|
|
| MAT5460 | Lattice Theory | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Dr. Öğr. Üyesi Şerife YILMAZ | | Co-Lecturer | Assoc. Prof. Dr. Funda Karaçal | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | This course introduces lattices both as partially ordered sets and as algebras. From the partial order point of view, we treat Hasse diagrammes, complete lattices, Brouwerian lattices . From the algebraic point of view, we treat the homomorphism theorems, special classes such as modular, distributive, and Boolean algebras as well as the representation theory for finite lattices and its relation to classical propositional logic. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | familiar with the notions of partially ordered sets , including lattices and Bool algebras, Free lattices and has seen the connection to various topics in algebra, analysis. | 1,2 | 1 | | PO - 2 : | work with the basic concepts of lattice theory : modular lattices, distributive lattices;Boolean algebras. | 2,3,4 | 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), PO : Learning Outcome | | |
| Posets; Chains; Diagrams; Graduated posets; Lattices; Distributivity ; Semimodularity; Complemented Modular lattices; Ouasi-orderings; Morphisms and Ideals; Congruence Relations; Lattice polynomials; Boolean algebras; Brouwerian lattices; Newman Algebras; Ortholattices. |
| |
| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Posets | | | Week 2 | Diagrams | | | Week 3 | Graduated posets | | | Week 4 | Lattices | | | Week 5 | Distributivity | | | Week 6 | Semimodularity | | | Week 7 | Complemented modular lattices | | | Week 8 | Mid-term exam | | | Week 9 | Ouasi-orderings | | | Week 10 | Morphisms and ideals | | | Week 11 | Congruence relations | | | Week 12 | Lattice polynomials | | | Week 13 | Boolean algebras | | | Week 14 | Brouwerian lattices | | | Week 15 | Newman algebras; Ortholattices | | | Week 16 | End-of-term exam | | | |
| 1 | Birkgoff, G., 1967; Lattice Theory, Providence, Rhode Island. | | | |
| 1 | Gratzer, G., 2003; General Lattice Theory, Birkhauser Verlag, Basel | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 21/11/2017 | 2 | 30 | | Homework/Assignment/Term-paper | 10 | | | 20 | | End-of-term exam | 16 | 08/01/2018 | 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 | 3 | 14 | 42 | | Sınıf dışı çalışma | 9 | 14 | 126 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Ödev | 1.5 | 1 | 1.5 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 198.5 |
|