idle bits (teaching).

odd. most of my students dislike spherical coordinates. it surprised me that everyone did one particular homework problem using them, though it was avoidable.

Let $\mathcal{S}$ be the part of the sphere $x^2+y^2+z^2=4$, $y \geq 0$, oriented in the direction of the positive $y$-axis. Compute $\iint_\mathcal{S} \vec{F} \cdot d\vec{S}$, where $\vec{F}$ is ..

[thinks]
[sighs]
[gives up]

.. some vector field that has nice derivatives. (i forget.)

when i wrote the solutions, i used a parametrization with coordinates $x$, $z$. out of 100+ homeworks, only 1-2 students did the problem the same way that i did it.

---

on a related note, i have a soft heart. since it's finals week, i'm letting my undergrad graders off and grading the last homework and quiz myself.

no good deed goes unpunished. i thought that this week would be mathematically luxurious: spend all day with research and other matters. instead, even though classes are over, i am still working on teaching things ..!

my weekend, at a glance.

friday: i've an idea for a lemma.

saturday: the idea fails.

sunday: i realise that i'm proving too much; the lemma is "if and only if" and i just need the "only if" part (which is separate from friday's idea). proof done, cut and dried!

well, it's over, at least.

my last lecture for 2010 is done.
if i were less tired, then i might be happy.

(more on this, later)
anyways, back to work ..

---

a friend asked me last night how this semester went, particularly in terms of teaching. i didn't blink at all, and said:

"it was like an open wound for 2 months."

this, of course, scandalised him, so i had to explain:

the best mathematicians i know can switch modes very quickly:

two hours ago, they could be talking with their doctoral students, working out details. one hour ago, they would be teaching and talking about standard things. upon the hour, they would start brainstorming with me about ideas for a paper.

i don't have that ability, not yet anyway. between job applications, an NSF grant application, two conferences, and finding time for another paper, teaching often felt like an afterthought.

so i was surprised when one of my students chose to tell me how much he enjoyed my class. my own opinion was that it went sub-optimally, desolately.

at any rate, i feel wounds of the mental sort. i'm glad that the job applications are done, up to january.

it's been a while since i've "felt like a mathematician," struggling with new problems and looking for appropriate perspectives in which to think about certain problems. this week will be a good research week. maybe i'll accomplish something after all.

review sessions: an ambivalence.

philosophically, i am opposed to review classes for caΙculus classes. it's similar in view to why some believe that bicycle helmets do not save many cyclists' lives, but not as extreme.

perhaps i take an overly personal, extreme view on the subject, but:

if you have been listening to me all semester, then you know what's relevant and what's not.

i understand if, at a random moment, that you mightn't have a good picture of the course as a whole. then again, that's the point of studying outside of class. there is the old standby rule that for every 1 hour of lecture, one should spend 1 hour studying the material outside of class.

so if you haven't been listening, then why should i bother repeating myself? what evidence do i have that you will listen to me, this second time around?!?

realistically, these days one covers a lot of material in a calcuΙus course. it's hard to keep all the information in one's head, all at once, so it is good to remind the student of what has been discussed.

then again, isn't studying the responsibility of the student? looking over notes, working out more practice problems?

maybe i'm just become old-fashioned. it's harder to be a teacher, these days: one has to motivate students, all the time, while still show them nontrivial things. myself, i am not a natural teacher: i'm not patient enough.

some days i wonder if i should quit the business of mathematics!

on maths .. and grammar.

is "aforementioned" an appropriate word for maths papers?

this is an artificial sort of work, like "actuality" that is best avoided, i think, but modifiers like "as indicated above" or "previously discussed" become repetitive after a while.

on exposition.

since october i've been repeating this mantra: in december, i'll have my life back. by then i'll be a mathematician again.

(this was in regards to job applications, research travels, and other promises i meant to keep.)

to be fair, i was half-right. there is still one survey article to finish ..

