MT565 Topics in Semigroup Theory I

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

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

Update Time: 09.05.2024 11:39