#800: the storm before the calm.

last week [1] was not unproductive, but i felt otherwise.

i was traveling the week before;
i'll be traveling for the next month.

at the time i thought it was pointless to formalise a schedule. my agenda was clear, but not much went according to plan. there wouldn't have been enough time for everything.

1. i revised a preprint which i thought i wouldn't have to revise again;
2. the last addition to another preprint is less clear than i thought. my coauthor/mentor was out of town, so it will have to wait until i see the other coauthors in finland.
3. it turns out that i'm giving 2 talks, not 1. also, finnish-styled seminars are 2 hours long, not 1. (the newly added talk is next week; the other one is 3 weeks hence.)

of my original plans, one goal was to read and learn 'section 1's from a few different sub-areas, as to prepare for the forthcoming research meetings in my travels.

so i did read a little, but only a little. i guess i'll have to rely on the kindness of colleagues again, and ask them to explain simple things to me.

anyway, off to the airport!

[1] actually, it was 6 days: close to the same.

avoiding the office, again.

now that i think about it, i quite like working in libraries. i've spent the last two afternoons working in the sci/math/engineering library, in the building next to my department.

unlike a coffeehouse, there's less chatter .. especially in the summer, when most of the students are away. only a few tables are occupied in the whole place.

quiet and spacious:
a winning combination!

then again, it's not unlike a coffeehouse, too; next to the library entrance is an einstein bros. bagels stand. although food isn't permitted, coffee is.

odd, though: for a library, i see few people with books.

everyone has their laptop open. i seem to be in the old-fashioned minority, working with a book open.

anyways, back to work ..

sometimes we run away from problems, other times we run towards them.

i spent most of yesterday (tuesday) trying to finish writing one paper. at some point, i couldn't write any longer, so i went out for a road run.

around mile 2 i started thinking about this one research problem that i had set aside, about a year ago.

it's one of those obsessions, the kind that saps away your weekends, if given half a chance.

[as posted in 2009]

(in fact, i had promised that i wouldn't publish anything in the field of geοmetric measure theory until i had solved this problem.)

when it came time to the end of my usual route, i slowed down.

the paper's already behind schedule;
i promised my co-authors already.
if i go home now, i'd have to start writing again.

so i ran another 2 miles, just so i could think about this problem a little longer.

in media res

the conference ended on sunday at noon.

maybe i was naive .. but before meeting a few remaining colleagues that evening, i thought i could accomplish something in the afternoon.

how wrong i was.

to be fair, this wasn't in the plan. while i was away, i expected to

• give a few talks,
• read a little for collaborations, when i had the time,
• ask people what they've been thinking about, and so doing, learn a little from them.

well, i did learn something, after all.

my joint results can be improved .. which means another (short) round of rewriting and revision.

[see last post for a few details.]

[sighs]
so much for planning ahead.

so i spent that afternoon, trying to remember what i had written before, what needed to be changed for the better .. \-:

---

as for monday, i wrote it off.

i was able to catch up on some arguments i had read and learned before. for the most part, though, i found it impossible to focus on anything other than my immediate travels,

• waiting for the train to arrive,
• looking for the right subway train and station,
• shuffling through lines at the airport,
• wondering how late the bus will be, after all ..

.. yes, a long day.

perhaps all of those discrete moments of thought paid off, though. this morning i woke up, suddenly realising what i had to do, why it would work .. for the most part, anyway.

bloggish hearsay.

i used to think that this blog was somewhat anonymous, but i'm now mistaken. i've arrived at the conference venue last night. today, two separate colleagues have mentioned this blog to me.

[winces]

two weeks ago, i googled myself. this blog also appears.

[sighs]

they say that people who fake their deaths are rarely undiscovered. it is too difficult not to be oneself, not to reveal something key as to dispel one's anonymity.

so i suppose it had to happen.

---

so yes, i've already ran into many colleagues at this conference, from years before. that's the key about conferences. you needn't know everyone -- only enough of them.

tomorrow is my talk. we'll see how many of my colleagues are forgiving .. \-:

working, in transit.

on the road, again.

my 3-day visit ended yesterday night, and tomorrow begins a conference at another university. as for today, i'm cooling my heels in downtown chicago.

it's strange, looking for a workplace in unfamiliar territory. this isn't my town, you see.

i recall a few colleagues here and there but, having planned briefly and badly, it would be imposing to call them up now.

i don't feel like sneaking into university buildings, either; on the off chance, i hate being asked to leave, for no good reason.

that leaves one option left: the city library.

---

that said, the chicago public library is fascinating. the lobby looks like that of a museum, kin to the new york public library, grander than what has been done in the carnegie libraries of pittsburgh.

on floor 4 (the business, science, and technology section) they have a nontrivial collection of mathematics books in their QA section ..

.. granted, i couldn't find anything by maz'γa or by salοff-cοste, but they do provide the fundamentals, such as various books in analysιs, (abstract) algebra, geοmetry, etc.

this place looks like the stacks of a university library .. but for the public. it impresses me. if i were a chicagoan, i'd be proud.

---

as for the workload today, mostly i'm reflecting on some suggestions colleagues gave me, over the last few days. i think i can improve one of my joint results, which subsequently changes the nature of one particular follow-up project. at first i was worried ..

