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Information
| Code | MT551 |
| Name | Semigroup Theory |
| 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 | Doç. Dr. LEYLA BUGAY |
| Course Instructor |
Prof. Dr. HAYRULLAH AYIK
(A Group)
(Ins. in Charge)
|
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 | ||