Aleksandr L. Korovin

In modern education, a transdisciplinary approach is increasingly used, bringing it to a new, higher level of knowledge. Mathematics is of crucial importance in the emergence of unique transdisciplinary scientific fields such as cybernetics, artificial intelligence (AI), big data, etc. The aim of the article is to substantiate the need for the introduction of a course "Mathematical foundations of artificial intelligence" in universities and its transdisciplinary role in teaching. When substantiating the transdisciplinary role, it is taken into account that artificial intelligence systems are based on discrete sections of mathematics and sections of computer science. These sections synthesize a new, previously disparate problem field, built on top of the traditional grid of the studied disciplines. Based on the study of these sections, a transdisciplinary style of thinking and a new holistic worldview, readiness for a systemic solution of complex problems of nature and society are developed. In the study, the leading role was played by the methods of systems analysis of the AI development and its mathematical foundations, which are important in improving the performance of computers. In accordance with the culturological approach, the study highlights the most significant components of the mathematical culture of AI research, which are mathematical modeling and discrete mathematics. As a result of the systems analysis, the structural elements of the profile content of the course (module) "Mathematical foundations of AI" for the implementation of the transdisciplinary role of this course are identified. “Curriculum” conceptual provisions on the development of recommendations for the content of typical curricula for teaching the course “Mathematical Foundations of AI” in universities were identified. It is important for students to understand that mathematics is unified and that there is an internal logic to mathematics. Therefore, it is important to teach AI systems based on a logically correct relationship between discrete and continuous mathematics. The specified course represents the basis for the development of general professional competences in the field of AI including: the ability to develop original algorithms and software products for solving professional tasks; the ability to develop and upgrade software and hardware for information and automated systems. The proposed course contributes to the development of general professional competences in the field of AI for the training of students in various fields. The theoretical and practical significance of the study lies in the fact that the structural elements and didactic provisions for selecting the profile content of the course “Mathematical Foundations of AI” have been identified and characterized.