MT567 Topics in Group Theory I

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

Information

Code MT567
Name Topics in Group Theory I
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 Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ


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

Update Time: 09.05.2024 11:39