Precondition
Must have taken a group theory course.
Resources
A COURSE IN THE THEORY OF GROUPS, DEREK J.S.B ROBINSON, SPRINGER-VERLAG,NEW YORK, 1996.
Notes
Group Theory books and e-books can be used.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the definition of free group. |
| LO02 | Knows basic properties of free groups. |
| LO03 | Knows the existence and basic properties of free group F(X). |
| LO04 | Knows the Schreier's Method and its certain properties. |
| LO05 | Knows the Nielsen's Method , its certain properties and further applications. |
| LO06 | Knows the presentation of direct product of two groups. |
| LO07 | Knows the Tietze transformations. |
| LO08 | Knows certain group presentations. |
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. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 2 |
| 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. | 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. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | 2 |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 3 |
| 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. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definition of free groups and elementary properties | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 2 | Existence and further properties of F(X) | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 3 | The Schreier transversals and generators | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 4 | The Schreier generators | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 5 | Freeness of the generators | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 6 | Certain conclusions of Schreier's method | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Introduction to the Nielsen's method. | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 8 | Mid-Term Exam | Lecture, Problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Nielsen's method and its basic properties | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 10 | Further applications of Nielsen's method | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Free presentations of groups | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Problem Çözme, Alıştırma ve Uygulama |
| 12 | Direct products | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 13 | Tietze transformations | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 14 | Certain group presentations | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 15 | Certain group presentations -continue | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Problem Çözme, Alıştırma ve Uygulama |
| 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 | ||