We present a conceptual proof of the Cauchy-Binet theorem about determinants to show how much one can gain by investing a bit more in conceptual development, comparing this treatment with the usual one in terms of laborious matrix calculations. The purpose is to stimulate a conceptual understanding and to overcome the usual empiricism, which is an obstacle to a real understanding of mathematical knowledge. The article also aims to show that mathematical terms could be understood as dynamic processes, based on the interaction between intensional and extensional aspects. As it is not really possible to answer any question about the nature of mathematical objects definitively, much less to limit the possible interpretations of mathematical concepts, processes of concept evolution are of great importance to mathematics as a human activity.
| Published in | Science Journal of Education (Volume 2, Issue 4) |
| DOI | 10.11648/j.sjedu.20140204.16 |
| Page(s) | 137-140 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Mathematics Education, Semiotics, Determinants
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| [2] | DIEUDONNÉ, J. (1970) The work of Nicholas Bourbaki. Amer. Math. Monthly 77 (1970), p. 134-145. |
| [3] | GREUB, W. H. (1967) Linear Algebra. New York: Springer. |
| [4] | JAKOBSON, R; HALLE, M. (1956) Fundamentals of Language. Mouton Den Haag. |
| [5] | OTTE, M. (2006) Proof Analysis and Continuity, Foundations of Science, vol. 11, 121-155. |
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APA Style
Michael F. Otte, Tânia M. M. Campos, Luiz G. X. de Barros, Geslane F. S. Santana. (2014). A Result in the Theory of Determinants from a Semiotic Viewpoint. Science Journal of Education, 2(4), 137-140. https://doi.org/10.11648/j.sjedu.20140204.16
ACS Style
Michael F. Otte; Tânia M. M. Campos; Luiz G. X. de Barros; Geslane F. S. Santana. A Result in the Theory of Determinants from a Semiotic Viewpoint. Sci. J. Educ. 2014, 2(4), 137-140. doi: 10.11648/j.sjedu.20140204.16
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Download@article{10.11648/j.sjedu.20140204.16,
author = {Michael F. Otte and Tânia M. M. Campos and Luiz G. X. de Barros and Geslane F. S. Santana},
title = {A Result in the Theory of Determinants from a Semiotic Viewpoint},
journal = {Science Journal of Education},
volume = {2},
number = {4},
pages = {137-140},
doi = {10.11648/j.sjedu.20140204.16},
url = {https://doi.org/10.11648/j.sjedu.20140204.16},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjedu.20140204.16},
abstract = {We present a conceptual proof of the Cauchy-Binet theorem about determinants to show how much one can gain by investing a bit more in conceptual development, comparing this treatment with the usual one in terms of laborious matrix calculations. The purpose is to stimulate a conceptual understanding and to overcome the usual empiricism, which is an obstacle to a real understanding of mathematical knowledge. The article also aims to show that mathematical terms could be understood as dynamic processes, based on the interaction between intensional and extensional aspects. As it is not really possible to answer any question about the nature of mathematical objects definitively, much less to limit the possible interpretations of mathematical concepts, processes of concept evolution are of great importance to mathematics as a human activity.},
year = {2014}
}
TY - JOUR T1 - A Result in the Theory of Determinants from a Semiotic Viewpoint AU - Michael F. Otte AU - Tânia M. M. Campos AU - Luiz G. X. de Barros AU - Geslane F. S. Santana Y1 - 2014/09/20 PY - 2014 N1 - https://doi.org/10.11648/j.sjedu.20140204.16 DO - 10.11648/j.sjedu.20140204.16 T2 - Science Journal of Education JF - Science Journal of Education JO - Science Journal of Education SP - 137 EP - 140 PB - Science Publishing Group SN - 2329-0897 UR - https://doi.org/10.11648/j.sjedu.20140204.16 AB - We present a conceptual proof of the Cauchy-Binet theorem about determinants to show how much one can gain by investing a bit more in conceptual development, comparing this treatment with the usual one in terms of laborious matrix calculations. The purpose is to stimulate a conceptual understanding and to overcome the usual empiricism, which is an obstacle to a real understanding of mathematical knowledge. The article also aims to show that mathematical terms could be understood as dynamic processes, based on the interaction between intensional and extensional aspects. As it is not really possible to answer any question about the nature of mathematical objects definitively, much less to limit the possible interpretations of mathematical concepts, processes of concept evolution are of great importance to mathematics as a human activity. VL - 2 IS - 4 ER -
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