there are some really random convexity results in functional analysis. here's one. if X is a banach space, and not reflexive, then X'''' is not strictly convex. ' denoting continuous dual.
Right. For every subspace (this is finite-dimensional in our book, but I expect it holds in infinite dimensions as well) $V^\perp = \big((V^\perp){}^\perp\big){}^\perp$.
X'' is the closure of X in the weak or strong operator topology, with X a subalgebra of operators on hilbert space and ' denoting commutant. lots of closure-like operators around.
hah, i had some fun with the local network. the client sent us files that expanded into pathnames that were too long for windows (which tops out before 300 characters). windows let our IT people create those files/paths but once they're created you can't open them.
yeah, they fixed the stuff i was going after. they are hesitant to change anything from the form/format the client gave us for legal reasons so i had to really spell out what it was OK for them to do and not do in the email.
even metadata can sometimes be an issue, such as filenames. i made clear, please create a new local copy, don't fiddle with the original. that smoothed things over.
hah, that would have been me. my only activity was co-running a club that i created, and in a field (chemistry) that i was not interested in going into.
i think that came up in my interviews.
thankfully there are schools that don't do interviews.
one time i interviewed a guy who had a really stellar resume, but he couldn't say even the first thing about any of his experiences. and he should have been able to. e.g. interning for a senator. meeting two presidents. it gave the impression that maybe it was all a ruse and he had made it all up.
Yeah, most of the time my interviewees are smart enough to have one or two questions prepared for me. Not too hard to think of a few things to ask an alumnus. This kid didn't have anything.
berkeley had funding for graders some, but not all of the time. it was always an open question at the beginning of the year, whether your stuff would be graded. and by whom.
one summer i was taken off of grading for an analysis class because the instructor, all of two years my senior, didn't want an undergrad grading for his class. i hope he did it himself.
it's a great custom. in produce that is paid by quantity instead of weight they let you type in how much you should pay.
at iowa when i didn't have a grader i'd tell people to just handwrite anything they wanted me to check on the tops of their assignments. of course, only the A students actually did that, and of course they were right every time.
there are good things to be said for students evaluating work. it helps you understand what your own work looks like.
