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Lecturer(s)
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Zdráhal Tomáš, doc. RNDr. CSc.
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Course content
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Polynomials Algebraic and functional definition of polynomials. circuits Ideals factor circuits. Homomorphic mapping circuits. Divisibility and its use The greatest common divisor and least common multiple. Euclidean and Gauss integral domains. Divisibility of integers integrity and the integrity of the whole field of Gaussian numbers. Congruence in the domain of integers. Divisibility of polynomials integrity of one indeterminate over the domain of integers. Adjunction, algebraic and transcendental elements. The root of the polynomial field, algebraically closed field.
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Learning activities and teaching methods
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Lecture
- Homework for Teaching
- 50 hours per semester
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Learning outcomes
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The aim of the course is to provide deeper insight into selected topics algebra (polynomials, divisibility) in order to extend and update knowledge of algebra courses for teaching degree in mathematics for 2nd grade of primary school. The subject was upgraded under the project "Study to expand vocational qualifications (§ 6 Decree č.317/2005 Coll.)", Reg CZ.1.07/1.3.00/19.0014.
Ability to abstract relations and operations in numeric domains to more general integral domains.
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Prerequisites
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Active knowledge of algebra within the teaching of mathematics for 2nd grade of primary school.
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Assessment methods and criteria
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Student performance
Understand the differences between functional and algebraic polynomial, solve problems involving polynomials. Credit will be awarded if the compulsory consultation of the last student in the test can solve at least 2 of the 3 given exercises - these are formulated at the end of each chapter the subject prescribed for Algebra 1 textbook Blazek J. et al.: Algebra and theoretical arithmetic 2 (So all the exercises of the parties 57-185). It is therefore recommended that you forward to solve all the exercises, the test will be possible to use this custom solution - but it will be demonstrated active understanding summoned solutions! It will also be necessary to demonstrate a basic knowledge of substances (in particular definitions and theorems (without proof)) in the range of the prescribed textbook chapters (pp. 57-185).
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Recommended literature
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Bican L. (1979). Lineární algebra. SNTL Praha.
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BLAŽEK, J. a kol.:. (1985). Algebra a teoretická aritmetika 1. Praha: SPN.
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Blažek, J. a kol. (1985). Algebra a teoretická aritmetika 2.
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