A New Approach to Teaching Mathematics in Universities

The aim of this paper is to develop a methodology for teaching mathematics at universities that makes extensive use of modern digital and information technologies. The relevance of developing a new methodology for teaching higher mathematics at universities is driven by several factors. Firstly, it is necessary to increase students’ motivation for studying at university by explicitly demonstrating the connection between abstract mathematical knowledge and real-world physical and technical processes. Secondly, it is necessary to develop students’ skill in consciously using artificial intelligence to gain new knowledge, rather than mindlessly obtaining ready-made solutions. Thirdly, it is necessary to make applied mathematical software packages a working tool for solving mathematical, physical, and technical problems.

Methods. To improve student academic performance and motivate them to study complex disciplines such as mathematics and computer science, it is proposed to consider the possibilities of the educational approach: mathematics, computer science, and engineering. This approach involves the extensive use of modern software tools for studying higher mathematics, physics, and other general professional disciplines. Mathematics, computer science, and engineering enable the transition from solving complex abstract mathematical problems “on paper” to the use of modern mathematical software packages not only for analytical but also for numerical solutions of differential equations, as well as numerical integration. Essentially, computer science becomes a tool for studying mathematics.

Results. This article presents a methodology for implementing the educational approach: mathematics, computer science, and engineering in higher mathematics classes at universities. Three case studies are presented demonstrating solutions to standard problems in mathematical analysis and mathematical statistics using mathematical software packages and programming skills. An example of an analytical and numerical solution to a Cauchy problem using the Smath Studio mathematical package is considered. The same mathematical package was used to solve an integration problem analytically and numerically (Monte Carlo method). The possibility of using the Python programming language to write applications for statistical data processing is demonstrated. The formulation of the problems allows students to independently choose the solution method for the given problem.

Conclusion. This educational approach, discussed in this article, enables the widespread use of modern information and digital technologies for the study of higher mathematics at universities. This approach increases students’ interest in the subjects they study and develops skills in using the Python programming language and the Smath Studio software package for the analytical and numerical solution of complex mathematical problems.

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