MT550 Semigroup Constructions and Presentations

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

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

Update Time: 09.05.2024 11:37