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.

1. Turchin V.F. Fenomen nauku. Kibernetichtskiy podkhjd k evolyutsii = The Phenomenon of Science: A Cybernetic Approach to Evolution. 2th ed. Moscow: Publishing House ETS; 2000. 368 p. (In Russ.)

2. Whittlestone J., Nyrup R., Alexandrova A., Dihal K., Cave S. Ethical and Societal Implications of Algorithms, Data, and Artificial Intelligence. London: Nuffield Foundation; 2019. 58 p.

3. Yarkova Е.N. Utilitarianism as a philosophy of education. Obrazovanie i nauka = The Education and Science Journal. 2016;5(134):11–24. (In Russ.) doi:10.17853/1994-5639-2016-5-11-24

4. Sukhomlin V.A., Zubareva E.V. Curriculum paradigm – the methodological basis of modern education. Sovremennye informacionnye tekhnologii i IT-obrazovanie = Modern Information Technologies and IT Education. 2015;11(1):54–61. (In Russ.)

5. Projdakov E.M. Tree of computer science. In: Naukovedcheskie issledovaniya. Sbornik nauchnyh trudov RAN. INION. Centr nauchno-informacionnyh issledovanij po nauke, obrazovaniju i tehnologijam = Science Studies. Proceedings of the Russian Academy of Sciences (RAS). Institute of Scientific Information for Social Sciences (INION). Centre for Scientific and Informational Research in Science, Education and Technology. Moscow: Publishing House Direct Media; 2012:120–137. (In Russ.)

6. Kelly K. Neizbezhno. 12 tekhnologicheskikh trendov, kotorye opredelyayut nashe budushchee = The Inevitable: Understanding the 12 Technological Forces That Will Shape Our Future. Translated from English by Konstantinova Yu., Mamedova T. Moscow: Publishing House Mann, Ivanov i Ferber; 2017. 352 p. (In Russ.)

7. Krushanov А.А. Relationship between basic research and technical and technological development as a historically variable relationship. In: Vzaimosvyazj fundamentaljnoj nauki i tekhnologii kak object filosofii nauki = Relationship of Fundamental Science and Technology as an Object of Philosophy of Science. Moscow: Publishing House IFRAN; 2014:222–226. (In Russ.)

8. Kaldewey D., Schauz D. Transforming pure science into basic research: the language of science policy in the United States. In: Kaldewey D., Schauz D., eds. Basic and Applied Research: The Language of Science Policy in the Twentieth Century. New York, Oxford: Berghahn Books; 2018:104–140.

9. Garis H. How will the artilect war start? In: Goertzel B., Goertzel T., eds. The End of the Beginning. Life, Society and Economy on the Brink of the Singularity. Leeds, UK: Humanity+ Press; 2015:117–124.

10. Odinets V.P. Appearance of the name of the discipline “computer science” – dictates of time. Vestnik Syktyvkarskogo universiteta = Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer Science. 2016;1(21):58–68. (In Russ.)

11. Kalyaev I.A. Artificial intelligence: whither goest thou? Ekonomicheskie strategii = Economic Strategies. 2019;5:6–18. (In Russ.) doi:10.33917/es-5.163.2019.6-15

12. Glushkov V.M. Kibernetika. Voprosy teorii i praktiki = Cybernetics. Questions of Theory and Practice. Moscow: Publishing House Nauka; 1986. 488 p. (In Russ.)

13. Bushmeleva N.A., Baklashova T.A. Methodological teaching system of mathematical foundations of formal languages as a means of fundamentalization of education. Evrazijskij maatematichskij zhurnal = Eurasian Mathematical Journal. 2017;13(8):5141–5155. (In Russ.)

14. Thiruvengadam S., Tan J.S., Miller K. Artificial intelligence using hyper-algebraic networks. Neurocomputing. 2020;399:414–448.

