MT519 Introduction to Group Presentations

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

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

Update Time: 17.06.2024 04:01