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Lecturer(s)
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Course content
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1- Set theory, induction principle 2 - Relations 3 - Basic combinatorics 4 - Combinatorics 5 - Advanced combinatorics, multinomical Theorem 6 - Landau symbols, Stirling formula, asympthotic functions 7 - Principle of inclusion and exclusion 8 - Probability basics 9 - Discrete distributions 10 - Algorithm complexity estimate 11 - Euclidean algorithm 12 - Diofantic equations 13 - Discrete mathematics applications
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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, Test
Active attendance on the seminars. 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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Hindls, R. a kol. Statistika v ekonomii. Professional Publishing, 2018. ISBN 978-80-88260-09-7.
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Keller, M., Trotter, W. Applied combinatorics. Independent. 2017. ISBN 9781973702719.
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Kurgalin, S., Borzunov, S. Discrete Math Workbook. Springer, 2018. ISBN 3319926446.
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Matoušek, J., Nešetřil, J. Kapitoly z diskrétní matematiky.. Praha: Karolinum, 2019. ISBN 9788024617404.
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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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