15. Savchuk M.M., Fesenko A.V. Quantum computing: survey and analysis. Cybernetics and Systems Analysis. 2019;55:10–21.

16. Rosenberg G., Salomaa A. Handbook of Formal Languages. Vol. 1. Berlin, Heidelberg: Springer-Verlag; 1997. 873 p.

17. Liu R., Yang B., Zio E., Chen X. Artificial intelligence for fault diagnosis of rotating machinery: a review. Mechanical Systems and Signal Processing. 2018;108:33–47.

18. Naschie M.S. Cellular automata based on the golden mean number system as a foundation for artificial intelligence and artificial life. International Journal of Artificial Intelligence and Mechatronics. 2020;8(6):54–58.

19. Knut D.E. The Art of Computer Programming. Vol. 4. A Combinatorial Algorithms. Part 1. USA: Addison-Wesley Professional; 2014. 912 p.

20. Graham R.L., Knuth D.E., Patashnik O. Concrete Mathematics. A Foundation for Computer Science. USA: Addison-Wesley Professional; 1994. 657 p.

21. Perminov E.A., Testov V.A. Mathematisation of specialised disciplines as the basis for fundamentalising IT training in universities. Obrazovanie i nauka = The Education and Science Journal. 2024;26(7):12–42. (In Russ.). doi:10.17853/1994-5639-2024-7-12-43

22. Gnatyshina Е.V., Nikitin P.I. STEM-education: theoretical foundations and component composition. Vestnik Yuzhno-uraljskogo gosudarstvennogo gumanitarno-pedagogicheskogo universiteta = Bulletin of the South Ural State Humanitarian and Pedagogical University. 2024;2(180):95–111. (In Russ.) doi:10.25588/CSPU.2024.180.2.005

23. Solodikhina М.V., Solodikhina А.А. Developing critical thinking in master’s students with STEM cases. Obrazovanie i nauka = The Education and Science Journal. 2019;21(3):125–153. (In Russ.) doi:10.17853/1994-5639-2019-3-125-153

24. Kirillov N.N., Ermakov А.S., Ermakov D.S. “Big ideas” in school natural science education. Nizhegorodskoe obrasovanie = Nizhny Novgorod Education. 2020;2:5–11. (In Russ.)

25. Wynn С.M., Wiggins A.W. The Five Biggest Ideas in Science. New York: John Wiley&Sons; 1996. 208 p.

26. Kolmogorov А.N. Scientific foundations of the school course of mathematics. First lecture. Matematika v shkole = Mathematics in School. 1969;3:12–18. (In Russ.)

27. Semenov А.L., Abylkasymova А.E. Training the future mathematics teacher: the key to change. Vestnik Moskovskogo universiteta. Seriya 20. Pedagogicheskoe obrasovanie = Lomonosov Pedagogical Education Journal. 2024;2(2):24–28. (In Russ.) doi:10.55959/LPEJ-24-13

28. Gyongyosi L., Imre S. A survey on quantum computing technology. Computer Science Review. 2019;31:51–71.

29. Panov А.D. Technological singularity, Penrose’s theorem on artificial intelligence and the quantum nature of consciousness. Informathionnee tekhnologii = Information Technology. 2014;5:1–32. (In Russ.)

30. Krantz S. G. The Proof is in the Pudding. A Look at the Changing Nature of Mathematical Proof. New York: Springer Nature; 2011. 277 p.

31. Heylighen F. (Meta)systems as constraints on variation: a classification and natural history of metasystem transitions. World Futures: Journal of General Evolution. 1995;45:59–85.

32. Permimov Е.А. About the relevance and methodology aspects of teaching the mathematical modeling to pedagogical students. Obrazovanie i nauka = The Education and Science Journal. 2014;1(2):17–33. (In Russ.). doi:10.17853/1994-5639-2014-2-17-33

33. Permiunov E.A., Anakhov S.V., Grishin A.S., Savitskiy E.S. On the research of the methodology of mathematization of pedagogical science. International Journal of Environmental & Science Education. 2016;16:9339–9347. doi:10.17853/1994-5639-2016-1-4-20