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Lecturer(s)
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Course content
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Exercise: 1. Function - basic properties. Limit. Asymptotes. Aplication in theoretical economics. 2. Derivative and its practical use - extrems, monotony, curvature. Graphs of functions. Aplication in theoretical economics. 3. Primitives. Integrals - geometric interpretation, practical use. Aplication in theoretical economics. 4. Numerical methods for equations solving. Function of several variables - partial derivatives, extremes. Aplication in theoretical economics. 5. Vectors, matrices - their applications for solving of linear equations systems. 6. Mathematical programming - linear. Mathematical programming - non-linear. Applications in optimization of production. 7. Series - types, conditions of convergence. 8. - 9. Probability theory - random variable, probability function, density function. Matrix algebra and integral to solve probability problems. 10. Stochastic processes - transition matrix, steady state vector. Simulations. 11. - 12. Financial and insurance mathematics.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments)
- Class attendance
- 56 hours per semester
- Home preparation for classes
- 24 hours per semester
- Preparation for credit
- 10 hours per semester
- Preparation for exam
- 30 hours per semester
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Learning outcomes
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Repeat the stated topics and extend students' knowledge concerning aplications of the mentioned mathematical methods in economics, finance, insurance etc. and show the solutions of selected problems with a special software (Excel, Mathematica, sCalc, LINDO etc.).
Students obtain knowledge in given course in accordance with requirements and course programme.
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Prerequisites
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Basic knowledge of mathematics, computer skills.
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Assessment methods and criteria
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Student's performance analysis, Written assignment
Credit: surrender two interim assignments, test.
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Recommended literature
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Anděl, J. Matematika náhody. Praha, 2003. ISBN 80-86732-07-X.
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Cipra, T. Pojistná matematika - teorie a praxe. Praha, 1999. ISBN 80-86119-17-3.
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Cipra, T. Praktický průvodce finanční a pojistnou matematikou.. Ekopress, Praha, 2003.
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Dlouhý, M. Simulace pro ekonomy. Praha, 2005. ISBN 80-245-0973-3.
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Hillier, F., Lieberman, G. Introduction to Operations Research. San Francisco, 2000. ISBN 0-07-241618-1.
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Jablonský, J. Operační výzkum. Praha, 2002. ISBN 80-86419-42-8.
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Macháček, O. Finanční a pojistná matematika, Praha. Prospektrum, 1995. ISBN 80-7175-035-2.
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Pánková, V. Nelineární modely a metody. Praha, 2002. ISBN 80-245-0426-X.
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Pelikán, J. Diskrétní modely. Praha, 1999. ISBN 80-7079-179-9.
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Radová, J. a kol. Finanční matematika pro každého příklady + CD ROM, Grada Publishing, Praha, 2007. ISBN 978-80-247-2364-8.
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Radová, J., Dvořák, P., Málek, J. Finanční matematika pro každého. 6. vyd. Grada Publishing, 2007. &, &. ISBN 978-80-247-2233-7.
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Rektorys, K. Přehled užité matematiky. Praha, 1968.
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RICHARDSON, C., H. Financial Mathematics. New York: READ BOOKS, 2008. ISBN 978-14-437-2142-4.
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