Skip to Main Content

Modelling and Data Analysis
2025. Vol. 15, no. 4, 122–137
doi:10.17759/mda.2025150408
ISSN: 2219-3758 / 2311-9454 (online)

Algebraic curves of higher orders in teaching higher mathematics. Methods of constructing algebraic curves

 
Audio is AI-generated
1

,

PDF (RUS)
Online translation in english
GS
Information
in Google Scholar
Metrics

Abstract

Context and relevance. In the working programs of the disciplines "Geometry and Topology", "Mathematical Analysis", "Mathematics" and others, included in the educational programs of specialties in information technologies, an important place is occupied by the concept of an algebraic curve. The development of this concept requires students to have the ability to think abstractly and often cause significant difficulties. Purpose. To improve the quality of learning the educational material on disciplines related to the concept of an algebraic curve, while using software tools for visualization various algebraic curves and families of algebraic curves. Another equally important goal is to describe issues that can become the topics of term papers and theses. Hypothesis. The use of software tools for visualizing various algebraic curves and families of algebraic curves allows the teacher to present the material in the most understandable way, and students to better understand the material and acquire the skills of solving problems on the construction of algebraic curves. Methods and materials. Most of the exercises in this article involve writing a computer program that visualizes algebraic curves and their families. Results. A system of tasks has been developed that allows students to construct algebraic curves using computer programs. Conclusions. The use of the developed system of educational tasks has confirmed the importance of using special software tools for mastering the theory of algebraic curves.

General Information

Keywords: higher education, methods of teaching mathematics, analytical geometry, visual images, algebraic curves, methods of constructing algebraic curves, geometric images of algebraic curves, pedal curve of a curve, pedal curve of a parabola, geometric transformations, cissoidal transformations

Journal rubric: Method of Teaching

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2025150408

Received 17.10.2025

Revised 27.10.2025

Accepted

Published

For citation: Kulanin, Y.D., Stepanov, M.E. (2025). Algebraic curves of higher orders in teaching higher mathematics. Methods of constructing algebraic curves. Modelling and Data Analysis, 15(4), 122–137. (In Russ.). https://doi.org/10.17759/mda.2025150408

