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List of publications on a keyword: «set theory»

  • Application of set theory and logic in the design of intelligent educational environments

    Proceeding
    Modern educational process: psychological and pedagogical support, educational strategies
    Authors:
    Ivan A. Rozhkov, Aleksandr E. Sergeev
    Work direction:
    Инновационные технологии в образовании
    Abstract:
    The article examines the fundamental role of the apparatus of discrete mathematics, in particular set theory and mathematical logic, in the design and development of intelligent educational environments (IEDs). The key tasks of IEDs are analyzed, such as knowledge formalization, adaptive planning of learning trajectories, gap diagnosis and generation of personalized tasks, the solution of which is based on operations on sets, Boolean algebra, logical rules and predicate calculus. It is proved that the use of these formal methods makes it possible to move from intuitive design of educational content to a precise, algorithmically controlled process, which is a critical factor in improving the quality and accessibility of education. The work highlights promising areas of integration of these disciplines into modern EdTech solutions.
    Keywords:
    adaptive learning, personalization, set theory, intellectual educational environments, mathematical logic, knowledge formalization, ontologies, logical inference
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  • SELECTED ISSUES OF DEVELOPING A THEORETICAL MODEL OF AN INTELLIGENT DIGITAL KNOWLEDGE MONITORING SYSTEM

    Proceeding
    The Topical Issues of the Humanities and Social Sciences: from Theory to Practice
    Author:
    Roman I. Kondratov
    Work direction:
    Тенденции развития цифрового образования
    Abstract:
    The article discusses approaches to the development of a mathematical model of digital knowledge monitoring based on a semantic network. The hierarchical structure of training within the framework of the implementation of the state standard is presented. The analysis of the requirements for the semantic network within the framework of the claimed model is carried out. The article also describes approaches to the representation of the learning process in the form of an oriented graph of the development of educational programs.
    Keywords:
    set theory, semantic network, individual educational trajectories, digital knowledge monitoring, intelligent learning systems, oriented graph
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