The search for ways to modernize contemporary higher education in the context of the rapid development of Data Mining technologies highlights an important scientific and practical challenge: the formation of conceptual foundations for the methodology of managing the educational process. This methodology should facilitate the development of fundamentally new strategic approaches to training specialists within large educational systems, such as universities, institutes, and colleges. At the core of this research lies the concept of a “collective” system of learning knowledge, which serves as an integral product of the activities of a large educational system. Modeling the evolution of such a system presents a highly complex task, requiring consideration of the synergy of numerous hard-to-formalize factors. These include aspects related to individual’s psychology, memory, conflicts, and motivations. The development of mathematical models for the evolution of “collective” learning knowledge necessitates the use of advanced tools of nonlinear analysis, including the theory of global attractors for multivalued dynamical systems, the theory of extremal problems for nonlinear differential-operator equations and inclusions. Furthermore, modern Data Mining technologies play a crucial role in uncovering hidden regularities within educational processes and enhancing their management efficiency. This paper is focused on consideration of this complex set of challenges.