Updating the content and technologies of teaching mathematical analysis under the influence of digital transformation of the professional activities of information security specialists

Abstract

The digital transformation of the professional activities of information security specialists, manifested in the transition to cloud infrastructures, the integration of machine learning into intrusion detection systems, and the emergence of quantum threats, necessitates a rethinking of the role of mathematical analysis in their system of training. The apparatus of this discipline acquires new dimensions in the context of proactive risk modeling, analysis of distributed network topologies and optimization of parameters of intelligent systems, where methods of optimization of functions of many variables, properties of continuous distributions, Fourier series with integral transforms, as well as elements of differential equations for dynamic modeling of threats gain particular significance, while some traditional sections, such as multiple and curvilinear integrals, demonstrate reduced applied relevance according to comparative expert assessments of industry representatives, teachers of specialized disciplines and mathematicians. The updated educational model, which presupposes the profiling of task material, the systematic application of interactive programming environments with libraries of symbolic and numerical computations, as well as project forms of activity at the intersection of mathematics and information security, provides a statistically significant increase in the quality of material assimilation and the formation of the ability for meaningful interpretation of mathematical results in a professional context. This approach leads to the effect of cumulative advantage in mastering subsequent disciplines, strengthening functional connections between fundamental training and applied competencies without a significant increase in academic load, due to the redistribution of efforts from reproductive to constructive forms of educational work. Differentiation of pedagogical techniques depending on the level of students’ initial mathematical preparation additionally increases efficiency and motivation. The presented provisions reveal the systemic nature of the gap between the classical structure of the course and current professional needs, determining justified guidelines for the modernization of content and technologies of training in the conditions of continuous evolution of the landscape of information threats, which allows specialists to assess the relevance of the material and the expediency of referring to the full text for the implementation of recommendations in the practice of higher education.