The relevance of this study lies in the fact that with the development of technology and software, the needs for calculating increasingly complex problems are developing, most of which can no longer be solved by analytical methods. This creates a need to find new and effective ways to solve problems with higher accuracy and speed. The purpose of the study is to familiarize yourself with the methods and tools that are used to solve, model and analyze problems in various fields, to prepare students of higher educational institutions to solve mathematical problems in various fields of scientific and technical activity. Among the methods used, one can distinguish the analytical method, the Gauss method, the Runge-Kutta method, the least squares method, Newton's method and others; for their implementation, various programming languages ​​can be used, such as Python, Mathcad, MATLAB, Comsol and others. During the study, the principles and implementations of various methods that are used in programming, as well as their advantages and disadvantages, were examined. This will allow students to more effectively solve real problems in various fields, and also prepare for further professional activities in research institutions and industrial companies. Of great importance is the analysis of the operation of various software in order to assess their effectiveness in the solution process and select the optimal method for specific tasks, in particular for the quick and accurate resolution of tasks and the resources they require. The ability to use the results obtained in practical activities to develop new programs and algorithms will improve the accuracy and efficiency of numerical calculations, which in turn can help improve various processes and develop technologies. It is worth noting that this will provide an opportunity to improve the quality of student learning in higher education institutions, and will also allow them to gain in-depth knowledge in this area and improve their programming skills.

Keywords: algorithms, higher education institutions, programming, comparative analysis, technology.