MATHEMATICAL COMBAT MODELS AS A MEANS OF IMPROVING THE PROFESSION-FOCUSED TEACHING OF MATHEMATICS IN MILITARY UNIVERSITIES - Fursenko, Oleksandr; Chernovol, Nataliya; Bobrytska, Halyna (Physical and Mathematical Education, 2024)
Formulation of the problem. The teaching of mathematical disciplines in higher military educational institutions is focused primarily on providing a tool for studying the exact sciences. At the same time, the possibilities of mathematics still need to be fully utilized in particular disciplines. In this situation, cadets and students often need more motivation to study this science. Therefore, it is important to show examples of its application in military affairs at the beginning of the study of higher mathematics. An example of such an application is the mathematical modeling of combat operations. Problems of this type help create a learning environment that helps increase cadets' motivation to study these disciplines and deepen their professional knowledge. There is a significant base of tasks of this type. Still, with the development of modern military technologies and the development of mathematics, this base needs to be updated and rethought.Materials and methods. The study used a stochastic approach to study combat models: introduction of the states of the corresponding system, construction of a graph of transitions from one state to another with an indication of intensities, and writing the corresponding system of Kolmogorov differential equations.Results. A detailed description of the solution of an example of a stochastic model of "poorly organized combat" is given for teaching certain sections of applied mathematics and supplementing the traditional teaching methodology with this material to increase the motivation to study mathematical disciplines by cadets and students of military universities. In the proposed example, the states of the system are considered, a graph is constructed, intensities are written out during the transition from one state to another, a system of Kolmogorov's differential equations is written out, the method of solving this system and the solutions themselves are indicated, and the final formulas for calculating the mathematical expectations of the final number of combat units of each side and the probability of victory of each side are given.Conclusions. The paper presents a detailed description of the application of the stochastic approach to the construction of combat models. This example demonstrates the step-by-step implementation of this approach. It can be used in teaching "Probability Theory," "Markov's processes," "Mathematical Modeling, and Optimization of Research," etc., in higher education institutions.
Keywords: discrete-state and continuous-time Markov process; the Kolmogorov differential equations; the intensity; effective rate of fire; combat unit