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Lecturer(s)
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Dofková Radka, doc. PhDr. Ph.D.
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Bártek Květoslav, Mgr. Ph.D.
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Bártková Eva, Mgr. Ph.D.
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Uhlířová Martina, RNDr. Ph.D.
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Wossala Jan, Mgr. 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)
- Semestral Work
- 6 hours per semester
- Homework for Teaching
- 14 hours per semester
- Attendace
- 26 hours per semester
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Learning outcomes
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Revision of secondary-level knowledge with emphasis placed on accuracy of mathematical statements and mutual relations between mathematical theories (set theory, predicate logic, binary relations).
The knowledge gained in the TMA1 course of study is a prerequisite to successful studies in other subjects and shall be applied in the students´ teaching practice.
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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, Didactic Test, Seminar Work
Active participation in lessons, continuous tests (60%), elaboration of a seminar paper. Written and oral exam.
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Recommended literature
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Cotton, T. (2013). Understanding and Teaching Primary Mathematics. Edinburg: Pearson.
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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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Emanovský, P., Novák, B. (2000). Matematické praktikum. Olomouc: UP.
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Fox, S., Surtees, L. (2010). Mathematics Across the Curriculum. London.
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Kirkby, D. (1986). Investigation Bank Book 5, 7, 17. Shefiield: Dickens a Son.
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Kline, M. (1998). Mathematics for the Nonmathematician. New York: Dover Pub.
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Novák, B., Eberová, J., Stopenová, A. (2004). Základy elementární matematiky v úlohách. Olomouc.
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Perný, J. (2009). Kapitoly z elementární aritmetiky II.. Liberec: TU.
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Perný, J. (2010). Kapitoly z elementární aritmetiky I.. Liberec: TU.
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Pound, L., Lee, T. (2011). Teaching Mathematics Creatively. New York.
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Schuster, L., Anderson, N., C. (2005). Good Questions for Math Teaching. California: Sausalito.
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Stopenová, A. (2013). Matematika 1 (Aritmetika a algebra). Olomouc: UP.
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STOPENOVÁ, A. (2003). Základy matematiky 1. Olomouc.
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