| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Lattice Theory I | MAT613 | Elective | Doctorate degree | 1 | Fall | 8 |
Name of Lecturer(s)
Prof. Dr. Halis AYGÜN
Associate Prof. Dr. Vildan ÇETKİN
Learning Outcomes of the Course Unit
1) State the partial order and total order relations and their properties
2) Explain the notion of a lattice which is a special partially ordered set, that is a extension of the unit interval
3) Explain the several different lattices and also some of their properties
4) State the concepts of algebraic lattices and investigate the realtions between the algebaric structures and the lattice structures
5) Explain the prime and irreducible elements andl state the relatons which are constructed by these elements
6) Explain the concepts of filter and ideal in lattices
7) Explain the notion of continuity on lattices
8) State the concepts of category and functor and some of their fundamental properties
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 6 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 7 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 8 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Abstract algebra I-II
Course Contents
Candidates are provided with in-depth knowledge on partially and totally ordered sets, lattices, algebraic properties of lattices, distributive lattices and lattices with negations, Boole algebra, triangular norms, quantale lattices, semi-lattices, lattice isomorphisms, complete and complaetely distributive lattices, prime and irreducible elements, continuous and semi-continuous lattices, ideals and filtes, categories and functors, frames and locales, sublocales and Stone spaces.
Recommended or Required Reading
Planned Learning Activities and Teaching Methods
Assessment Methods and Criteria
Language of Instruction
Turkish
Work Placement(s)
Not Required