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Information
| Code | MT568 |
| Name | Topics in Semigroup Theory II |
| Term | 2024-2025 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. HAYRULLAH AYIK |
| Course Instructor |
1 |
Course Goal / Objective
The aim of this course is to teach the notions of semigroup generating set and semigroup presentations, generating sets and presentations of certain special semigroups and efficiency of semigroups to the students.
Course Content
In this course definitions of semigroup generating set and semigroup presentations, the methods of finding generating sets and presentations, generating sets and presentations of certain special semigroups and efficiency of semigroups are described.
Course Precondition
NONE
Resources
Miscellaneous Articles
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes the semigroup presentation. |
| LO02 | Recognizes finding the semigroup presentations that describes group. |
| LO03 | Recognizes finding the minimal presentations. |
| LO04 | Recognizes the notion efficiency of semigroups. |
| LO05 | Recognizes to be finitely presented. |
| LO06 | Recognizes the notion semigroup rank. |
| LO07 | Recognizes the idempotent rank of certain transformation semigroups. |
| LO08 | Recognizes finding the presentations of certain semigroups. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows the results of previous research in a special field of mathematics | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her 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. | 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. | 5 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Sets up original problems in her field and offers different solution techniques | 5 |
| PLO08 | Bilgi - Kuramsal, Olgusal | It 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. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have foreign language knowledge 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 | It 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 | Semigroup presentation and certain properties | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Certain finitely generated semigroups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Certain finitely presented semigroups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Efficiency of semigroups, monoids and groups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | Adian graphs | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Semigroup presentations that defines group | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Finding a presentation of a semigroup | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 8 | Mid-Term Exam | Review and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Finding a presentation of a semigroup | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | The presentation of Rees matrices semigroup | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | The presentation of Schützenberger product | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | The presentation of direct product | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Semigroup presentation and word problem | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Strong semilattices of semigroups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 15 | The presentations of strong semilattices of semigroups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 16 | Term Exams | Review and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review and 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 | ||