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Lecturer(s)
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Břehovský Jiří, Mgr. Ph.D.
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Course content
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The seminar is focused on secondary school mathematics from the point of view of elementary and secondary school teacher. The subject is taught in Czech. Seminar: 1. Entrance test. Setting of papers. Credit conditions. 2. Manipulation with arithmetical and algebraic expressions. Powers with ratioanal exponent. Logarithms. 3. Propositional calculus. 4.Equations (quadratic, algebraic of higher degree, reciprocal, with the unknown in absolut value). Graphical solution. Systems of equations. 5. Equations (exponential, logarithmic, irrational, with the unknown in denominator). Graphical solution. 6.Moivre theorem. Binomial and trinomial equations. 8. Theory of numbers. Number representation system. Divisibility. Proof-problems. Real number as a sum of the infinite series. 9. Sequences, series (esp. arithmetic, geometric). 10. Combinatorics. Combination, variation, permutation. 11.Binomial theorem, Pascal triangle. 12.Probability. 13. Word problems (problem given by the words). 14.Reserve. Credits.
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Learning activities and teaching methods
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Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments), Written assignment presentation and defence, Working activities (workshops)
- Home preparation for classes
- 20 hours per semester
- Class attendance
- 22 hours per semester
- Preparation for credit
- 18 hours per semester
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Learning outcomes
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The seminar is focused on secondary school mathematics, especially on such topics they don´t include theoretical mathematical subjects - equations, inequalities, adaptation of algebraic expressions, proof-problems, propositional calculus, word-problems, combinatorics.
Knowledge of secondary school mathematics from the point of view of the future teacher of elementary school, obtaining of the university top view on some conventional and less conventional themes of secondary school mathematics.
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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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Combined examination
Active participations on seminars, successfully absolved tests, paper on different themes. Knowledge of secondary school mathematics (by curriculum of gymnasium), essential course of calculus and algebra.
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Recommended literature
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Učebnice matematiky pro gymnázia..
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POLÁK, J. Přehled středoškolské matematiky. Praha, Prometheus, 2015. ISBN 978-807-1964-582.
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Polák, J. Středoškolská matematika v úlohách I. Praha, Prometheus, 2006. ISBN 80-7196-337-2.
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