Mathematics and computer science as the foundation for synergy between fundamental and applied knowledge in contemporary higher education

Introduction. As a result of the digital revolution, the entire system of scientific knowledge has undergone a metasystemic transition to a fundamentally new level of research. This level of research is based on the triad: model, algorithm, and programme. Aim. The present research aims to develop the theoretical and methodological foundations for integrating fundamental and applied knowledge through the modernisation of mathematical and computer training for university students, thereby enhancing their general cultural development and professional success. Methodology and research methods. In this research, the systemic and synergetic approaches, alongside the cultural studies approach, play leading roles. Results. The methodological aspects of the synergy between fundamental and applied knowledge in higher education, as well as the role of mathematics and computer science within this context, have been examined. The levels of synergy between fundamental and applied knowledge in higher education have been identified and characterised. It has been established which specific content within specialised teaching of the mathematical foundations of computer science plays a crucial role in the proficient and effective use of computer algebra systems and computer technologies. The significant role of incorporating a discrete mathematics component in teaching the mathematical foundations of computer science has been substantiated. Scientific novelty. The theoretical and methodological foundations for the synergy between fundamental and applied knowledge have been established, based on the modernisation of mathematical and computing education for students in higher education institutions. Drawing on a new “mathematical-computational” research culture, the levels of synergy between fundamental and applied knowledge in the modernisation of higher education have been identified and characterised. The importance of fostering non-mathematics students’ understanding of the role of Big Ideas, and the methods of modern mathematics and computer science derived from them, within their chosen professional fields has been substantiated, with the aim of achieving a high level of IT proficiency. Practical significance. The features of modernising core educational programmes and curricula for student training have been described, based on the characterised levels of synergy between fundamental and applied knowledge in higher education. The methodological specifics of selecting content for the mathematical foundations of computer science have also been outlined.