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Information
| Code | MTS384 |
| Name | Lattice Theory |
| Term | 2024-2025 Academic Year |
| Semester | 6. 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 | Doç. Dr. DİLEK KAHYALAR |
| Course Instructor |
1 2 |
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
A course in universal algebra, Stanley Burris, H.P. Sankappanavar
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes the Lattices and its examples. |
| LO02 | Recognizes the isomorphic Lattices, sublattices and their examples |
| LO03 | Recognizes the Distributive and Modular Lattices and their examples. |
| LO04 | Recognizes the Complete and Algebraic Lattices and their examples. |
| LO05 | Recognizes the Closure operators of Lattices. |
| LO06 | Recognizes universal lattices and its examples. |
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. | 5 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 4 |
| 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. | 4 |
| 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. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 4 |
| 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 | 3 |
| 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. | 5 |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 2 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 4 |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 2 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 2 |
| 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. | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definitions of lattices and examples 1 | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Definitions of lattices and examples | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Isomorphic Lattices, and Sublattices | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Distributive and Modular Lattices 1 | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Distributive and Modular Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Complete Lattices, Equivalence Relations, and Algebraic Lattices | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Closure Operators 1 | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Summary | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Closure Operators | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Definitions of universal algebra and examples 1 | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Definitions of universal algebra and examples | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Isomorphic Algebras, and Subalgebras | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Algebraic Lattices and basis theorem 1 | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Algebraic Lattices and basis theorem | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Solving problems | Required readings | Öğretim Yöntemleri: Problem Çözme |
| 16 | Term Exams | summary | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | summary | 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 | ||