Course detail
Methods of Discrete Mathematics
FSI-SDMAcad. year: 2022/2023
The subject Methods of discrete mathematics gets students acquainted with basic areas of set theory, discrete mathematics, and applied algebra. The first area is formed by relations between sets and on sets with a stress on partially ordered sets. The next area covers Axiom of Choice and cardinal and ordinal numbers. After that, lattice theory is discussed with the main interest focused on the theory of Bolean algebras. Then the algebraic theory of automata and formal languages follows. The last area is an introduction to the coding theory. Thus, all the three areas represent theoretical fundamentals of informatics. With respect to the expansion of using computers in all branches of engineering, the acquired knowledge is necessary for graduates in mathematical engineering.
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Learning outcomes of the course unit
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Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
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Aims
Specification of controlled education, way of implementation and compensation for absences
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Prerequisites and corequisites
Basic literature
D.R.Hankerson at al.: Coding Theory and Cryptography, Marcel Dekker, Inc., New York -Basel, 2000. (EN)
M.Piff, Discrete Mathematics, Cambridge Univ. Press, 1991. (EN)
N.L.Biggs, Discrete Mathematics, Oxford Univ. Press, 1999. (EN)
Steven Roman, Lattices and Ordered Sets, Springer, 2008. (EN)
Recommended reading
J. Kopka: Svazy a Booleovy algebry, Univerzita J.E.Purkyně v Ústí nad Labem, 1991.
M. Demlová, V. Koubek: Algebraická teorie automatů, SNTL, Praha, 1990.
M.Novotný, S algebrou od jazyka ke gramatice a zpět, Academia, Praha, 1988.
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Tolerances, equivalences, preorders and orders
3. Ordered sets
4. Axiom of choice and equivalent statements
5. Ordinal and cardinal numbers
6. Lattices, irreducibility, ideals and filters
7. Boolean lattices and functions, applications
8. Complete lattices, closure operators
9. Galois connections, Dedekind-MacNeille completion
10.Formal languages
11.Finite automata
12.Grammars
13.Selfcorrecting codes
Exercise
Teacher / Lecturer
Syllabus
2. Tolerances, equivalences, preorders and orders
3. Ordered sets
4. Axiom of choice and equivalent statements
5. Ordinal and cardinal numbers
6. Lattices, irreducibility, ideals and filters
7. Boolean lattices and functions, applications
8. Complete lattices, closure operators
9. Galois connections, Dedekind-MacNeille completion
10.Formal languages
11.Finite automata
12.Grammars
13.Selfcorrecting codes