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Lecturer(s)
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Tříska Jan, Mgr. Ph.D.
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Laštovička Jan, Mgr. Ph.D.
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Kolařík Miroslav, doc. RNDr. Ph.D.
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Juračka Jakub, Mgr.
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Course content
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Introduction to propositional logic (axiomatic system, concept of proof). Introduction to predicate logic (language, notion of structure for language and truth in structure, example of PROLOG language). Brief on fuzzy logic and modal logic. Fundamentals of elementary number theory (divisibility, prime numbers, Euclidean algorithm, congruence modulo n and residue classes). Selected numerical functions, growth rates. Basic algebraic structures with one and two binary operations. Real number sequences, their properties and limits. Infinite series and their convergence and divergence criteria. Graphs (graph scores, Eulerian moves, vertex colouring of graphs, flows in networks). Probability (classical definition of probability, finite probability space, probability calculation, random variable, expected value, variance).
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Learning activities and teaching methods
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Lecture, Demonstration
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Learning outcomes
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Students will learn the basics of discrete structures and discrete mathematics used in computer science.
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Prerequisites
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KMI DISK1 Discrete structures 1
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Assessment methods and criteria
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Oral exam, Written exam
Completion of assigned tasks. Passing an oral or written examination.
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Recommended literature
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Bělohlávek R. (2020). Diskrétní struktury. Katedra informatiky, Olomouc.
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Bělohlávek R., Vychodil V. (2006). Diskrétní matematika pro informatiky I, II.. Katedra informatiky.
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Brookshear J. G. (2013). Informatika. Computer Press.
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Cormen T. H., Leiserson C. E., Rivest R. L., Stein C. (2009). Introduction to Algorithms. 3rd ed.. MIT Press.
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Goodaire E. G., Parmenter M. M. (2005). Discrete Mathematics with Graph Theory, 3rd ed.. Prentice Hall.
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Grimaldi R. (2003). Discrete and Combinatorial Mathematics. An Applied Introduction. 5th ed.. Pearson, Reading, MA.
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Maurer S. B., Ralston A. (2005). Discrete Algorithmic Mathematics. 3rd ed.. A K Peters/CRC Press.
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