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Lecturer(s)
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Zahrádka Jaromír, RNDr. Ph.D.
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Rak Josef, RNDr. Ph.D.
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Marek Jaroslav, Mgr. Ph.D.
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Course content
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Lecture topics by week of the semester: 1. Random experiment. Combinatorics. Laplace's definition of probability. Geometric definition of probability. Statistical definition of probability. Independence of phenomena. 2. Axiomatic definition of probability. Kolmogorov probability space. Properties of probability. Conditional probability. 3. Distribution function. The mean and variance of a random variable. 4. The most important discrete and continuous distributions of a random variable. 5. Mathematical statistics. Point and interval parameter estimates. Moment method. Hypothesis tests. 6. Approximation of data. The method of least squares. 7. Algebraic, trigonometric and exponential form of a complex number. Functions of complex variables. Euler's relations. 8. Fourier transform. 9. Interpolation. Lagrange and Hermite interpolation polynomial. 10. Approximate methods for calculating the roots of nonlinear equations. 11. Numerical derivation and integration. 12. Numerical solution of differential equations. Euler's method, Runga-Kutta method. The content of the exercises corresponds to the topics of the lectures.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Methods of individual activities, Laboratory work
- Preparation for a credit (assessment)
- 38 hours per semester
- Contact teaching
- 52 hours per semester
- Home preparation for classes
- 50 hours per semester
- Preparation for an exam
- 30 hours per semester
- Term paper
- 40 hours per semester
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Learning outcomes
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The aim of the course is to introduce students to the possibilities of practical use of mathematical models in practice. Emphasis is placed on understanding the main ideas of mathematical methods and the ability of students to solve practical problems independently with the use of suitable software.
The module is focused to introduce students to the area of numerical mathematics, theory of probability and descriptive statistics.The module should increase logical and mathematical skills of the students.
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Prerequisites
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Within the subject, the knowledge of mathematical analysis, linear algebra, theory of functions of a complex variable and ordinary differential equations is required.
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Assessment methods and criteria
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Oral examination, Written examination, Home assignment evaluation, Work-related product analysis, Self project defence
At least 80% active participation in exercises. A maximum of 3 absences can be replaced by elaboration of a semester work. Credit test + semestral work (according to the teacher's decision in the form of Moodle or written). Recurring student can choose either a 80% participation and recognition test from last year, or at least 50% attendance and a new credit test. Classification E 50% - 55%, D 56% - 62%, C 63% - 69%, B 70% - 76%, A more than 77%. The course is completed by written exam, at least 50% of success is required. An oral form of the exam is optional, upon a student's request.
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Recommended literature
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ANDĚL, Jiří. Základy matematické statistiky. Vyd. 3.. Praha: Matfyzpress, 2011. ISBN 978-80-737-8162-0.
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AYRES, Frank a MENDELSON, Elliot. Schaum's Outline of calculus. New York: Mcgraw-Hill, 2009. ISBN 0071160361.
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HAMHALTER, Jan a Jaroslav TIŠER. Funkce komplexní proměnné. 2. vydání.. Praha: ČVUT, 2017. ISBN 978-80-01-06317-0.
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HOROVÁ, Ivana a Jiří ZELINKA. Numerické metody. 2., rozš. vyd. Brno: Masarykova univerzita v Brně, 2004. ISBN 80-210-3317-7.
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HSU, Hwei P. Schaum's outlines: probability, random variables, and random processes. 3rd ed. New York: McGraw-Hill, 2014. ISBN 0071822984.
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JEVGRAFOV, Marat Andrejevič. Funkce komplexní proměnné. Praha: SNTL, 1981.
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