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 <https://www.math.wisc.edu/~keisler/calc.html>. 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 schools, colleges, or universities teach true infinitesimal calculus?*


A colleague in Italy has told me about a conference a few months ago on using infinitesimals in teaching in Italian highschools. This NSA (nonstandard analysis) conference was apparently well attended (over 100 teachers showed up). 


In Geneva, there are two highschools that have been teaching calculus using ultrasmall numbers for the past 10 years. 


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.


Note 1 in response to Dan's comment: usually nowadays the term *infinitesimal calculus* is used as a dead metaphor for "the calculus". Thus, calculus courses routinely go under the name "infinitesimal calculus" for historical reasons, whereas in point of fact no infinitesimal ever appears on the blackboard. When I refer to "true infinitesimal calculus" I mean calculus with infinitesimals (as explained above) as opposed to ordinary "infinitesimal calculus" as found in Thomas-Finney and other textbooks.


Note 2 in response to Pietro's comment: I should clarify that calculus using infinitesimals is not limited to Keisler's book. There are several books of this sort, including some that are unrelated to Robinson's theory, such as those by A. Kock and J. Bell.


Note 3: thanks to Bjørn Kjos-Hanssen for the update on the history of TIC teaching at the University of Hawaii.



Which universities teach true infinitesimal calculus?
Since you mentioned University of Hawaii --


[David Ross](http://www.math.hawaii.edu/~ross/) regularly teaches nonstandard analysis and infinitesimal calculus at University of Hawaii in various forms, for instance 


* [MATH 649K](http://www.math.hawaii.edu/~ross/649.htm) (a regular grad course), Spring 2008
* [MATH 699](http://www.math.hawaii.edu/~ross/699.htm) (reading course), Spring 2011


We also usually cover the topic in our senior-level course on mathematical logic (MATH 455), although I suppose a lot of universities do that.


**But** infinitesimal calculus is not part of our standard calculus syllabus.


