Hostname: page-component-89b8bd64d-4ws75 Total loading time: 0 Render date: 2026-05-06T14:16:39.304Z Has data issue: false hasContentIssue false
  • English
  • Français

The Problem of University Courses on Infinitesimal Calculus and Their Demarcation from Infinitesimal Calculus in High Schools1

Published online by Cambridge University Press:  21 May 2015

Otto Toeplitz
Otto Toeplitz*
Affiliation:
Translated into English by Michael N. Fried and Hans Niels Jahnke*
Get access Rights & Permissions [Opens in a new window]

Extract

When the Association of German Scientists and Physicians last met in Düsseldorf exactly twenty-eight years ago on September 24, a debate took place following lectures by Felix Klein and Alfred Pringsheim on roughly the same topic to which I would like to direct your attention today. The printed report of the Düsseldorf debate only remarked that, “It is not possible to go into details here,” so one can only guess how two of the most powerful teacher personalities among German mathematicians of that time had confronted one another with their diametrically opposed views on this topic and how they did so with their characteristically lively spirit.

Information

Type
Historical Document in Translation
Information
Science in Context , Volume 28 , Special Issue 2: Knowledge in the Making , June 2015 , pp. 297 - 310
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

1

Lecture presented at the congress at Düsseldorf during the meeting of the Reichsverband on September 24, 1926 [footnote in the original].

References

Corry, Leo. [1996] 2004. Modern Algebra and the Rise of Mathematical Structures, 2nd revised edition. Basel and Boston: Birkhäuser Verlag.CrossRefGoogle Scholar
Dedekind, Richard. 1893. Was sind und was sollen die Zahlen? Braunschweig: F. Vieweg.Google Scholar
DMV (German Mathematical Society). 1899. “Bericht über die Jahresversammlung zu Düsseldorf am 19. bis 24. September 1898.” Jahresbericht der Deutschen Mathematiker-Vereinigung 7:3–9.Google Scholar
Kiepert, Ludwig & Stegemann, Max. 1888. Grundriss der Differential- und Integralrechnung. 5th Edition, Hannover: Helwingsche Verlagsbuchhandlung.Google Scholar
Kiepert, Ludwig, and Stegemann, Max. 1905. Grundriss der Differential- und Integralrechnung. 10th Edition, Hannover: Helwingsche Verlagsbuchhandlung.Google Scholar
Klein, Felix. [1895] 1896. “Über Arithmetisierung der Mathematik. Vortrag, gehalten in der öffentlichen Sitzung der K. Gesellschaft der Wissenschaften zu Göttingen am 2. November 1895.” Zeitschrift für mathematischen und naturwissenschaftlichen Unterricht 27:143–149.Google Scholar
Klein, Felix. 1899. “Über Aufgabe und Methode des mathematischen Unterrichts an den Universitäten.” Jahresbericht der Deutschen Mathematiker-Vereinigung 7:126–138.Google Scholar
Klein, Felix. [1908] 1939. Elementary Mathematics from an Advanced Standpoint. Part I: Arithmetic, Algebra, Analysis. Part II: Geometry. Translated by E. R. Hedrick and C. A. Noble. New York: Dover Publications.Google Scholar
Klein, Jacob. [1934, 1936] 1968. Greek Mathematical Thought and the Origin of Algebra. Translated by Eva Brann. Cambridge MA: MIT Press. Originally published as “Die griechische Logistik und die Entstehung der Algebra.” In Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik (Abteilung B: Studien) 3(1):18–105 and 3(2):122–235.Google Scholar
Kowalewski, Gerhard. 1910. Die klassischen Probleme der Analysis des Unendlichen: ein Lehr- und Übungsbuch für Studierende zur Einführung in die Infinitesimalrechnung. Leipzig: Engelmann.Google Scholar
Pringsheim, Alfred. 1899. “Zur Frage der Universitätsvorlesungen über Infinitesimalrechnung.” Jahresbericht der Deutschen Mathematiker-Vereinigung 7:138–145.Google Scholar
Tobies, Renate. 2012. Iris Runge: A Life at the Crossroads of Mathematics, Science, and Industry. Basel: Birkhäuser.CrossRefGoogle Scholar