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Information
| Code | MT565 |
| Name | Topics in Semigroup Theory I |
| 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 | Doktora 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 certain special transformation semigroups and notions of minimal generating set and rank to the students.
Course Content
In this course n. Symmetric group, Full/Partial transformation semigroup, Singuar transformations semigroup, order-preserving transformations semigroup, order-preserving and order-increasing (order-decreasing) transformations semigroup, and notions of their minimal generating sets and ranks are descibed.
Course Precondition
Take a basic algebra course
Resources
Miscellaneous Articles
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes the n. Symmetric group. |
| LO02 | Recognizes the Full transformations semigroup. |
| LO03 | Recognizes the Partial transformation semigroup. |
| LO04 | Recognizes the Singular transformations semigroup. |
| LO05 | Recognizes the order-preserving transformations semigroup |
| LO06 | Recognizes the order-preserving and order-decreasing transformations semigroup. |
| LO07 | Recognizes the order-preserving and order-increasing transformations semigroup |
| LO08 | Recognizes minimal generating sets and ranks of these 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. | 3 |
| 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 | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Sets up original problems in her field and offers different solution techniques | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | It 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. | 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 | n. Symmetric group. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Generating sets and rank of n. Symmetric group. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım |
| 3 | Full transformations semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Generating sets and rank of Full transformations semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım |
| 5 | Partial transformations semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Generating sets and rank of Partial transformations semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Singular transformations semigroup, its generating sets and rank | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Lecture, problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Order-preserving transformations semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Generating sets and rank of Order-preserving transformations semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım |
| 11 | Order-preserving and order-decreasing transformations semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 12 | Generating sets and rank of order-preserving and order-decreasing transformations semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Order-preserving and order-increasing transformations semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 14 | Generating sets and rank of order-preserving and order-increasing transformations semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Generating sets and rank of partial order-preserving transformations semigroup. | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 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 | ||