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Information
| Code | MT550 |
| Name | Semigroup Constructions and Presentations |
| 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 | Prof. Dr. GONCA AYIK |
Course Goal / Objective
The aim of this course is to teach students more advanced topics and presentations in semigroup structures.
Course Content
In this course (minimal) generating sets, rank, 0-simple semigroups and ranks, Rees matrix semigroups, transformation semigroups, matrix semigroups, known presentations, general methods for finding presentations, special linear semigroups, general linear semigroups, the wreath product, the Schützenberger product, the Bruck-Reilly extension, strong semilattices of monoids are described.
Course Precondition
Take a basic algebra course
Resources
Miscellaneous Articles
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Realizes (minimal) generating sets of semigroups. |
| LO02 | Realizes ranks of semigroups. |
| LO03 | Realizes 0-simple semigroups and ranks. |
| LO04 | Realizes Rees matrix semigroups. |
| LO05 | Realizes transformation semigroups. |
| LO06 | Realizes matrix semigroups. |
| LO07 | Realizes known presentations. |
| LO08 | Realizes general methods for finding presentations. |
| LO09 | Realizes special linear semigroups. |
| LO10 | Realizes general linear semigroups. |
| LO11 | Realizes the wreath product. |
| LO12 | Realizes the Schützenberger product. |
| LO13 | Realizes the Bruck-Reilly extensions. |
| LO14 | Realizes strong semilattices of monoids. |
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. | 4 |
| 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. | 5 |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 4 |
| 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. | 5 |
| 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 | (Minimal) Generating sets of semigroups | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Ranks of semigroups | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | 0-simple semigroups and ranks | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Rees matrix semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | Transformation semigroups | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Matrix semigroups | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Known presentations | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Lecture and solving problem | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | General methods for finding presentations | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Special linear semigroups | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | General linear semigroups | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | The wreath product | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | The Schützenberger product | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | The Bruck-Reilly extensions. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Strong semilattices of monoids | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 16 | Term Exams | Lecture and solving problem | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Lecture and solving problem | 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 | ||