What are some "homeless" topics in the undergrad math curriculum? I don't mean the usual "everyone should take this course" debate, but stuff that slips through the cracks b/c there's no standard course to fit it into. Ex: Fourier series, polyhedra, multivariable real analysis. #mathsky #teachmath - ThreadSky

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billarama.bsky.social • 3 days ago

What are some "homeless" topics in the undergrad math curriculum? I don't mean the usual "everyone should take this course" debate, but stuff that slips through the cracks b/c there's no standard course to fit it into. Ex: Fourier series, polyhedra, multivariable real analysis. #mathsky #teachmath

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sbagley.bsky.social•2 days ago

Functional calculus generally and the calculus of variations specifically. Category theory (though I'll accept the position that this is grad not undergrad).

floerist.bsky.social•2 days ago

Absolutely seconding calculus of variations here!

billarama.bsky.social•1 day ago

I'd call this an instance of a general underemphasis on learning how to parameterize things.

profkinyon.bsky.social•1 day ago

I guess you mean topics which could, in principle, be covered in undergrad with a minimum of prereqs. A couple of things come to mind close to my own interests:
Semigroups/monoids (algebra courses usually just cover groups & rings),
Latin squares (combinatorics courses usually skip them)

profkinyon.bsky.social•1 day ago

I'm not saying those topics *should* be done, but I think they fit your criteria.

billarama.bsky.social•1 day ago

I'm thinking of particular stuff that at some point in grad school you are expected to have seen but that never quite shows up in a course. Latin squares fits. Monoids maybe a little more specialized for that description.

profkinyon.bsky.social•1 day ago

Oh, that's what you meant. Well, in that case: tensor products. Over the years I've heard *many* grad students complain that they are expected to already know it when it was never covered in undergrad.

billarama.bsky.social•1 day ago

Oh, yes, definitely. That's an excellent one.

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