Subject: Re: Topic Appropriateness
From: Kirby Urner (pdx4d@teleport.com)
Date: Tue Sep 19 2000 - 18:04:16 EDT
At 01:16 AM 09/19/2000 EDT, RAYFan@aol.com wrote:
>In a message dated 9/18/00 1:43:31 AM Pacific Daylight Time,
>pdx4d@teleport.com writes:
>
><< As I recall, that's the book we used my freshman year at
> Princeton University. _Honors_ Calculus though, with
> Dr. Thurston (topologist). Dunno if still used -- this
> was 1976-77. >>
>
>Hi Kirby-
>
>Are you sure this wasn't Spivak's regular calculus text? His Calculus on
>Manifolds is a very thin paperback book - only 137 pages.
>
>Ray
Yeah, musta been, as ours was hard cover and I think thicker.
Apologies. And sounds like Spiv's regular text is pretty normal
fare for honors calc at the fresh/soph level. Thought "manifolds"
was in the title, but that was probably from perusing other
texts by this author at the local Powell's (good math collection).
Responding to another post re "what is the integral, really...",
it's my impression that math is so far rather poorly served by
useful animations, video clips, visualizations. Would be cool
if math profs had access to DVD juke box, with thumbnail
key frames linked to 2-3 minute clips -- suitable for projecting
in the context of a lecture/presentation. These animations
could be "abstract" and could be more than just animated versions
of what's already standard in text books (e.g. "area under curve"),
although those too would help.
In other words, I'm for getting away from the prejudice that
resorting to visuals, especially animations, is always too informal
vs. the purely symbolic approach. The emphasis on the crypto-symbolic
to the exclusion of the visual is too Gaussian/Bourbakian for my
taste, if you know what I mean.
Also, specifically with regard to integration/differentiation,
I think more could be done than is with the movie metaphor,
instead of always area under a curve. Snap shots, even with
fast film, involve delta t (time interval). A movie camera
is like a differentiator, taking snaps of changes (dF(t)/dt).
A movie projector is like an integrator, playing back the
changes to show a 'running total' (the cummulative effect).
Kirby
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