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Lecturer(s)
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Šulc Hynek, doc. Ing. Ph.D.
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Course content
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1. Mathematical problems, their role in teaching, their role in mathematics as a science, application problems 2. Concepts of correctness of a problem, solvability, uniqueness. Approaches to problem solving, exact and approximate solutions 3. Statement and predicate logic, sets and operations on them 4. Types of proofs, application problems related to logic and sets 5. Numerical sets, number systems, computer arithmetic 6. Complex numbers. 7. Algebra, modification of algebraic expressions, use of CAS 8. Sequences and their properties. 9. Recurrence, differential equations, limit of a sequence 10. Finite and infinite series 11. Functions and their properties 12. Equations, inequalities and their systems, direct and iterative solutions 13. Elements of differential calculus, applications
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Learning activities and teaching methods
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- Contact hours
- 52 hours per semester
- Preparation for an examination (30-60)
- 25 hours per semester
- Individual project (40)
- 25 hours per semester
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| prerequisite |
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| Knowledge |
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| to apply basic knowledge of linear algebra (matrix calculus, systems of linear algebraic equations) to apply basic knowledge of mathematical analysis (sequences, series, differential and integral calculus) |
| Skills |
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| to solve systems of linear algebraic equations (using direct methods) to solve problems with sequences and series to determine derivatives and integrals of elementary functions to describe, explain and apply the properties of elementary functions of one real variable |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| to formulate high school mathematics problems to know different methods and approaches for solving them to choose appropriate techniques for interpreting solution methods to know the basics of science communication |
| Skills |
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| to describe and explain the role of problems within the discipline prepare assignments for mathematical problems, assess their solvability and complexity in terms of teaching to describe and explain methods of solving problems in secondary school mathematics |
| Competences |
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| N/A |
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Individual study |
| Seminar |
| Skills |
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| Lecture |
| Seminar |
| Individual study |
| Competences |
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| Lecture |
| Seminar |
| Individual study |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Seminar work |
| Skills |
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| Combined exam |
| Seminar work |
| Competences |
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| Seminar work |
| Combined exam |
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Recommended literature
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Calda, Emil. Sbírka řešených úloh : středoškolská matematika pod mikroskopem. 1. vyd. Praha : Prometheus, 2006. ISBN 80-7196-319-4.
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Petáková, Jindra. Matematika : příprava k maturitě a k přijímacím zkouškám na vysoké školy. 1. vyd. Praha : Prometheus, 1998. ISBN 80-7196-099-3.
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Polák, Josef. Didaktika matematiky : jak učit matematiku zajímavě a užitečně. III. část, Historie matematiky pro učitele. 1. vydání. 2016. ISBN 978-80-7489-327-8.
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Polák, Josef. Didaktika matematiky : Jak učit matematiku zajímavě a užitečně. 1. vyd. Plzeň : Fraus, 2014. ISBN 978-80-7238-449-5.
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Polák, Josef. Didaktika matematiky I. část. 2014. ISBN 978-80-7238-449-5.
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Polák, Josef. Didaktika matematiky II. část. ISBN 978-80-7489-326-1.
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Polák, Josef. Didaktika matematiky: Jak učit matematiku zajímavě a užitečně. II. část. Obecná didaktika matematiky.. Plzeň : Fraus, 2016. ISBN 978-80-7489-326-1.
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Polák, Josef. Přehled středoškolské matematiky. 10. vydání. 2015. ISBN 978-80-7196-458-2.
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Polák, Josef. Středoškolská matematika v úlohách II. 2., upr. vyd. Praha : Prometheus, 2011. ISBN 978-80-7196-419-3.
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Polák, Josef. Středoškolská matematika v úlohách I. Praha : Prometheus, 2006. ISBN 80-7169-337-2.
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