In the era of digital transformation in higher education, learning management systems (LMS) accumulate huge arrays of data on student activity. However, these data are still rarely used for the systematic improvement of teaching fundamental mathematics courses. The article proposes an approach to improving the effectiveness of teaching Mathematical Analysis and Linear Algebra and Analytical Geometry based on the analysis of big data generated in a university LMS. Methods for data collection, cleaning, and clustering, the construction of predictive models for identifying students at risk, and the creation of adaptive learning scenarios are described. The results of a pilot implementation of the proposed methodology at a technical university (n=487) demonstrate an increase in the average grade by 0.36-0.34 points and a decrease in the proportion of dismissed students by 4.2 percentage points. Particular attention is paid to integrating the proposed approach with current studies on the information and educational environment. Pedagogical conditions, limitations, and prospects for using learning analytics to personalize the mathematical training of engineering students are discussed.