.. but being more to do with research than, say, a statement of teachιng philosophy, i don't mind it at all. in fact, i'm enjoying it.

for one thing, writing makes me feel like i know something well.

it's been more than a year and 1/2 since i first worked out these details regarding de giοrgi's approach to reguΙarity theory (for certain ellιptic PDE) and only now does it feel .. natural.

that's the feeling, anyway: let's see if i can convince others of the same, through this article ..

the more i think about it, the more i like this idea of writing notes and expositions. in this last conference at οberwolfach, i was struck by the clarity of the research notes that colleagues of mine had written.

this is in regards to a generalised radεmacher theorem, in the setting of certain metrιc measure spaces.

the first proof was quite hard. there's a history of several versions of notes by several authors, in efforts to understand this result.

i liken it, actually, to how anyone in the open-source software community can contribute code for a particular program task. on the other hand, the best code gets passed around and used, for the greater good.

so i'm tempted to write my own notes on other subjects. specifically, there are a lot of folklore theorems out there, in this intersection between analysιs on metric spaces and geοmetric measure theory.

i could be deluding myself into thinking that my perspective is overly valuable .. but maybe by expositing, i can help as others have helped me.

come on .. just use mathjοbs ..

argh. why can't schools just go on mathjοbs? why?!? [1]

the most annoying part is that these nonconformist schools all seem to be using the same template! it's like wearing a flannel shirt to a bar, these days.

(e.g. enter username, password, re-enter password,
choose a secret question, insert answer ..!)

at this point i am paying very close attention to asterisks.

if i don't see a *,
then it's not necessary information,

ergo: i'm not filling it in.

on a related note: i apologize to all my letter writers who have to go through the same glut of websites, in order to submit those letters.

[1] to be fair, i suspect we mathematicians have it easy: 90% of jobs can be found on mathjοbs, and the format is pretty uniform. the experience i've heard from the humanities people is quite painful.

fatalism is freedom.

there is a certain illusion that conferences cast,
a suspension of reality.

for my own part, i spent a week hearing lectures, discussing a little mathematics with colleagues, and having a bit of fun.

reality set in, once i boarded the plane back to the states:

i have to write a caΙculus lecture for tomorrow,
wednesday is the next big deadline for job applications,

what other promises do i have to keep?

---

it's been an unproductive few months, due to bad planning: between NSF grants, job applications, and traveling, i've had little time to sit down and think through ideas, cut a path through a decent theorem.

i've been ill at ease, most of the time, mostly because of jobs. everyone i talk to: they feel the same way. it's crippling! sometimes i feel like half my mindspace is lost, because of these stewing, festering thoughts.

maybe that will change in december. by then these matters will be out of my hands.

maybe i'll get a job with plenty of time for research, maybe i'll find a job where i'll never do research again. maybe i'll disappear for a while.

regardless of what happens, why not make the most of these final months of my (first) postdoc?

i never realised how much time i had, as a student, to learn new things and to work on projects that didn't seem a good fit for what i knew (or not knew).

all things being equal, i'll probably feel that way about my time as a postdoc. i might as well try and stop history from repeating itself.

besides, what do i have to lose? (-:

ein wenig Beratung

word of advice: if you go away to a remote place, with other researchers, for a mathematics conference ...

1. never ever try to drink suisse or germans under the table; they ever win.
2. germans love foosball, we're playing around the world.
3. before that, someone pulled out their laptop and we sang "country roads" by john denver.

i'm just sayin' .. just be prepared.

---

epilogue. i wouldn't call last night a bad idea, but .. well, such nights come with a price. maybe it's for the best that this conference was a week long, and no longer.

on an unrelated note: sometimes the black forest is actually white in color:

in which i leave my fate to chance (epilogue added).

this has been a strange conference. the talks have mostly been expositions, not the original research of the speakers.

i don't mind it; in fact i quite like it. some topics are old and i haven't thought of them in a while, others are quite new and i am learning new things. it reminds me (and rightly so, as the organizers tell me) of "thursday seminars" of yore. rarely do i hear old friends and colleagues speak for longer than the restriction of 20 minutes at a conference ..

.. in science, i suppose they would call it a journal club.

i had known some weeks in advance that my talk would be part 3 of a 3-part series, but all week i had been fretting and editing, in reaction to what other speakers have discussed. tonight, at 9am i stopped, went downstairs, and started singing karaoke to a live guitar that a friend played until 1am. (there was also a bit of beer.)

it was then that i realised: f-ck. i have 10 pages or so of notes. by standard scales, that 100 minutes of talking: impossible! it also occurred to me that i had many topics, and it shouldn't my decision to choose what is relevant for the audience: rather, the audience should choose.

so i left a 1 euro coin with a colleague to-night; tomorrow i poll the audience: what do you want to hear? if there is no vote, then i flip the coin and decide what to talk about, for 50 minutes!

---

epilogue. in the end, i ran out of time. in 65 minutes i covered 5 pages; i had forgotten that this crowd loves to ask questions (and besides, my presentation style was sloppy).

i later apologized to some of the participants for going so slowly. they simply blinked, and said that i was going quite fast.

these are my colleagues; imagine, then, how my students are faring ..!