19

My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by Keisler. Two of my colleagues in Belgium are similarly teaching TIC at two universities there. I am also aware of such teaching going on in France in the Strasbourg area, based on Edward Nelson's approach, though I don't have any details on that.

Which universities teach true infinitesimal calculus? Anyone with any additional information in this direction is requested to provide it.

This is cross-posted here.

A colleague in Italy has recently told me about a conference on using infinitesimals in teaching in Italian highschools. This NSA (nonstandard analysis) conference was apparently well attended (over 100 teachers showed up). Anybody with more information about this (who to contact, what the current status of the proposal is, etc.) is hereby requested to provide such information here.

Our experiences teaching calculus with infinitesimals were detailed in this 2017 publication in Humanistic Mathematics.

Mikhail Katz
  • 49,567
  • 2
    You should mention crossposts. – quid Dec 10 '14 at 15:31
  • 2
    Always include the question in the body. Here, it seems like you are really trying to start a discussion, so it's not clear what your question is. "Who is teaching X?" is only barely related to mathematics. – Thomas Andrews Dec 16 '14 at 17:10
  • 1
    In Bar Ilan university in Israel Prof. Mikhail Katz teaches TIC. Here is his website: http://u.cs.biu.ac.il/~katzmik/ – Ofek Gillon Apr 19 '15 at 11:35
  • Smooth infinitesimal analysis is 'truer'. –  Jun 22 '16 at 22:26
  • 1
    In what sense? @mister – Mikhail Katz Jun 23 '16 at 11:34
  • 1
    Just looked at the Keisler book, which is an attempt to implement NSA. You wouldn't realize that having an explicit term for the increment of x allows the Taylor formula to apply exactly to secants, and that neglecting the incremental terms in the derivative yields the continuous case. –  Jun 24 '16 at 01:03

3 Answers3

3

Concordia University (Edmonton, Alberta, Canada), with William Freed as professor. See "The Joys of Teaching Infinitesimal Calculus".

  • 1
    That's interesting. How long has Professor Freed been teaching based on this method? Which textbook does he use? – Mikhail Katz Jan 13 '18 at 16:58
  • 1
    @Mikhail Katz I don't know. I was not his student. All I know, from scarce e-mail messages that I exchanged with him some years ago is that he wrote his own textbook (it's unpublished) and that he used to teach with some standard calculus textbook (I don't remember which one... Thomas' Calculus? Or maybe Stewart...) and complemented it with his own notes with the infinitesimals things. xD His textbook is very rare: http://mathforum.org/kb/message.jspa?messageID=7437511 –  Jan 13 '18 at 17:32
  • 1
    https://en.wikipedia.org/wiki/Concordia_University_of_Edmonton –  Jan 13 '18 at 17:52
0

2 years of the degree course in Bologna University,Italy is pretty good if you want to learn true infinitesimal calculus !!

All The Best !

lola
  • 17
0

In june 2018 I became aware of a program teaching calculus with infinitesimals in Puerto Rico, which was the subject of this 2018 publication in The Mathematics Enthusiast.

Mikhail Katz
  • 49,567