What enabled the production of mathematical knowledge in complex analysis?

José Gerardo Piña-Aguirre; Rosa María Farfán Márquez

doi:10.29333/iejme/12996

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José Gerardo Piña-Aguirre ¹ ^* , Rosa María Farfán Márquez ¹

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¹ Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (Cinvestav-IPN), México City, MEXICO^* Corresponding Author

Abstract

With the objective of identifying intrinsic forms of mathematical production in complex analysis (CA), this study presents an analysis of the mathematical activity of five original works that contributed to the development of Cauchy’s integral theorem. The analysis of the mathematical activity was carried out through the identification of the types of expressions used and the way they were used by the historical subjects when communicating their results, to subsequently identify transversal elements of knowledge production. The analysis was refined by the notion of confrontation, which depicts the development of mathematical knowledge through the idea of building knowledge against previous knowledge. As a result of the study we established epistemological hypothesis, which are conceived as conjectures that reveal ways in which mathematical knowledge was generated in CA.

Keywords

mathematics education
epistemological analysis
complex analysis
qualitative documentary research
epistemological hypothesis
confrontation

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 18, Issue 2, May 2023, Article No: em0734

https://doi.org/10.29333/iejme/12996

Publication date: 01 Apr 2023

Online publication date: 25 Feb 2023

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How to cite this article

APA

Piña-Aguirre, J. G., & Farfán Márquez, R. M. (2023). What enabled the production of mathematical knowledge in complex analysis?. International Electronic Journal of Mathematics Education, 18(2), em0734. https://doi.org/10.29333/iejme/12996

Vancouver

Piña-Aguirre JG, Farfán Márquez RM. What enabled the production of mathematical knowledge in complex analysis?. INT ELECT J MATH ED. 2023;18(2):em0734. https://doi.org/10.29333/iejme/12996

AMA

Piña-Aguirre JG, Farfán Márquez RM. What enabled the production of mathematical knowledge in complex analysis?. INT ELECT J MATH ED. 2023;18(2), em0734. https://doi.org/10.29333/iejme/12996

Chicago

Piña-Aguirre, José Gerardo, and Rosa María Farfán Márquez. "What enabled the production of mathematical knowledge in complex analysis?". International Electronic Journal of Mathematics Education 2023 18 no. 2 (2023): em0734. https://doi.org/10.29333/iejme/12996

Harvard

Piña-Aguirre, J. G., and Farfán Márquez, R. M. (2023). What enabled the production of mathematical knowledge in complex analysis?. International Electronic Journal of Mathematics Education, 18(2), em0734. https://doi.org/10.29333/iejme/12996

MLA

Piña-Aguirre, José Gerardo et al. "What enabled the production of mathematical knowledge in complex analysis?". International Electronic Journal of Mathematics Education, vol. 18, no. 2, 2023, em0734. https://doi.org/10.29333/iejme/12996