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The article is devoted to the description of didactic approaches that allow to integrate the theory and practice of teaching students of mathematical specialties by updating informative intra- and interdisciplinary connections of mathematical disciplines and informatics.Methods for implementing cognitive visualization taking into account the specifics of mathematics and computer science are given. The interpretation of interdisciplinary connections (as a category of teaching didactics) and visual modeling in relation to teaching mathematics are also clarified.The article describes a variant of the organization of content in the computer means of teaching (CMT) students of the classical university in mathematical analysis. The content of this course in one or another volume is a mandatory component of mathematical training in universities, it is consistently associated with the content of the course of school mathematics and is widely used in applied problems.On the basis of the analysis of semantics and logic of construction of formulations of those properties which are repeated in relation to various mathematical objects, the variant of content didactic clustering at which such concepts as “convergence”, “uniform convergence”, “differentiability”, etc., act as patterns in the organization of the maintenance of computer means of training is presented.

The problem and the goal.The urgency of the problem of mathematical description of dynamic adaptive testing is due to the need to diagnose the cognitive abilities of students for independent learning activities. The goal of the article is to develop a Markov mathematical model of the interaction of an active agent (AA) with the Liquidator state machine, canceling incorrect actions, which will allow mathematically describe dynamic adaptive testing with an estimated feedback.The research methodologyconsists of an analysis of the results of research by domestic and foreign scientists on dynamic adaptive testing in education, namely: an activity approach that implements AA developmental problem-solving training; organizational and technological approach to managing the actions of AA in terms of evaluative feedback; Markow’s theory of cement and reinforcement learning.Results.On the basis of the theory of Markov processes, a Markov mathematical model of the interaction of an active agent with a finite state machine, canceling incorrect actions, was developed. This allows you to develop a model for diagnosing the procedural characteristics of students ‘learning activities, including: building axiograms of total reward for students’ actions; probability distribution of states of the solution of the problem of identifying elements of the structure of a complex object calculate the number of AA actions required to achieve the target state depending on the number of elements that need to be identified; construct a scatter plot of active agents by target states in space (R, k), where R is the total reward AA, k is the number of actions performed.Conclusion.Markov’s mathematical model of the interaction of an active agent with a finite state machine, canceling wrong actions allows you to design dynamic adaptive tests and diagnostics of changes in the procedural characteristics of educational activities. The results and conclusions allow to formulate the principles of dynamic adaptive testing based on the estimated feedback.