WebMath: mathematical exposition

[Dave Rusin]

I will be interested to hear of your conclusions.

For the most part I don't think there has been great use made of these
tools for the purposes of exposition. It's just too time-consuming to
do it well, I suppose. I can vouch for many uses of the web for math using 
the tools you mentioned to perform things which don't work well in print;
but it's stretching things a little to call this "exposition".

I think the most progress has been made in the use of hypertext: there are
now ample opportunities to say, "click here for more information about..."
I use this a lot in my web pages (math-atlas.org). I think you could
point to the "encyclopedia" at mathworld.com as an example of hypertext
run amok. (Surely not _every_ occurence of a work needs to be highlighted?)

There are also plenty of websites which take advantage of interactivity in
a way not possible with a printed resource. I'm thinking of the search
engines at Mathematical Reviews for example (first class! even handles
multi-alphabet searches reasonably) which allow me to search for papers
in ways I could never do with paper. Also MathSearch (www.maths.usyd.edu.au)
is a good example of automated, up-to-date, filtered searches for web
material. I have high hopes for the Euler project in this direction too
(www.emis.ams.org/projects/EULER/)

I don't know that I think animation helps very much except I suppose for
exposition of something like dynamical systems, and I don't know of
any sites which actually do that! I suppose it could be handy to be
able to manipulate geometric objects and so to really "see" them. There's a
polyhedron site which tries this (www.georgehart.com/virtual-polyhedra/vp.html)
but I never succeeded in loading a VRML viewer so I can't tell you if it
really works!

Likewise you can judge for yourself whether these graphics help to
understand maps on a complex domain: http://www.math.psu.edu/dna/complex-j.html

Many of the textbook publishers are pushing websites to complement their
calculus (say) books. I don't think these are going to improve our students'
performance, but in principle they do can illustrate some things well.
I can't remember the URLs but I've seen them illustrate convergent
sequences, linearity of graphs seen sufficiently close up, that sort of thing.


dave
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