Integration, a genetic introduction
DOI:
https://doi.org/10.7146/nomad.v7i1.146657Abstract
The genetic method of O.Toeplitz is a structuring of conventional instructional material using historical insights and historical problems, not for a history course, but for the better understanding of modern mathematics by students today. The paper which follows describes an introduction to integration suitable for a first course in analysis, in the style of Toeplitz. After two examples of the Greek method of exhaustion (intended for lecturers rather than students), historical developments from the 17th and 19th centuries pinpoint the conceptual steps which a student must take in a conventional first course in analysis up to the Riemann integral.
References
Birkhoff, G. ed. (1973). A Source Book in Classical Analysis. Cambridge, US: Harvard University Press.
Boyer, C.B. (1949). The history of the calculus. New York: Dover reprint 1959.
Burn, R.P. (1997). Numbers and Functions. Cambridge University Press.
Cauchy, A-L. (1821). Analyse Algébrique. Éditions, Paris: Jacques Gabay. Reprint 1989. Cauchy, A-L. (1823). Résumé des leçons sur le Calcul Infinitésimal. Paris: Ellipses reprint.
Darboux, G. (1875). Mémoire sur la théorie des fonctions discontinues. Annales Sci. École Normale Supérieure. Sér.2, 4, 57-112. https://doi.org/10.24033/asens.122
Euler,L.(1748).Introductioinanalysininfinitorum.Vol.1.Englishtranslation 1988.Berlin: Springer.
Fauvel, J. and Gray, J. (1987). The History of Mathematics, a Reader. Open University Press.
Freudenthal, Hans, (1983). Didactical Phenomenology of Mathematical Structures. Dordrecht: D. Reidel.
Hawkins, T. (2nd ed. 1975). Lebesgue's theory of integration. New York: Chelsea.
Katz, V.J. (1993). A history of mathematics. New York: Harper-Collins.
Mahoney, M.S. (1994). The mathematical career of Pierre de Fermat. New York: Princeton University Press.
Struik, D.J. ed. {1969).A Source Book in Mathematics, 1200 -1800. Cambridge, US: Harvard University Press.
Thomas, J. (1875) Einleitung in die Theorie der bestimmten Integrate. Halle.
Toeplitz, O. (1963) The Calculus, a genetic approach. English translation. Chicago: Chicago University Press.
Whiteside, D.T. ed. (1967). The Mathematical Papers of Isaac Newton, vol I. Cambridge, UK: Cambridge University Press.
Whiteside, D.T. ed. (1968). The Mathematical Papers of Isaac Newton, vol II. Cambridge, UK: Cambridge University Press.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
