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A Result in the Theory of Determinants from a Semiotic Viewpoint

Received: 21 August 2014     Accepted: 30 August 2014     Published: 20 September 2014
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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.

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), 2014. Published by Science Publishing Group

Keywords

Mathematics Education, Semiotics, Determinants

References
[1] CANTOR , Georg. (1980) Gesammelte Abhandlungen mathematischen und philosophischen Inhalts: Mit erläuternden Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor-Dedekind herausgegeben von E. Zermelo. Heidedelberg: Springer..
[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.
[6] REID, C. (1970) Hilbert. New York: Springer.
[7] RUSSELL, B. (1998) Introduction to Mathematical Philosophy. London: Routledge.
Cite This Article
  • 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

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    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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    AMA 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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  • @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}
    }
    

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    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
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Author Information
  • Universidade Anhanguera de S?o Paulo (UNIAN) Programa de Pós-gradua??o em Educa??o Matemática, S?o Paulo, Brasil

  • Universidade Anhanguera de S?o Paulo (UNIAN) Programa de Pós-gradua??o em Educa??o Matemática, S?o Paulo, Brasil

  • Universidade Federal do Mato Grosso (UFMT), Cuiabá, Brasil

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