3/ the last step is wondering when the induced maps are isomorphisms.

I think I have most of this... Just got myself in a tangle with showing when ker(g f) --> ker(g) is subjective.

2/ today I've been thinking about what happens when you join two of these maps together, and the answer is really satisfying.

No doubt this is all well-known to people who know this sort of thing, but it's been fun to discover for myself

Yes, not ideal, but what I've inherited Means I'm running back and forth a bit, but it's only AS across 2 years, so it's manageable.

Hoping to get enough momentum to get two classes next year!

I believe there's a cool application of the IVT, that if you have a 4-legged stool on an uneven (but continuous) floor, you can rotate it and there exists a point where it won't wobble... Trying to recall how that works

It's continuous in p, so if you fix a and b and twiddle p, you're all good

Accords with "harmonic oscillator" in physics too, which refers to any solution of the wave equation.

Very helpful, thanks.
I'm also using the PowerPoint annotate tool, but I obviously need to play with the settings.
Ta

Hi Emily, do your students copy this down, or is it saved electronically afterwards?
What software/equipment are you using to write on the board with such a fine pen?
Microsoft ink on my smart board seems so coarse compared to this!