Course detail
Ordered Sets and Lattices
FSI-9UMS Acad. year: 2024/2025 Summer semester
Students will get acquainted with basic concepts and results of the theory of ordered sets and lattices used in many branches of mathematics and in other disciplines, e.g., in informatics.
Language of instruction
Czech
Supervisor
Department
Entry knowledge
The knowledge of the subjects General Algebra and Methods of Discrete Mathematics taught within the Bachelor's study programme is expected.
Rules for evaluation and completion of the course
The students will be assessed by means of a written and oral exam at the end of the semester.
The presence at lectures is not compulsory, it will therefore not be checked.
Aims
The goal of the subject is to get students acquainted with the theory of ordered sets with a stress to the lattice theory.
The students will learn basic concepts and results of the theory of orderd sets and lattices including their applications.
The study programmes with the given course
Programme D-APM-K: Applied Mathematics, Doctoral, recommended course
Programme D-APM-P: Applied Mathematics, Doctoral, recommended course
Type of course unit
Lecture
20 hours, optionally
Syllabus
1. Basic concepts of the theory of ordered sets
2. Axiom of Choice and equivalent theorems
3. Duality and monotonne maps
4. Down-sets and up-sets, ascending and descending chain conditions
5. Well ordered sets and ordinal numbers
6. Cardinal numbers, cardinal and ordinal arithmetic
7. Closure operators on ordered sets
8. Ideals and filters
9. Modular and distributive lattices
10. Boolean lattices