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Lecturer(s)
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Course content
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1 - Number sets, basic operation with sets, mathematical induction; 2 - Relations, composition of relations and their basic properties, mapping, ordered sets; 3 - Elementary combinatorial computations, permutations, variations, composition of permutations and their properties; 4 - Combination numbers, Pascal's triangle, Binomial formula; 5 - Multinomial coeficients, Multinomial formula; 6 - Asymptotic estimates of functions, Landau's symbol O, estimates of n!, Stirling's formula; 7 - Inclusion and exclusion formula, number of permutations without fixed point; 8 - Finite probability spaces, random variable, mean value; 9 - Some discrete distribution, random walk in one dimension; 10 - Asymptotic estimates of complexity of algorithms; 11 - Modular arithmetics, congruences, Euklides algorithm, Bezouts coeficients; 12 - Diofantic equations, Fermat's last theorem; 13 - Some practical applications of discrete mathematics. LMS MOODLE:
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming)
- Class attendance
- 18 hours per semester
- Preparation for classes
- 50 hours per semester
- Preparation for credit
- 50 hours per semester
- Preparation for exam
- 50 hours per semester
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Learning outcomes
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The course is targeted at fundamental combinatorial reasoning. Basic concepts, methods and models of discrete mathematics are explained. Finally, applications on word problems are practised.
The student understands the basic concepts and principles of discrete mathematics. On a variety of word problems, he/she demonstrates the utilization of the fundamental techniques of combinatorial calculations.
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Prerequisites
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Mathematics I (MATEA, MATI, MATIA).
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Assessment methods and criteria
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Oral examination, Written examination, Combined exam, Test
Active attendance on the seminars (two absences alowed). Two credit tests - minimum 50% of points each. Written exam test at minimum 50% of points. Oral exam.
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Recommended literature
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Keller, M., Trotter, W. Applied combinatorics. Independent. 2017. ISBN 9781973702719.
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Matoušek, J., Nešetřil, J. Kapitoly z diskrétní matematiky.. Praha: Karolinum, 2007. ISBN 978-80-246-1411-3.
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Nýdl, V. Diskrétní matematika v příkladech, díl 1.. Č. Budějovice, PF JU, 2006.
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Nýdl, V., Thatte, B.D. Seminář z diskrétní matematiky 1 - Seminar in Discrete Mathematics 1. České Budějovice, 2011. ISBN 978-80-7394-327-1.
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Vilenkin, N., J. Kombinatorika.. Praha: SNTL, 1977.
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