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Lecturer(s)
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Dofková Radka, doc. PhDr. Ph.D.
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Stopenová Anna, PaedDr. Ph.D.
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Uhlířová Martina, RNDr. Ph.D.
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Course content
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The revision of high school curriculum with the emphasis on the accuracy of the mathematical formulation and the continuity of mathematical knowledge. - Propositional calculus. Proposition, negation of the proposition. Composite proposition. Propositional logic. Logical equivalence between propositional formulae. Predicate logic. Propositional function, composite propositions. Quantified proposition. Mathematical formula. Mathematical proofs. Mathematical definition. Concept, the content and extent of the concept. - Basic terms related to the set theory. Set representations, set relations. Polar set (potential theory). Set operations, properties of set operations. Verification of set equations. - Cartesian product of sets and its graphic representation. Binary relations. Properties of binary relations ? reflexivity, symmetry, transitivity, antireflexivity, antisymmetry, connectivity. Equivalence relations, set decomposition on the basis of equivalence relations. Ordering, well-ordered sets. - Composite relation. Mapping relations, types of mapping, one-to-one mapping, similarity mapping. Functions. Equivalent sets and similar sets. Equivalence relation properties and similarity relation with respect to ordered sets.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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There will be the emphasis on the accurancy of mathematical diction (mathematical conceptions, definitions and theorems) and the connection between mathematical knowledge and other subjects - main conceptions of the set theory, the sententional and predicate logic, the binary relation in the set and between the sets, the quality of binary relations.
To provide the students with a professional view of primary school mathematics curriculum
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Prerequisites
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Foundation mathematics in extent basic and central school
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Assessment methods and criteria
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Mark, Oral exam, Written exam
Active participation in the lessons, elaboration and submitting of a seminar paper. Written and oral exam.
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Recommended literature
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COUFALOVÁ, J. (1990). Základy elementární aritmetiky. Plzeň.
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DRÁBEK, J. a kol. (1985). Základy elementární aritmetiky pro studium učitelství 1. st. ZŠ. Praha.
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Eberová, J. (2003). Základy matematiky 2. Olomouc.
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EBEROVÁ, J., STOPENOVÁ, A. (1997). Matematika 1. Olomouc.
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NOVÁK, B., EBEROVÁ, J, STOPENOVÁ, A. (2004). Základy elementární matematiky v úlohách. Olomouc.
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Stopenová, A. (2003). Základy matematiky 1. Olomouc.
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