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Lecturer(s)
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Janečková Miroslava, PaedDr. PhD.
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Course content
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1. Mathematical thinking, mathematical logic, statement, statement of negation. 2. Composition statement. 3. Logically equivalent propositional formula. 4. Propositional form, variable, composed propositional form. 5. Rules of correct reasoning. 6. Expressing quantity, quantified statement, its negation. 7. Sets. Expression of sets. Venn diagram. 8. Branch truth of the predicate 9. Power set. 10. Relations between sets. 11. Operations with sets. 12. Tasks with union of two sets with non-empty intersection.
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Learning activities and teaching methods
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unspecified, unspecified, unspecified
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Learning outcomes
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This subject builds on the knowledge of mathematics that students have gained until maturita exame, it gives the basic knowledge of mathematical logic and set theory. It provides the student an introduction to the mathematical theory of elementary arithmetic and geometry and the theory of teaching mathematics with a focus on special needs of primary school teachers. Student develops the ability to use mathematical logic for the development of mathematical thinking. Special emphasis is placed on creative and independent work with concepts, on gradual building, acquisition, precise and concise use of technical language. The most essential symbolism is introduced to allow the use of clear entries for deeper understanding and strengthen a thorough mastery of the elements of the minimum of technical language.
Student is able to: - Determine the truth value of the statement, complex statement, negating quantified statement and justify their solutions, - Purely symbolic notation of mathematical objects, using the symbols of mathematical language in written expression, - Formulate a precise definition of the concepts introduced even more knowledge of the fundamentals of propositional logic and set theory to express - right after the linguistic and mathematical, - Solve problems using propositional calculus, knowledge about sets and set operations, - Represent a set Venn diagram, - Use the definitions to prove the claim about relationships between sets.
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Prerequisites
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The subject requires no specific prerequisites.
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Assessment methods and criteria
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unspecified
Active participation in the seminar. Compliance test (70% pass). Seminar work.
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Recommended literature
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Bělík, M. Matematika pro kombinované studium učitelství 1. stupně ZŠ. Ústí nad Labem, 1989.
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Blažek, J. a kol. Algebra a teoretická aritmetika I, SPN, Praha. 1985.
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Divíšek J. a kol. Didaktika matematiky pro učitelství 1. stupně ZŠ. Praha, 1989.
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Drábek J. a kol. Základy elementární aritmetiky pro studium učitelství 1. st. ZŠ, SPN Praha. 1985.
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Kaslová, M. Předmatematické činnosti v předškolním vzdělávání. Praha, 2010. ISBN 978-80-86307-96-1.
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Melichar J., Svoboda J. Rozvoj matematického myšlení I pro studium učitelství pro mateřské školy, UJEP, Ústí nad Labem. Ústí nad Labem, 2003.
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Opava Z. Matematika kolem nás, Albatros Praha. 1989.
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Perný Jaroslav. Kapitoly z elementární aritmetiky I. Liberec: TU v Liberci, 2010.
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