On Fri, 05 Jul 2013 23:20:40 -0600, Robert Hansen <email@example.com> wrote:
> > On Jul 5, 2013, at 11:47 PM, "Louis Talman" <firstname.lastname@example.org> wrote: > >> It wasn't until I took my first calculus course as a freshman in >> college that I encountered real concern about >>proofs and derivations. >> I was fortunate in that my professors there made proofs and derivations >> about half of their >>calculus sequence---all four semesters of it. And >> they examined us on those proofs and derivations, not only in >>the >> calculus sequence, but in the junior and senior comprehensive exams all >> math majors had to pass in order to >>be graduated. > > I meant to ask, do you think this is common today in college?
I think it was uncommon then in college. And is still uncommon today.
I did my graduate work at the University of Kansas, probably a second tier school in mathematics. While there, I had a half-time appointment, teaching lower division courses. Their calculus sequence was much different from the one I had taken, and much like the ones taught at the colleges and universities where I've held appointments since. Plus ca change, plus c'est la meme chose.
> > >> (Many of my colleagues during that first calculus sequence would not >> have agreed that any of this proof-and->>derivation business was >> "fortunate"; a substantial fraction of them show themselves to be >> completely at sea at >>that business.) > > What happened to those students? Did they swim or sink?
At mathematics, most of them sank. And those people found non-mathematical things to pursue. (Here I include physics, which doesn't, as a rule, take a deep interest in the structure of mathematics---only in what it will do for them.)
> > > Bob Hansen >
-- --Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State University of Denver