TÜRKÇE
ENGLISH
Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (MASTER) (WITH THESIS) | |
| Code | MT009 |
| Name | Abelian Groups |
| Term | 2024-2025 Academic Year |
| Term | Fall |
| 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 Instructor |
Prof. Dr. YILMAZ DURĞUN
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
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 |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Homework | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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 | ||