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Modelling and Data Analysis
2024. Vol. 14, no. 1, 170–195
https://doi.org/10.17759/mda.2024140111
ISSN: 2219-3758 / 2311-9454 (online)

Computational Experiment in Teaching Higher Mathematics by the Example of Number Theory

 
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Abstract

The article continues the cycle of methodological developments of the authors [1] – [17]. It discusses some problems related to ways to improve the culture of mathematical thinking of mathematics students. The authors rely on the experience of working at the Faculty of Information Technology of MSUPE.

General Information

Keywords: higher education, methods of teaching higher mathematics, computer calculations, computational experiment, theory of numbers, prime numbers, twin numbers, fours of prime numbers, Diophantine equations, irrational numbers

Journal rubric: Method of Teaching

OpenAlex citations: 6

OpenAlex trends: Artificial Intelligence in Education, Educational Innovations and Challenges, Regional Economic Development and Innovation

Information about the work in OpenAlex

Number of citations: 6

Topics

Artificial Intelligence in Education

This cluster of papers explores the intersection of education and technology, focusing on topics such as artificial intelligence in educational systems, distance learning, depression diagnosis using neural networks and fuzzy logic, e-learning platforms, and pedagogical innovation. It also delves into the application of digital technologies in teaching and learning processes, knowledge management in educational settings, and the impact of digital transformation on education.

Number of works: 14182  |  Total number of citations: 18505

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Educational Innovations and Challenges

This cluster of papers explores the digital transformation and its impact on higher education institutions, focusing on topics such as educational technology, distance learning, e-learning, university management, and student experience. It discusses the challenges, opportunities, and risks associated with the integration of digital technologies in higher education, as well as the pedagogical approaches driving this transformation.

Number of works: 86064  |  Total number of citations: 128385

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Regional Economic Development and Innovation

This cluster of papers focuses on the strategizing of regional and national development, with an emphasis on innovation ecosystems, sustainable development, digital transformation, vocational education, and economic growth. It explores the intersection of global and national interests with regional strategic priorities, as well as the role of leadership in driving strategic initiatives. The papers also delve into the challenges and opportunities presented by globalization and the pursuit of sustainable socio-economic growth.

Number of works: 27611  |  Total number of citations: 18753

Topic detailsв OpenAlex

Work details in OpenAlex

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2024140111

Received 10.01.2024

Accepted

Published

For citation: Kulanin, Y.D., Stepanov, M.E. (2024). Computational Experiment in Teaching Higher Mathematics by the Example of Number Theory. Modelling and Data Analysis, 14(1), 170–195. (In Russ.). https://doi.org/10.17759/mda.2024140111

© Kulanin Y.D., Stepanov M.E., 2024

License: CC BY-NC 4.0

References

  1. Stepanov M. E. The image of a force field as a heuristic model in mathematics.    Modeling and data analysis. Proceedings of the Faculty of Information Technologies of MGPPU. – Issue 3., 2007.
  2. Stepanov M. E. Klein's Erlangen program and triangle geometry. Modeling and data analysis. Proceedings of the Faculty of Information Technologies of MGPPU. - 2015. No. 1. pp.100-135.
  3. Stepanov M. E. Klein's Erlangen program and the geometry of triangles (Part two). Modeling and data analysis. Proceedings of the Faculty of Information Technologies of MGPPU. – 2016. No. 1. pp.60-115.
  4. Stepanov M. E. Klein's Erlangen program and triangle geometry Modeling and data analysis. Mathematical education. 2017. No.3(83). pp.28-42.
  5. Stepanov M. E. Computer technologies as a means of introducing the student to mathematical reality. Modeling and data analysis. Scientific journal. – Issue 1, 2018.
  6. Kulanin E.D., Nurkaeva I.M. On two geometric problems on the extremum. Math at school. 2019. No. 4. pp. 35-40.
  7. Kulanin E.D., Nurkaeva I.M. Once again about the Mavlo problem. Mathematics in school. 2020. No. 2. pp. 76-79.
  8. Kulanin E.D., Stepanov M. E., Nurkaeva I.M. Propaedeutics of solving extreme problems in the school course of mathematics. Modeling and analysis of data. 2019. No. 4. pp.127-144.
  9. Kulanin E. D., Nguyen Wu Quang, Stepanov M. E. Tangible objectivity with computer support. Modeling and data analysis. Scientific journal. 2019. No. 4. pp.145-156.
  10. Kulanin E.D., Stepanov M. E., Nurkaeva I.M. The role of imaginative thinking in scientific thinking. Modeling and data analysis. 2020. Vol.10. No.2 Pp.110 - 128. 
  11. Kulanin E.D., Stepanov M. E., Nurkaeva I.M. On various approaches to solving extreme tasks. Modeling and data analysis. 2020. Vol.11. No. 1. P.40 - 60.
  12. Lungu K.N., Norin V.P., Pismennyi D.T., Shevchenko Yu.A., Kulanin E.D. Collection of problems in higher mathematics with control papers. Moscow, 2013. Volume 2 (8th edition).
  13. Stepanov M.E. From experience in the field of typhlopedagogics. Modeling and data analysis. 2017. No. 1. pp.42-53.
  14. Stepanov M.E. Some questions of the methodology of teaching higher mathematics. Modeling and data analysis. 2017. No. 1. pp.54-94.
  15. Kulanin E.D., Stepanov M. E. From the experience of working in the remote mode Learning Modeling and data analysis. 2022. Vol.12. No.3. pp.58-70.
  16. Kulanin E.D., Stepanov M. E. Comprehensive consideration of mathematical concepts as a methodological technique. Modeling and data analysis. 2022. Vol.12. No.4. pp.67-84.
  17. Kulanin E.D., Stepanov M. E. On visualization of solutions to some extreme problems. Modeling and data analysis. 2022. Vol.12. No. 4. pp.94 - 104.
  18. Arnold V. I. About teaching mathematics. SUCCESSES OF MATHEMATICAL SCIENCES, vol. 53, issue 1 (319).
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  20. Prahar K. Distribution of primes. M., Mir, 1967.
  21. Serpinsky V. What we know and what we don't know about primes. M. – L. State Publishing House of Physics. – mate. literatures. 1963.
  22. ru.wikipedia.org › The numbers are twins.
  23. Zenkin V. I. Distribution of prime numbers: Elementary methods. Kaliningrad, 2008.
  24. Depman. I. Perfect numbers. Kvant, 1991, No. 5.

Information About the Authors

Yevgeny D. Kulanin, Candidate of Science (Physics and Matematics), Professor, Moscow State University of Psychology and Education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0001-6093-7012, e-mail: lucas03@mail.ru

Mikhail E. Stepanov, Candidate of Science (Education), Associate Professor, Department of Applied Mathematics, Faculty of Information Technologies, Moscow State University of Psychology and Education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0003-4803-8211, e-mail: mestepanov@yandex.ru

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