MT551 Semigroup Theory

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

Information

Code MT551
Name Semigroup Theory
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 Yüksek Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Doç. Dr. LEYLA BUGAY


Course Goal / Objective

The aim of this course is to teach semigroups and semigroup structures, semigroups homomorphism, congruences, Ideals and Rees congruences, simple and zero simple semigroups to the students.

Course Content

In this course semigroups and examples of semigroups, Monogenic semigroups,Ordered sets , semilattices and lattices, Equivalence relations, Congruences, Semigroup homomorphism, free semigroup, Presentations of semigroups and monoids, Ideals and Rees congruences, Green Equivalences, Structure of D-classes, Regular D-classes, Regular semigroups, Simple and zero simple semigroups, Completely simple semigroups are described.

Course Precondition

To have taken a basic algebra course.

Resources

Fundamentals of Semigroup Theory - John M. Howie

Notes

Semigroup Theory e-books can be used.


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Recognizes the structure of semigroups.
LO02 Recognizes the structure of semigroup homomorphisms.
LO03 Recognizes the structure of semilattices.
LO04 Recognizes the structure of congruences.
LO05 Recognizes the structure of ideals and Rees congruence.
LO06 Recognizes the structure of Green's equivalences.
LO07 Recognizes the structure of regular D-classes.
LO08 Recognizes the structure of simple and zero-simple semigroups.


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. 5
PLO02 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in his area of ​​expertise and other areas of mathematics.
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. 4
PLO06 Bilgi - Kuramsal, Olgusal Effectively uses the technical equipment needed to express mathematics.
PLO07 Bilgi - Kuramsal, Olgusal poses original problems related to field and presents different solution techniques. 4
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. 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. 4
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. 5
PLO13 Yetkinlikler - Öğrenme Yetkinliği Adheres to the ethical rules required by its scientific title 5


Week Plan

Week Topic Preparation Methods
1 Semigroups and examples of semigroups Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım
2 Monogenic semigroups Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Problem Çözme
3 Ordered sets , semilattices and lattices Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
4 Equivalence relations Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
5 Congruences Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
6 Semigroup homomorphism, free semigroup Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
7 Presentations of semigroups and monoids Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
8 Mid-Term Exam Lecture, Problem Solving Ölçme Yöntemleri:
Yazılı Sınav
9 Ideals and Rees congruences Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
10 Green Equivalences Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Problem Çözme
11 Structure of D-classes Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Problem Çözme
12 Regular D-classes Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Problem Çözme
13 Regular semigroups Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Problem Çözme
14 Simple and zero simple semigroups Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Problem Çözme
15 Completely simple semigroups Reviewing the relevant chapters in the Sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Problem Çözme
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 11:37