Skip to main content Accessibility help
×
Home
Hostname: page-component-568f69f84b-r4dm2 Total loading time: 0.224 Render date: 2021-09-20T06:20:44.450Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

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*
Affiliation:
Translated into English by Michael N. Fried and Hans Niels Jahnke*

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.

Type
Historical Document in Translation
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.)

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 7:39.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 27:143149.Google Scholar
Klein, Felix. 1899. “Über Aufgabe und Methode des mathematischen Unterrichts an den Universitäten.” Jahresbericht der Deutschen Mathematiker-Vereinigung 7:126138.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 7:138145.Google Scholar
Tobies, Renate. 2012. Iris Runge: A Life at the Crossroads of Mathematics, Science, and Industry. Basel: Birkhäuser.CrossRefGoogle Scholar
2
Cited by

Linked content

Please note a has been issued for this article.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *