to some, time is not money; paper is.

student effort has many means of measurement:

• i've seen many students spend hours and hours at the math help desk, working out all the homework problems as tutors start and end their shifts.
  
  some of my students look sleep-deprived. the programmers in the group look "screen shocked" -- that is, the dull, sleepy look that comes from staring at a screen for too long.
  
  
• on the other hand, when looking at their write-ups, they are miserly with paper. they seem to make a "budget" in advance, say 1/3 or 1/4 of a page, per problem.
  
  if the work for the problem exceeds this quota, they may very well choose not to do the rest!
  

my only conclusion is that, for most people, time is not easily or actively measured in cost, so it is easily wasted. on the other hand, a new notebook has a visible price tag. let's give them the benefit of the doubt: maybe they are environmentalists and want to save trees! (:

after the last lecture, still teaching to do, still learning to do.

despite the end of lectures, i still find myself doing teaching errands.

the review sheet that i promised my students is late;
i'll finish it tomorrow.

admittedly, they already have practice tests [1] from which to study, as well as the previous review sheets for the midterms.

still, a promise is a promise. it will all be done tomorrow anyway, with time to spare for research.

---

in other news, today i learned about sharp maχimal functiοns. roughly speaking, one applies the maxιmal operator not to a function, but a kind of "dιscretized gradiεnt" of the function.

as for why, there is a characterization of Sobοlev spaces (on euclιdean spaces) in terms of them, due to Calderón.

sobοlev spaces still amaze me, despite first learning about them years ago. if you're an analyst, they are simply what you want them to be, when you need them. (-:

on a slightly related note, i should have kept being lazy (see earlier post). evidently, someone had proven the result i was thinking about, some years ago.

---

[1] this wasn't my idea. another instructor, who is in charge of writing the final, has been giving out these practice tests to her students. it's only fair that my students are equally prepared.

work and play .. and food?!?

most of you have probably already seen geοrge w. hart's doubly-linked bagel. if you haven't, a picture is below.

a "Mathematιcally Cοrrect Breakfast" by g.w. hart.

apparently there remains a(n open?) problem: Modify the cut so the cutting surface is a one-twist Mobius strip. (You can still get cream cheese into the cut, but it doesn't separate into two parts.)

i applaud that man. in the mornings, it's hard enough to slice a bagel lengthwise !.. before coffee, that is.

one more day ..

last day of classes:
two lectures left, and then some. [0]

---

11am is an awkward time in the morning to teach. it immediately precedes lunch, which has been one of its few good points. on the other hand, it shortchanges the morning, makes it an ineffectual time for work. [1]

on good weeks i've diligently woken up every morning at 7:30am. having written my lectures during the preceding afternoon, the span of 8-10am is enough to think a little and work on research.

sure, it doesn't make for very good lectures afterwards. then again, i was hired as a research pοstdoc, not for my ability to teach.

the problem, however, is that not every week is a "good" week.

i'm looking forward to next week, just as i enjoyed thanksgiving holiday.

when i wake up on monday, i won't have to consider compromises. i won't have to debate whether there is enough time, before class, to work on the next stage or step in my research.

maybe i will productive, maybe not .. but i want to have the chance to try, without having to deal with perceived sacrifices ..

---

[0] if i've learned any lessons as a teaching, then they consist of miscellany about human nature. for example,

1. humans regret loss more than than they appreciate gain. i told my students that i will not hold any appointments next week. to me, 5 scheduled office hours, spread over three days, are enough. (my plan was not to have disparate meetings interrupt good days of research, next week.)
   
   so next week will be fine. on the other hand, students have been asking for appointments like crazy for this week. today i have two .. [sighs]
   
   
2. procrastination: in general, humans will never do anything unless absolutely necessary. this semester my classes have had a LΟN-CAΡA lab component to their coursework. usually one assignment is due, every week, and my TAs are in charge of setting the deadlines.
   
   two weeks ago, my TAs have assigned three labs, and all of them are due next week. i can see their reasoning: the students have had difficulty getting each lab done on time, so a long stretch of time would be better, right?
   
   summarily, i've been getting consistent complaints from students about "how they are supposed to finish 3 labs in one week .." [sighs]

[1] for some reason, i never refer to teaching as "work." instead, "work" is always research to me. that probably suggests something about my perspective on academia, but those are thoughts for another day.

missed opportunities (also: post #700 ..!)

on a random whim i was clicking through mathematics blogs today. i found out that i completely missed this year's MaBloWriMo phenomenon.

for those not in the know, it's a play on NaNoWriMo (National Novel Writing Month).

apparently there was quite a lot of contributions and much of it was differential geometry .. which would have been helpful when i was learning about the metrιc aspects of Riccι curvaturε ..

[sighs]

maybe next year?

in other news: this will be my 700th math blog post, to date.

i don't think of it as an achievement. rather, it's a testament to how hard it is for me to shut up. \-:

in which laziness has no reward.

for one of my projects at hand, i think i have attempted all the obvious things that i can think of attempting. i have recorded the statements of theorems, examples, and well-known facts, in order to determine whether i can make a logical yet interesting observation ..

