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Lecturer(s)
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Bílek Jiřina, doc. RNDr. CSc.
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Course content
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Week 1: Elementary knowledge of divisibility, word problems. Prime numbers. Knowledge of ancient mathematics. Week 2: Factorization algorithms, classical and newer. Examples of working with the calculator with CAS functions. 3rd week: Encryption - sample available to elementary school pupils. Modern encryption using divisibility knowledge. 4th week: Diophantine equations - tasks available to primary school pupils. Pythagorean triads and triangles, generating method. Pell's equation, chain fractions, ancient Indian mathematics. Week 5: Decomposition of polynomials into factors. Kronecker's divisibility algorithm. Examples of working with the calculator with CAS functions. 6.-8. week: Solving algebraic equations. Cubic equation and its solution including knowledge of the history of mathematics. Week 9: Development of algebra from "classical" to "modern". Examples of structures from the area of "modern" algebra. Boolean algebra. 10th week: Puzzler "play on fifteen", permutations, sign of permutations, positions that (not) can be folded. Definition of determinant. 11-13. Geogebra not only draws but also calculates and even proves. Systems of equations not only linear - how to solve them?
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Learning activities and teaching methods
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Lecture, Seminar
- Contact hours
- 39 hours per semester
- Preparation for comprehensive test (10-40)
- 30 hours per semester
- Presentation preparation (report) (1-10)
- 10 hours per semester
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| prerequisite |
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| Knowledge |
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| Assumptions Knowledge of elemental algebraic methods on outcome level of courses KMT/ELA and KMT/LA is assumed. 1. Acquire skills in solving linear congruency and their systems. 2nd Acquire skills in solving linear Diophantin´s equations and their systems with emphasis on verbal. 3rd Acquire skills in solving basic problems with the issue of numerical polynomials bodies and bodies of the residual classes. No prerequisites. |
| learning outcomes |
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| Learning outcomes and gained competencies: Student can solve simpler algebraic equations and inequalities, handles elementary operations in propositional calculus and set theory, applies theoretical knowledge on sets, set operations and Venn diagrams, has knowledge of elementary and linear algebra. |
| teaching methods |
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| Lecture |
| Seminar |
| assessment methods |
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| Test |
| Skills demonstration during practicum |
| Seminar work |
| Individual presentation at a seminar |
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Recommended literature
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? STANOVSKÝ, DAVID ? BARTO,LIBOR. Počítačová algebra. Praha, 2017. ISBN 978-80-7378-340-2.
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Dlab, Vlastimil, Bečvář, Jindřich. Od aritmetiky k abstraktní algebře. Praha, 2017. ISBN 978-80-260-9838-6.
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Procházka, Ladislav a kol. Algebra. Praha, Academia, 1990. ISBN 80-200-0301-0.
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