© Kulanin Y.D., Stepanov M.E., 2025

License: CC BY-NC 4.0

References

  1. Дьедонне Ж. Линейная алгебра и элементарная геометрия. М., Наука, 1972.
    Dieudonné, J. Linear Algebra and Elementary Geometry. Moscow, Nauka, 1972.
  2. Куланин Е. Д., Нгуен Ву Куанг., Степанов М. Е. Осязаемая предметность с компьютерной поддержкой. // Моделирование и анализ данных. 2019. Том № 4. С. 145–156.  DOI: https://doi: 10.17759/mda.2019090412
    Kulanin E. D., Nguyen Vu Quang, and Stepanov M. E. Tangible Subjectivity with Computer Support. // Modeling and Data Analysis. 2019. Vol. 09. No. 4. Pp. 145–156. DOI: https://doi: 10.17759/mda.2019090412
  3. Куланин Е. Д., Степанов М. Е. Использование образов в преподавании высшей математики. // Моделированиеианализданных. 2024. Том № 2. C. 192–225. DOI:  https://doi. org/10.17759/mda.2024140212
    Kulanin E. D., Stepanov M. E. Using Images in Teaching Higher Mathematics. // Modeling and Data Analysis. 2024. Vol. 14. No. 2. Pp. 192–225. DOI: https://doi.org/10.17759/mda.2024140212
  4. Куланин Е. Д., Степанов М. Е. О визуализации решений некоторых экстремальных задач. // Моделирование и анализ данных. 2022. Том № 4. C. 94–104. DOI: https://doi. org/10.17759/mda.2022120407
    Kulanin E. D., Stepanov M. E. On the visualization of solutions to some extremal problems. // Modeling and Data Analysis. 2022. Vol. 12. No. 4. Pp. 94–104. DOI: https://doi.org/10.17759/mda.2022120407
  5. Куланин Е. Д., Степанов М. Е., Нуркаева И. М. Роль образного мышления в  научном мышлении. // Моделирование и анализ данных. Том 10. № 2. C. 110–128. DOI:  https://doi:10.17759/mda.2020100209
    Kulanin E. D., Stepanov M. E., Nurkaeva I. M. The Role of Imagination in Scientific Thinking. // Modeling and Data Analysis. 2020. Vol. 10. No. 2. Pp. 110–128. DOI: https://doi:10.17759/mda.2020100209
  6. Куланин Е.Д., Степанов М. Е. Всестороннее рассмотрение математических понятий как методический прием. // Моделированиеианализданных. 2022. Том № 4. C. 67–84.  DOI:https://doi.org/10.17759/mda.2022120405
    Kulanin E.D., Stepanov M. E. Comprehensive Review of Mathematical Concepts as a  Methodological Approach. // Modeling and Data Analysis. 2022.Vol. 12. No. 4. Pp. 67–84. DOI: https://doi.org/10.17759/mda.2022120405
  7. Куланин Е.Д., Степанов М. Е. Вычислительный эксперимент в преподавании высшей математики на примере теории чисел.  // Моделирование и анализ данных. 2024. Том 14. № 1. C. 170–195.  DOI: https://doi.org/10.17759/mda.2024140111 12.
    Kulanin E.D., Stepanov M. E. Computational Experiment in Teaching Higher Mathematics on the Example of Number Theory. // Modeling and Data Analysis. Vol. 14. No. 1. Pp. 170–195. DOI: https://doi.org/10.17759/mda.2024140111 12.
  8. Куланин Е.Д., Степанов М. Е. Вычислительный эксперимент в преподавании высшей математики. Комбинаторика и её приложения. // Моделирование и анализ данных. Том 14. № 3. C. 174–202. DOI: https://doi.org/10.17759/mda.2024140310
    Kulanin E.D., Stepanov M. E. Computational Experiment in Teaching Higher Mathematics. Combinatorics and Its Applications. // Modeling and Data Analysis. 2024. Vol. 14. No. 3. Pp. 174–202. DOI: https://doi.org/10.17759/mda.2024140310
  9. Куланин Е.Д., Степанов М. Е. Из опыта работы в режиме дистанционного обучения // Моделирование и анализ данных. Том 12. № 3. C. 58–70. DOI: https://doi. org/10.17759/mda.2022120305
    Kulanin E.D., Stepanov M. E. From the experience of working in remote mode education // Data modeling and analysis. 2022. Volume 12. No. 3. pp. 58-70. DOI: https:// doi. org/10.17759/mda.2022120305
  10. Куланин Е.Д., Степанов М. Е. Использование образов в преподавании высшей математики. // Моделирование и анализ данных. Том 14. № 2. C. 192–225. DOI: https://doi. org/10.17759/mda.2024140212
    Kulanin E.D., Stepanov M. E. Using Images in Teaching Higher Mathematics. // Modeling and Data Analysis. 2024. Vol. 14. No. 2. Pp. 192–225. DOI: https://doi.org/10.17759/mda.2024140212
  11. Куланин Е.Д., Степанов М. Е., Нуркаева И.М. О различных подходах к решению экстремальных задач. // Моделирование и анализ данных. 2021. Том № 1. C. 40–60. DOI: https://doi.org/10.17759/mda.2021110104
    Kulanin E.D., Stepanov M. E., Nurkaeva I.M. On Different Approaches to Solving Extreme Problems. // Modeling and Data Analysis. 2021. Vol. 11. No. 1. Pp. 40–60. DOI: https://doi.org/10.17759/mda.2021110104
  12. Куланин Е.Д., Степанов М.Е. Алгебраические кривые низших порядков в препо­давании высшей математики // Моделирование и анализ данных. Том 15. № 1. C. 210–251. DOI: https://doi.org/10.17759/mda.2025150111
    Kulanin E.D., Stepanov M.E. Algebraic Curves of Lower Orders in Teaching Higher Mathematics // Modeling and Data Analysis. 2025. Vol. 15. No. 1. Pp. 210–251. DOI: https://doi.org/10.17759/mda.2025150111
  13. Лунгу К.Н., Норин В.П., Письменный Д.Т., Шевченко Ю.А., Куланин Е.Д. Сборник задач по высшей математике с контрольными работами. Москва, 2013. Том 2 (8-е издание).
    Lungu K.N., Norin V.P., Pismenny D.T., Shevchenko Yu.A., Kulanin E.D. Collection of Problems in Higher Mathematics with Control Works. Moscow, 2013. Volume 2 (8th edition).
  14. Прасолов В. В. Геометрические задачи древнего мира. М., ФАЗИС, 1997.
    Prasolov, V. V. Geometric Problems of the Ancient World. Moscow, FAZIS, 1997.
  15. Савёлов А. А. Плоские кривые. Систематика, свойства, применения. (Справочное руководство). М., Гос. изд. физ.-мат. литературы. 1960.
    Savelov A. A. Flat curves. Taxonomy, properties, applications. (Reference manual). M., State Publishing House of Physics and Mathematics. literatures. 1960.
  16. Степанов М. Е., Куланин Е.Д. Множества точек, находящихся на рациональных расстояниях друг от друга. // Моделирование и анализ данных. Том 15. № 1. C. 210-251. DOI: https://doi.org/10.17759/mda.2025150111
    Stepanov M. E., Kulanin E.D. Sets of points located at rational distances from each other. // Modeling and Data Analysis. 2025. Vol. 15. No. 1. C. 210-251. DOI: https://doi.org/10.17759/mda.2025150111

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

Contribution of the authors

Kulanin E.D. — research ideas, writing and formatting of the manuscript, development of the methodology, research planning, and visualization of research results.

Stepanov M.E. — research ideas, writing and formatting of the manuscript, development of the described software, research planning, and visualization of research results.

All authors participated in the discussion of the results and approved the final text of the manuscript.

Conflict of interest

The authors declare no conflict of interest.

Metrics

 Web Views

Whole time: 0
Previous month: 0
Current month: 0

 PDF Downloads

Whole time: 1
Previous month: 0
Current month: 1

 Total

Whole time: 1
Previous month: 0
Current month: 1