.. or, as the advisor would have said,
whether a particular claim "follows from pure thought."

---

i'm convinced now that it's not easy. so i suppose it's time to sit down and read the papers in detail.

perhaps i should have done this from the very beginning; oh well. i guess i'm getting lazier with age.

strangers in lectures.

my morning lecture today: i'm about to finish an example and i turn to the class to describe the strategy involved. so i turn first to the classroom door; as it happens, a pretty girl is standing in the doorway, smiling sweetly at me.

wow. she arrived really late to class.
it's at least half over now.

then she waves at me.

this is weird, i think.
she doesn't seem to know me: probably not a student, then..

i wave back and say, "hi. who are you?"

(i imagine that, at this point,
the class has stopped taking notes.)

she then brandishes a thick folder. "i'm from ΟMET [1]. you requested a survey to evaluate your teaching?"

crap: it's today? it's now?!?
huh. that explains it;
i never pick up women in classrooms, anyway ..

"right," i reply, "just give me one more minute to finish this example."

as i'm walking back to the chalkboard, a random thought occurs to me. i pick up the chalk and then say to the evaluator: "you know, it's almost lunchtime. it would have been really cool if you were a pizza delivery guy instead."

the class erupts in laughter.

i never did get to see the look on the girl's face, because i'm sketching out the example at top speed and talking out the details as i pack my notes and belongings into my backpack.

i wonder if that will improve my teaching evaluations at all. (-:

---

on a somewhat related note, it seems i'm not an easy instructor at all. on the other hand, apparently i also rank a chili pepper. q-:


[1] i.e. οffice of measurεment and evaluatiοn of teaching.

in the mornings, it's important to have a routine.

on tuesday, thursday, and friday morning [1], i woke up and had a very specific agenda:

take the bus to campus,
meet a visiting colleague,
discuss math over a cup of coffee.

i try not to live under too many illusions, but so far this has gone well enough. whether it is truly a productive use of time, it has at least felt productive. in contrast, on most days of the week i feel as if i've accomplished absolutely nothing.

maybe we have discussed rather trivial things.
maybe this will lead to a new project.

who knows?
we'll work and we'll see;
that's all we can do, anyway.

that colleague leaves this weekend. i'll probably see him again in may.

---

so this morning i woke up without an agenda or much motivation. i couldn't decide what to work on.

in the end, i grew tired of standing indecisively in my living room. i packed a heavy backpack (as to be ready for any sort of math), went out, and bought a cup of coffee.

it seemed to help. i soon went to work on a long-neglected research problem, one i had set aside some months ago. it wasn't wholly unproductive.

[1] i teach on wednesday mornings. by thursday, we reached an interesting point in the discussion, so on friday morning, i decided to sacrifice an hour or two of sleep in favor of strong coffee and maths.

some days are ambitious, some are decidedly slow.

it wasn't until my second alarm that i woke up today. even now, i don't feel quite awake yet.

remind me not to have 10am meetings anymore; it's not that i can't wake up early .. it's troublesome, of course, but possible. i'm getting better at this, with age.

being awake enough to work on research is one thing. being awake enough to discuss research with another person is quite another.)

i don't feel very ambitious today.

like most days, i doubt that i will solve any big problems or prove any big theorems. on the other hand, for today the likelihoods of those events are even smaller than usual.

---

so i suppose that today is a good day for reading [1] -- the kind of preparation for those ambitious days -- and for discussions, where i do most of the talking and about ideas that are already familiar to me.

i suppose, once again, that maths is like running. you can't spend every day running your fastest without eventually reaching grave injury. the rest days are as important as the fast ones.

[1] already i picked up books from the maths library; one for a reference for a meeting .. in a few minutes, another a colleague suggested, and another because i was surprised at its existence.

soon: no more pencils, no more books, no more students' dirty looks .. (-:

if i could wish for anything, at this time, it would be this: that i could stop teaching and holding office hours, stop having research meetings and discussing new thoughts.

next year, i'll work on new research: i promise!
(as for teaching, i have no say in the matter.)

right now i'd just like a few weeks off to write up my results, cut up into two papers. when writing, i'm easily distracted: it's a work habit of mine that sorely needs improvement. i seem able to start a paper only by shutting myself away from the world, thinking obsessively about how i want it to read, and typing away.

put one way, i would like time away from work,
if only to be able to get some work done.

---

the opportunity is some to come, however.

for students, finals week is a headache. for lazy students who haven't prepared much, this is a nervous week full of intense studying and little sleep. for diligent students, they already know the material fairly well; along with tests of knowledge and skill, the week itself is a nervous test of patience.

for faculty, finals weeks is great. if there are no more lectures and if it is not yet holiday, then now, at last, there is uninterrupted time for work!

i may hold a few office hours, but otherwise i can spend most of each day writing .. well, apart from grading day, but i have no say in that matter, either. it could also be good to have a change; if i spend ALL my time writing, i might go a little crazy.

so i'm looking forward to finals week. by then, i'll stop being a teacher and i can be a proper researcher again.