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| MAT3009 | Introduction to Lattice Theory | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Funda KARAÇAL | | Co-Lecturer | Lecturer. Dr. Ümit ERTUĞRUL | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to introduce lattices as partial ordered set and algebras.By partial ordered set , hasse diagrams, complete lattices, Brouwerian lattices are given. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | teach the concept of partial ordered set | 1,2,3,4,5,6,7,8 | 1 | | LO - 2 : | understand lattice structure together examples | 1,2,3,4,5,6,7,8 | 1 | | LO - 3 : | understand distributive lattice structure and modular lattice structure. | 1,2,3,4,5,6,7,8 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Partial ordered set, lattice isomorphism, graded partial oredered set, Distributive lattices, Modular lattices, semi modular lattices, complemented modular lattices, Boolean lattices, Boolean algebras |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Posets | | | Week 2 | Lattice İsomorphisms, Self duality | | | Week 3 | Diagrams | | | Week 4 | Graded Posets | | | Week 5 | Lattices | | | Week 6 | Lattice examples | | | Week 7 | Distributive lattices | | | Week 8 | Modular lattices | | | Week 9 | Mid-term | | | Week 10 | semi Modular lattices | | | Week 11 | Complemented Modular Lattices | | | Week 12 | Boolean Lattices, Boolean Algebras | | | Week 13 | Boolean Lattice Examples | | | Week 14 | Lattice examples obtained from Algebraic Structures | | | Week 15 | Brouwerian Lattices | | | Week 16 | End-of-term exam | | | |
| 1 | Birkhoff, G; Lattice Theory, Providence, Rhode Island, 1976. | | | |
| 1 | Gratzer, G; General Lattice Theory, Birkhauser Verlag, Basel, 2003. | | | 2 | Davey, B. A., Prietsley, H. A.; Introduction to Lattices and Order, Cambridge University Press, Cambridge, 1990. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 22/11/2021 | 2 | 50 | | End-of-term exam | 16 | 12/01/2021 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 6 | 14 | 84 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 5 | 1 | 5 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 0 | 0 | 0 | | Proje | 0 | 0 | 0 | | Kısa sınav | 14 | 1 | 14 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 173 |
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