>The following year one of the intructors gave a special "honors" course
>for, I think, 2nd year students, using as a textbook Landau's introduction
>to calculus, which was written very much in the spirit of Landau (and
>Dedkind). (In those days, a first college course in calculus in the USA
>was often a second-year course.) It was a disaster. Many of the students,
>bright as many of them were, just didn't seem to be ready for such rigor.
>More than that, even those who performed well in the manner advocated by
>Landau and Dedekind spent so much time on fundamentals that they had
>difficulty in moving on to further courses in advanced calculus and
>differential equations. This was a case, I think, of too much, too soon.
It should be pointed out that Dedekind, at the beginning of his paper of
continuity and irrational numbers, wrote (and I have only a not very good
translation at hand at the moment)
``Even now such resort to geometric intuition in a first presentation of
the differential calculus, I regard as exceedingly useful, from the
didactic standpoint, and indeed indispensible, if one does not wish to lose
too much time.''
Bill Tait