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Course detail

(Ordered Sets and Lattices

Course unit code: FSI-9UMS
Academic year: 2016/2017
Year of study: Not applicable.
Semester: summer
Number of ECTS credits:
Learning outcomes of the course unit:
Not applicable.
Mode of delivery:
Not applicable.
Prerequisites:
Not applicable.
Co-requisites:
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
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.
Recommended or required reading:
Steve Roman, Lattices and ordered sets, Springer, New York 2008. (EN)
Jan Kopka, Svazy a Booleovy algebry, Univerzita J.E. Purkyně v Ústaí nad Labem, 1991 (CS)
Planned learning activities and teaching methods:
Not applicable.
Assesment methods and criteria linked to learning outcomes:
Not applicable.
Language of instruction:
Czech, English
Work placements:
Not applicable.
Course curriculum:
Not applicable.
Aims:
Not applicable.
Specification of controlled education, way of implementation and compensation for absences:
Not applicable.

Type of course unit:

Lecture: 20 hours, optionally
Teacher / Lecturer: prof. RNDr. Josef Šlapal, CSc.
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

The study programmes with the given course