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Information
| Code | MT0024 |
| Name | Lattice Theory |
| 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 | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | |
| Course Instructor |
1 |
Course Goal / Objective
Students recognize some basic definitions,examples, theorems and problems about Lattices.
Course Content
Some basic definitions and examples about Lattices, Isomorphic Lattices and sublattices, Distributive and Modular Lattices, Comlete and Algebraic Lattices, Closure Operators.
Course Precondition
NONE
Resources
A course in universal algebra, Stanley Burris, H.P. Sankappanavar
Notes
Kafes Teorisi-Thomas Donnellan Çeviren: Mehmet Terziler - Tahsin Öner
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | They learn the basic definitions and examples related to lattice theory. |
| LO02 | They learn isomorphic lattices, sublattices and their examples |
| LO03 | They learn distributive and modular lattices and their examples. |
| LO04 | They learn complete and algebraic lattices and their examples. |
| LO05 | They learn closure operators of lattices. |
| LO06 | They enhance their ability to solve problems in various contexts. |
| LO07 | They improve their problem-solving skills. |
| LO08 | They learn to construct logical arguments. |
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. | 4 |
| 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. | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 3 |
| 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. | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 4 |
| 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. | |
| 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. | 3 |
| 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. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Partially ordered sets and Their Properties. | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Cardinals and Ordinals | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Semilattices | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Complete Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Introduction to Algebraic Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Algebraic Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Required readings | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Representation by Equivalence Relations | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Free Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Congruence Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Varieties of Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Varieties of Finite Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Distributive Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Modular and Semimodular Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 16 | Term Exams | Required readings | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Required readings | 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 | ||