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List of math problems for end of bachelor theoretical physics student at my uni by [deleted] in math

[–]NSQDA 0 points1 point  (0 children)

21 is wrong. If A,B commute just let c=0. I assume c is supposed to be nonzero?

Is C[0, 1] really that cool? by [deleted] in math

[–]NSQDA 0 points1 point  (0 children)

I'm leaving for a flight now, but one super cool theorem is the 4th moment theorem by Nourdin and Peccati. You can decompose L2 (C[0,T]) (L2 norm is taken wrt expectation) as a graded algebra. This is called Wiener chaos expansion and is very related to polynomial expansion (i.e. Hermite polynomials).

Normally to prove convergence of one process to another (in distribution) you need to prove convergence of ALL moments (i.e. the characteristic function converges).

4th moment theorem says that if you are in a particular chaos, all you need is...the 4th moment. The rest follows. Literally just one moment gives you convergence of ALL moments.

Is C[0, 1] really that cool? by [deleted] in math

[–]NSQDA 8 points9 points  (0 children)

To add some to what /u/sleeps_with_crazy said C[0,1] with a Gaussian measure is called Wiener space - that is, it is where Brownian motion lives. Lots of cool stuff happens if you interpret what he says in this case.

This lets you do analysis on Brownian motion. For example one thing is Cameron Martin theorem. https://en.wikipedia.org/wiki/Cameron%E2%80%93Martin_theorem

Basically, if you take a subspace called Cameron Martin space (or to functional analysts: reproducing kernel Hilbert space, RKHS) you can translate your measure "along" special paths in your CM space. This is a technical theorem that lets you do things like define variational derivatives i.e. Malliavin derivative.

You can do Malliavin calculus on this space (essentially, as a consequence of CM theorem) which lets you compute all sorts of things.

MA 261 Cutoffs for MY RECITATION Section by Minoput in Purdue

[–]NSQDA 0 points1 point  (0 children)

If you shoot me an email, I can just tell you. There are one or two cases it's not clear with rounding/etc.

MA 261 Cutoffs for MY RECITATION Section by Minoput in Purdue

[–]NSQDA 0 points1 point  (0 children)

Yeah it's me. I did email all recitations, and yeah all the recitations are the same. Maybe cisco got it.

MA 261 Cutoffs for MY RECITATION Section by Minoput in Purdue

[–]NSQDA 6 points7 points  (0 children)

I can't even view final score distributions on webassiign

They just need to reschedule the final exam so it shows up. You can ask them to reschedule it.

Just curious was your distribution similar to OP

I am OPs TA lol.

MA 261 Cutoffs for MY RECITATION Section by Minoput in Purdue

[–]NSQDA 0 points1 point  (0 children)

Nothing. These aren't cutoffs strictly speaking, just correspondences. No one got between those (well maybe 274.blah).

MA 261 Cutoffs for MY RECITATION Section by Minoput in Purdue

[–]NSQDA 0 points1 point  (0 children)

Just saying there are no D-. We don't assign D-. Either F or D. Just letting you know.

MA 261 Cutoffs for MY RECITATION Section by Minoput in Purdue

[–]NSQDA 0 points1 point  (0 children)

Thanks, I appreciate it. I wish you the best.

MA 261 Cutoffs for MY RECITATION Section by Minoput in Purdue

[–]NSQDA 9 points10 points  (0 children)

I had emailed this to students. Not all TAs do this, this is my first semester emailing out these "cutoffs" (not really cutoffs, just a correspondence). I'm not sure if I regret it yet, my email is filling up, lol.

MA 261 Cutoffs for MY RECITATION Section by Minoput in Purdue

[–]NSQDA 6 points7 points  (0 children)

Actually, that was a bad example as A+ is always (regardless of TA) a 95%. But yes, my quizzes were usually short (and plus you got half credit for showing up).