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Information
| Code | MTS223 |
| Name | Transformation Semigroups |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 3 ECTS |
| National Credit | 2 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. HAYRULLAH AYIK |
| Course Instructor |
Prof. Dr. HAYRULLAH AYIK
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to make students comprehend full transformation semigroups, some special transformation semigroups and partial transformation semigroups.
Course Content
In this course full transformation semigroups, its some special subsemigroups (symmetric group, singular transformations semigroup , order-preserving transformations semigroup , etc), partial transformation semigroups , its some special subsemigroups (strictly partial transformation semigroups, 1-1 partial transformations semigroup, partial order-preserving transformations semigroup , etc) are described.
Course Precondition
NONE
Resources
Classical Finite Transformation Semigroups, Ganyushkin, Olexandr, Mazorchuk, Volodymyr
Notes
All articles about the topics.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognises full transformation semigroups. |
| LO02 | Recognises some special transformation semigroups. |
| LO03 | Compares the properties of some transformation semigroups. |
| LO04 | Recognises properties of elements of some special transformation semigroups. |
| LO05 | Uses the factorization method in some transformation semigroups. |
| LO06 | Recognises generating sets of some special transformation semigroups. |
| LO07 | Recognises partial transformation semigroups. |
| LO08 | Recognises properties of partial transformation semigroups. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 3 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 4 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 4 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 3 |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 3 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 4 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definition and basic properties of symmetric groups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Definition and basic properties of full transformation semigroups. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Comparison of the symmetric group and full transformation semigroup | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Properties of some special transformation semigroups | Review of the relevant pages from sourcesReview of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Properties of elements of some special transformation semigroups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 6 | Factorization in full transformation semigroups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 7 | Properties of factorization in full transformation semigroups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Generating set of some special transformation semigroups. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Properties of generating set of some special transformation semigroups. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Definition and basic properties of partial transformation semigroups. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Comparison of the full transformation semigroups and partial transformation semigroup | Review of the relevant pages from sourcesReview of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Generating set of partial transformation semigroups. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Idempotent generating sets | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Nilpotent generating sets | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 2 | 28 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 2 | 28 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 6 | 6 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 78 | ||
| Total Workload / 25 (h) | 3,12 | ||
| ECTS | 3 ECTS | ||