MT570 Topics in Group Theory II

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

Information

Code MT570
Name Topics in Group Theory II
Term 2022-2023 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. ZERRİN GÜL ESMERLİGİL


Course Goal / Objective

Bazı basit lineer grupların özellikleri ve bazı serbet grup yapılarının incelenmesi

Course Content

Free Groups and Elemantary proporties of Free Groups

Course Precondition

Take a basic algebra course

Resources

Miscellaneous articles

Notes

Lecture Notes


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Understands free group and free presentations.
LO02 Knows some popular groups.
LO03 Knows subgroup presentations.
LO04 Comprehend triangular groups.
LO05 Understands Euclidean, elliptic and hyperbolic states in triangular groups.
LO06 Knows group extensions.
LO07 Learns the kohomology of groups
LO08 Comprehend the Golod-Safarevic theorem and its results.
LO09 Learns some endless Fibonacci groups.


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 4
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 5
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.
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.
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 Free groups and elamantry properties of Free groups Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
2 Free presantation of groups Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
3 Examples of Presantation Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
4 Finitely generated Abelian groups Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
5 Some relations on groups and tree generated interesting groups Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
6 Presentations of subgroups Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
7 Coset Enumeration Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
8 Mid-Term Exam Lecture Discussion Ölçme Yöntemleri:
Yazılı Sınav
9 Triangels groups Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
10 Oklidian,elliptic and hiperbolic cases Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
11 Groups extantions and Theory of extantions Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
12 Cohomology of groups, Local Cohomology and p-groups Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
13 Presentations of Groups extantions Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
14 Golod-Safarevic Theorem Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
15 Some unfinitely Fibonacci groups Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
16 Term Exams Lecture Discussion Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Lecture Discussion 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: 17.11.2022 10:55