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Restarting high school topology
- May 21st, 2008
My two high-school kids came by today. We’ve been trying to get a new teaching session together since early February, but they had a hell of a time all through February, and all our appointments ended up canceled with little or no notice; and then I spent March and April on tour.
We pressed on with knot theory. Today, we discussed knot sums, prime knots, knot tabulation, behavior of the one invariant (n-colorability) we know so far under knot sums, Dowker codes, and we got started on Conway codes for knots. Next week, I plan for us to finish up talking about the Conway knot notation, get the connection between rational knots and continued fractions down pat, and start looking into new invariants.
Anyone have a favorite invariant that you’d like me to talk about? I’m hoping (in my wildest most bizarre dreams) to get around to the Alexander polynomial and possibly even talk about Khovanov homology, but that depends a LOT on whether they’re prepared to continue through their summer holidays or not - and even then I doubt we’ll make it up to Khovanov.
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Michi is a PhD student working in homological algebra. This blog is his outlet for texts with some manner of thought put into them. Over at his LiveJournal intimate details and streams of consciousness might be found.
Not all here is mathematics. All here, though, are my personal thoughts and opinions. Please read the about page (linked above) for more details.
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One Person had this to say...
I’d say my extensions of coloring sets to coloring spans, but that’s a bit much, eh?
If you’re doing the knot group (you *are* doing the knot group, right) then it shouldn’t be hard to do the quandle. And the connection from quandles to colorings is pretty straightforward. In fact, you *could* do coloring matrices for tangles…
Then there’s the Bracket, of course…
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