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Lecturer(s)
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Příhonská Jana, doc. RNDr. Ph.D.
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Course content
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1. Introduction into combinatory - historical respect. Basic concepts of combinatory. 2. Logical tree of al possibilities, combinatory rule of sum and product, variation and permutation with or without frequency 3. Combination with or without frequency, binomial coefficients and their properties. Simple equations. 4. Pascal triangle. Binomial theorem and application. 5. The use of graph theory in problem solving in combinatory. 6. Introduction into calculus of probabilities: stochastic space as a model of random attempt. Notation, absolute and relative rate and their properties. 7. Event and its probability: certain, impossible, possible event, random event and operation with them, classical formula of probability 8. Basic theorems - probability of intersection (in)depending events, probability of union of events. Applications. 9. Probability in practice life - solution of model situation. 10. Introduction into statistics: basic concepts, statistic classification, statistical set, rate and frequency distribution, graph and mapping, frequency diagram. 12. Characteristics of statistical set: arithmetic average, weight and running average, harmonic mean. Median, modus. 12. Adding (equitable) characteristics of statistical set - data dispersion, mean-root-square error, statistic dependence of statistical symbol, coefficient of correlation. Application. 13. Students' presentation. 14. Students' presentation, reserve.
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Learning activities and teaching methods
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Dialogue metods(conversation,discussion,brainstorming), Active metods (simulation, situational contingency methods, drama,acting, namagerial acting )
- Class attendance
- 28 hours per semester
- Preparation for credit
- 14 hours per semester
- Home preparation for classes
- 8 hours per semester
- Semestral paper
- 10 hours per semester
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Learning outcomes
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Combinatorial problems at primary school. The foundations of probability and processing statistical data. Using of modern information technologies (presentation software, interactive boards, application Microsoft Office Excel). An electronic processing of solution of problems and their presenation.
Using different methods of problems solving. Active use of application PowerPoint, Microsoft Excel, SMART Notebook.
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Prerequisites
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Knowledge of secondary school mathematics.
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Assessment methods and criteria
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Student's performance analysis
Credit: Participation on seminars. Working out seminar work. The course is held in Czech language, the requirements are stated in the Czech version.
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Recommended literature
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Hejný, M. a kol. Teória vyučovania matematiky 2.. Bratislava, SPN, 1999.
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Kouřim, J. a kol. Základy elementární geometrie pro učitelství l. st. ZŠ. Praha, SPN, 1985.
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Odvárko, O.:. Metody řešení matematických úloh.. Praha, SPN, 1990. ISBN 80-04-20434-1.
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Płocki, A. Pravděpodobnost kolem nás - počet pravděpodobnosti v úlohách a problémech.. Univerzita J. E. Purkyně, Ústí nad Labem, 2001. ISBN 80-7044-355-3.
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Vilimovská, L. Aktivizující činnosti pro rozvoj kombinatorického myšlení žáků. TU v Liberci, 2012.
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Vrba, A. Kombinatorika 1. vydání. Praha, 1980. ISBN 23-034-80.
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