Abstract:

In this paper we use the numerical statistical method Monte-Carlo. It is a widely known tool for working with computer simulations of random variables. Over the years this method has gradually become widely used not only in statistics, but also in many mathematical fields and also in applications of statistics in natural sciences (chemistry, physics, biology, epidemiology). In our contribution we want to show the use of the method in teaching mathematical analysis and linear algebra in the first and second semesters of mathematics studies at our university. We gradually present examples of the use of this method in mathematical analysis - examples for calculating the values ​​of one-dimensional integrals, the size of planar formations, but also the determination of volumes of three-dimensional objects. Besides these possibilities, we also deal with the use of the method for solving systems of linear equations (using the fixed point method) and solving simpler types of differential equations. Each variant is carefully presented so that it can be implemented without problems by university students. In addition to the comprehensibility of the text, we also try to provide instructional examples so that each student understands the use of the method for their needs. At the end of the work we focus on a very important point of the whole method - the conditions and the way of verifying its convergence. Compared to other methods of numerical methods, where classical convergence is concerned, the Monte-Carlo method is almost certainly based on convergence and probabilistic error estimation, which is generally based on the central limit theorem and the Chebyshev inequality. Currently, this method is involved in COVID - 19 propagation simulation solutions, and therefore we encounter it indirectly every day.

Keywords:

Monte Carlo simulations, Statistics, Teaching, applications of statistics.