On the application of generative models in the e-learning system of mathematical disciplines

The existing tools for individual learning trajectory dynamic design are complemented by the generating technology of certification tasks and exam tickets. A set of exam tickets specially prepared by experts in the university course of the theory of functions of a complex variable was used as a source of high-quality, balanced sets of tasks. This significant training array of high-quality attestation tasks has significantly expanded the available data created at previous stages. The purpose of the performed research was to create methods that allow taking into account the experts' knowledge embedded in the available set of tasks. The implemented generation model when processing educational content uses as parameters the attributes assigned by experts to tasks: topic, complexity, and formed competencies. Two generation methods are proposed. The first one, probabilistic, uses only the frequency characteristics of the training set, approximating the probability distribution. The second one is based on generative-adversarial neural networks. Particular attention is paid to the discussion of the difficulties of the network implementation, including those related to the specific nature of the generative model.