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Lecturer(s)
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Švrček Jaroslav, RNDr. CSc.
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Course content
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1. Mathematical problems in education, classification of mathematical problems. 2. Mathematical problems of determination and proofs. 3. Basic methods for solving algebraical problems, method of adding up, the squares method, the estimates and inequalities method, the infinite-descent method. 4. Basic types of proofs, proof by contradiction, invariants and semiinvariants. 5. Induction in proofs. 6. Algebraical determining problems with parameters. 7. Basic methods of solving combinatorial problems, the Pigeonhole principle.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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Manage basic methods of problem-solving strategies.
2. Comprehension Identify basic problem-solving methods (non-geometrical).
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Prerequisites
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unspecified
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Assessment methods and criteria
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Seminar Work
Credit: the student has to solve 10 combinatorial problems (homework) assigned during the course and has to pass one written test (i.e. to obtain at least half of the possible points).
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Recommended literature
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Calda E. (2006). Sbírka řešených úloh (středoškolská matematika pod mikroskopem). Prometheus Praha.
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Herman J., Kučera R., Šimša J. (1998). Metody řešení matematických úloh I. MU Brno.
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ŠVRČEK J., CALÁBEK P. (2007). Sbírka netradičních matematických úloh. Prometheus Praha.
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Tabov J. B., Taylor P. J. (1996). Methods of problem solving (Book 1). AMT Canberra.
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Tabov J. B., Taylor P. J. (2002). Methods of problem solving (Book 2). AMT Canberra.
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