MT0024 Lattice Theory

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

Information

Code MT0024
Name Lattice Theory
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


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

Update Time: 12.06.2024 11:22