Abstract:

The contribution briefly describes several implementations of the Monte Carlo method for educational purposes. The Monte Carlo method is used to model various physical and other dynamic systems. It is widely used, for example, in quickly finding approximate results of various calculations, such as calculating a definite integral, determining the probabilities of events within certain phenomena, empirically determining the value of Ludolf’s number (π), cost estimates in certain situations, etc. It is an empirical-numerical method based on the use of values of random variables and probability theory. The first implementation is for the subject Modelling and Simulation of Systems, where this method is the content of teaching. It makes it possible to use simulation experiments to examine this method, to be convinced of its functionality and to find out how the accuracy of the method can be increased. The second implementation is a universal editor of the Monte Carlo method, which combines the methods of computer graphics and numerical mathematics to calculate an unknown area where a direct analytical solution does not exist, or we do not know it. Our goal was to implement a general-purpose interactive software that will allow the Monte Carlo method to determine the content of any irregular area in each image. The third implementation and use of the Monte Carlo method is for the discipline of programming. It combines the possibility of a programming environment and a graphical editor. It is a topic for a software solution to the problem of calculating an unknown area (2D image) drawn in a simple graphics editor.

Keywords:

Monte Carlo method, didactic software, interactive software, modelling of dynamic phenomena, simulation experiments, accuracy of the method.