Re: A well kept secret?

[John Baez <john.c.baez@gmail.com>]

Peter Easthope wrote:

They won it ... but how prevalent is the
> subject in undergraduate programs?  Vector
> algebra and analysis wasn't taught to engineers
> until what, 1900 or later.  Now it is ubiquitous.
>

Interestingly, in the late 1800s there was a period where quaternions were a
mandatory examination topic in Dublin - and in some American universities
they were the only advanced mathematics taught.  Gibbs, who chopped the
quaternion into its scalar and vector part and introduced the notation we
use today, was the first person to get an engineering PhD in the United
States, back in 1863.

Absolutely no offense to existing books but what
> about an energetic mathematician or two writing
> a _Schaum's Outline of Category Theory_? I'd
> expect it to sell off the shelves initially.
>

Great idea!

I think it's premature to introduce category theory in the undergrad
curriculum.  Why?  Merely because there aren't enough professors who'd see
how to teach the subject at that level.  It's bound to happen eventually -
but right now we need category theory to become a standard course at the
graduate level.

Whenever they get a good taste of category theory, math grad students are
eager to take a course on it.  They think it's exciting, and they see it as
a way to learn other subjects more efficiently.   But right now it's usually
taught as part of algebra, without enough detail, and without enough
attention to its applications outside algebra. So, sometimes students start
their own seminars on category theory!

Once most math grad students take a class on category theory, we'll get
professors who can conceive of teaching it at the undergrad level.

The only real question is whether our current civilization, based on burning
carbon, tearing up forests, and destroying oceans, lasts long enough to see
this change.

Best,
jb

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]