Course detail
Ordered Sets and Lattices
FSI-9UMS Acad. year: 2022/2023 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
Learning outcomes of the course unit
The students will learn basic concepts and results of the theory of orderd sets and lattices including their applications.
Prerequisites
The knowledge of the subjects General Algebra and Methods of Discrete Mathematics taught within the Bachelor's study programme is expected.
Planned learning activities and teaching methods
Regular lectures focused on basic principles and methods of the theory of ordered sets and lattices including examples..
Assesment methods and criteria linked to learning outcomes
The students will be assessed by means of a written and oral exam at the end of the semester.
Aims
The goal of the subject is to get students acquainted with the theory of ordered sets with a stress to the lattice theory.
Specification of controlled education, way of implementation and compensation for absences
The presence at lectures is not compulsory, it will therefore not be checked.
The study programmes with the given course
Programme D-APM-P: Applied Mathematics, Doctoral, recommended course
Programme D-APM-K: 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