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Lecturer(s)
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Pastor Karel, doc. Mgr. Ph.D.
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Dofková Radka, doc. PhDr. Ph.D.
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Zdráhal Tomáš, doc. RNDr. CSc.
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Course content
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1. Introduction: - Introduction to arithmetic and its significance in mathematics 2. Natural Numbers: - Definition of natural numbers - Peano arithmetic of natural numbers - Ordering of natural numbers - Natural numbers as an algebraic structure - Positional systems for natural numbers - Positional numeral systems - Natural numbers in the decimal system - Algorithms for operations with natural numbers 3. Integers: - Structure of integers (Z, +, .) - Ordering of integers - Absolute value of an integer and its use 4. Rational Numbers: - Construction of the quotient field over (Z, +, .) - Ordering of the field of rational numbers - Development of rational numbers in positional systems 5. Real Numbers: - Existence of gaps on the number line - Definition of a cut in the set of rational numbers - Approximation of real numbers - Incomplete numbers 6. Complex Numbers: - Construction of the field of complex numbers - Geometric model of the field of complex numbers - Absolute value of a complex number Basic literature is available in the relevant team in MS Teams under the name Kopecký - Aritmetika.pdf.
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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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Objectives of the Course: - Gain a deep understanding of different types of numbers (natural, integer, rational, real, complex) and their mathematical structures. - Ability to work with positional numeral systems and apply algorithms for number operations. - Understanding the construction and arrangement of number fields and the application of algebraic structures. Expected Outcomes: - Solid theoretical foundations in arithmetic and the ability to apply them in practice. - Practical skills in performing operations with different types of numbers and using positional numeral systems. - Analytical skills for solving problems related to numeral systems and applying absolute value. - Ability to apply acquired knowledge and skills in real situations and in teaching mathematics.
The knowledge gained in the WZAR 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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- Logical thinking ability - Knowledge of mathematical terms and notations - Motivation and interest in mathematics
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Assessment methods and criteria
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Oral exam, Didactic Test, Seminar Work
Active participation in seminars, preparation and submission of a seminar paper, 60% success rate in the test.
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Recommended literature
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BLAŽEK, J. a kol.: Algebra a teoretická aritmetika 1, 2. Praha: SPN, 1983, 1985.14-514-83, 14-470-85..
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EBEROVÁ, J. Základy matematiky 4. Olomouc : Vydavatelství UP, 2005. ISBN 80-244-0954-2.
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EBEROVÁ, J. Základy matematiky 6. Olomouc : Vydavatelství UP, 2006. ISBN 80-244-1208-X.
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KATRIŇÁK, T. a kol.: Algebra a teoretická aritmetika 1. Bratislava, Praha: ALFA, SNTL, 1985. 63-568-85..
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KOPECKÝ, M.: Aritmetika, pracovní skriptum, Olomouc, UP, 1999.
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NOVÁK, B., EBEROVÁ, J. STOPENOVÁ, A. Základy elementární matematiky v úlohách. Olomouc : Vydavatelství UP, 2004. ISBN 80-244-0853-8.
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ŠALÁT, T. a kol.: Algebra a teoretická aritmetika 2. Bratislava, Praha: ALFA, SNTL, 1986. 63-554-86..
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