MT549 Presentations of Groups II

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

Information

Code MT549
Name Presentations of Groups II
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 Prof. Dr. GONCA AYIK


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, The nilpotent Quotient algorithm and Golod-Shafarevich Theorem are descibed.

Course Precondition

Take a basic algebra course

Resources

Miscellaneous Articles

Notes

Lecture Notes


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Recognizes Alternating group, Braid groups and von Dyck group.
LO02 Recognizes triangle groups and free products.
LO03 Recognizes HNN extensions and Schur multiplicator.
LO04 Recognizes presentations of group extensions.
LO05 Recognizes Relation modules.
LO06 Recognizes finite p-groups.
LO07 Recognizes the Nilpotent Quotient Algorithm.
LO08 Recognizes the Golod-Shafarevich theorem.


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
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
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. 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. 3
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 Alternating groups and Braid groups Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
2 Von Dyck groups. Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
3 Triangle groups and free products Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Problem Çözme
4 HNN extensions . Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Problem Çözme
5 Schur multiplicator Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
6 Group extensions. Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım
7 Presentations of group extensions. Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
8 Mid-Term Exam Lecture, problem solving Ölçme Yöntemleri:
Yazılı Sınav
9 Relation modules, G-module Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
10 The augmentation ideal, derivations. Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
11 Free differential calculus. Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Problem Çözme
12 An algorithm for N/N' Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
13 Finite p-groups. Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
14 Nilpotent Quotient Algorithm Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
15 Golod-Shafarevich theorem Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
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: 09.05.2024 11:39