MT009 Abelian Groups

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

Information
Goal, Content & Resources
Course Learning Outcomes
Relation with Program Learning Outcome
Week Plan
Student Workload - ECTS

Information

Code MT009
Name Abelian Groups
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 Prof. Dr. YILMAZ DURĞUN


Course Goal

This course is devoted to the theory of abelian groups.

Course Content

The Most Important Types of Groups , Categories of Abelian Groups, Functorial Subgroups and Quotient Groups Direct Sums and Direct Products , Pullback and Pushout Diagrams , Direct Limits and Inverse Limits , Completeness and Completions, Direct Sums of Cyclic Groups , Cyclic Groups, Free Abelian Groups, Finitely Generated Groups , Linear Independence and Rank , Direct Sums of Cyclic p-Groups , Countable Free Groups , Divisibility , Injective Groups , Pure Subgroups , Bounded Pure Subgroups , Pure-Exact Sequences , Pure-Projectivity and Pure-Injectivity , Generalizations of Purity , Basic Subgroups

Course Precondition

NONE

Resources

Infinite Abelian Groups by Laszlo Fuchs

Notes

Abelian Group Theory Rüdiger Göbel, Elbert Walker


Course Learning Outcomes

Order Course Learning Outcomes
LO01 The Most Important Types of Groups , Categories of Abelian Groups, Functorial Subgroups and Quotient Groups Direct Sums and Direct Products , Pullback and Pushout Diagrams
LO02 Direct Limits and Inverse Limits , Completeness and Completions, Cyclic Groups, Free Abelian Groups, Finitely Generated Groups, Direct Sums of Cyclic p-Groups
LO03 Countable Free Groups , Divisibility , Injective Groups
LO04 Pure Subgroups , Bounded Pure Subgroups , Pure-Exact Sequences , Pure-Projectivity and Pure-Injectivity
LO05 Generalizations of Purity, Basic Subgroups


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. 3
PLO02 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in his 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. 2
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 poses original problems related to field and presents different solution techniques. 2
PLO08 Bilgi - Kuramsal, Olgusal 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. 3
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. 2
PLO13 Yetkinlikler - Öğrenme Yetkinliği Adheres to the ethical rules required by its scientific title


Week Plan

Week Topic Preparation Methods
1 Preliminaries Reading the lecture notes Öğretim Yöntemleri:
Anlatım
2 The Most Important Types of Groups Reading the lecture notes Öğretim Yöntemleri:
Anlatım
3 Categories of Abelian Groups Reading the lecture notes Öğretim Yöntemleri:
Anlatım
4 Functorial Subgroups and Quotient Groups Direct Sums and Direct Products Reading the lecture notes Öğretim Yöntemleri:
Anlatım
5 Pullback and Pushout Diagrams, Direct Limits and Inverse Limits Reading the lecture notes Öğretim Yöntemleri:
Anlatım
6 Completeness and Completions, Cyclic Groups Reading the lecture notes Öğretim Yöntemleri:
Anlatım
7 Cyclic Groups Reading the lecture notes Öğretim Yöntemleri:
Anlatım
8 Mid-Term Exam Reading the lecture notes Ölçme Yöntemleri:
Yazılı Sınav
9 Free Abelian Groups, Finitely Generated Groups, Direct Sums of Cyclic p-Groups Reading the lecture notes Öğretim Yöntemleri:
Anlatım
10 Countable Free Groups , Divisibility Reading the lecture notes Öğretim Yöntemleri:
Anlatım
11 Injective Groups, Pure Subgroups Reading the lecture notes Öğretim Yöntemleri:
Anlatım
12 Bounded Pure Subgroups , Pure-Exact Sequences Reading the lecture notes Öğretim Yöntemleri:
Anlatım
13 Pure-Projectivity and Pure-Injectivity Reading the lecture notes Öğretim Yöntemleri:
Anlatım
14 Basic Subgroups,Generalizations of Purity Reading the lecture notes Öğretim Yöntemleri:
Anlatım
15 ,Basic Subgroups Reading the lecture notes Öğretim Yöntemleri:
Anlatım
16 Term Exams Reading the lecture notes Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Reading the lecture notes 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