.. you see, i thought we had found a little pathology, in passing from euclidean to metric spaces, but similarly good behavior persists.

that's good, of course;
then again, i was hoping to show a negative result.

call me a naysayer, but one important point in the analysιs on metrιc spaces is to determine when euclidean phenomena fails in more general settings.

there's still work to do, but now it's more subtle. admittedly, i can't quite tell how it unfold, what factors are really at work.

then again, if i did know, then it wouldn't be research, right? (-:

customer satisfaction.

i received my teaching evaluations back, today.
overall, they aren't bad. among other things ..

• apparently i go too fast and don't do enough examples .. which isn't surprising. i've never had a class where students did not complain about the speed.
  
  on the plus side, apparently i'm mildly entertaining and not completely incomprehensible.


• as for a new complaint in calculus: apparently i speak more softly than i thought. (i blame the classroom.) at least the students were trying to listen, though ..


• in my analysis class, one student thought i "made good use of real world examples."
  
  i didn't realise that analysis was that readily applicable to the real world, but i suppose this is a good thing. (-:

while traveling; writing.

at some point, i will become responsible. i'll finish writing talks before embarking on the visit to where i'll give the talk.

until then,

• while traveling yesterday,
  my connection was 3 hours late,
  
  so i sighed, bought a cup of coffee,
  and wrote a few more slides of my talk.


• my spring term ended two weeks ago;
  as for my hosts, they have until mid-june.
  
  while they were teaching or holding office hours,
  i was adding a few more slides to the talk.

odd:
life has a way of working out, sometimes.

in other news, this talk is taking forever to write! [1] (-:

---

it feels like a strange time in my life. i feel like i've been doing a lot of writing, but not much thinking.

[1] it's my first colloquium, you see. call me nervous, but i've never really given a non-specialist talk before.

wanderlust 2010.

i'm traveling again. the summer will be piecemeal:

a few days in cincinnati,
a few days in champaign-urbana,
1 week at home,
1 week in jyväskylä,
2 weeks in helsinki,
1 week, visiting family,
5 weeks at home,
2 weeks in india,

and then the semester begins.

i keep forgetting that the same principle for weekly teaching schedules also applies to scheduling trips: don't underestimate how important large blocks of time are.

i know my trips will be productive [1].

there are more visits than conferences, which is nicer:
there's no fixed pace,
you already know with whom to talk and about what maths,
you have more resources at the ready: possibly an office, a printer, a library ..?

on the other hand, projects take time. papers take weeks, maybe months to write. NSF grant applications take a month, maybe two .. and then there are job applications.

[cringes]

getting older, i worry all the time. at least there's a 5-week block in july ..

[1] .. except visiting my parents, but that's to be expected.

mistaken identity, of sorts.

today i received an email from the university library services. my book is ready for pickup.

the thing is, i'm sure i requested a different book. what i wanted was sοbolev spaces by maz'γa. instead i'm supposed to pick up

Analysε harmoniquε non-commutativε sur cεrtains εspaces homogènεs; étudε de cεrtaines intégrales singulières par Ronald R. Cοifman et Guido Wεiss.

oh well. i guess i could always practice my french .. by reading about BM0? (-:

reflections after an analysιs class, part 3 of 3.

thinking back, i wonder if i taught this analysιs class at "too high" a level.

it's not an honors-level class [1].

moreover, it's the second "theοretical" course in the mathematιcs major, and the first in which students prove things that are not exercises in basic logic.

that said, most lectures went in the theorem→proof format, with some scattered examples and applications. among my regrets,

1. i should have asked more basic things, more often, like: "is this a cluster point?" or "can we use the bοundedness theorem in this setting?" to us, these are quick and obvious. on the other hand, students don't always check the hypotheses .. \-:


2. i should have added more examples. i don't think my students understood the definitions as well as i would have liked.

the one thing that i am pleased about was this: whenever possible, i explained the idea behind the proof intuitively, and then converting the "intuition" into a rigorous, logical argument.

this, i suppose, stemmed from how i prepared for lectures.

teaching calculus is one thing: you just compute from formulas, step by step, and warn students to be careful at certain parts.

for matters more theoretical, the only way i could remember what i'd discuss in class is by answering these questions:

what makes this important?
why is it true?

sure, these explications are not some topics (easily) testable on an exam.

then again, if you work with the hypothesis that the student does want to learn, to make sense of this thing called mathematιcs, then maybe it's worth the trouble to explain how we, as mathematicιans, actually approach the subject.

---

analysιs is not an easy subject .. at least the first time around. i don't think i made it particularly easy on the students.

then again, i don't think a math major should think that mathematics is easy.

to be honest, i think it instructive to encounter a theorem whose proof takes at least half a lecture (but no more than 1 1/2 lectures) and use it often throughout the rest of the course.

if anything, it teaches students that some theorems are worth the trouble, despite being difficult to prove.

despite being a postdoc (and leaving in another calendar year), part of me wanted to make sure these math majors did learn something, that they didn't see proofs merely as propaganda to be memorized or incantations to be recited, that the axiomatic method is a way of thinking. [2]

---

in the end, i don't have any fast, succinct morals about teaching a theoretιcal course.

i'm sure that i bored my students many times, and that i made them paranoid often enough to be careful. i hope they learned something ..

.. preferably about analysιs. (-:


[1] at this university, there are a handful of honors-level classes, which are intended to be accelerated in pace and/or more detailed in scope. in my department, there is an honors analysιs class combines "introduction to theοretical mathematιcs with a first course in analysιs.

it's quite a load on a student. then again, i took a similar class; afterwards, i realised that i wanted to be a mathematician.

[2] i guess i'm talking about what is sometimes called "mathematιcal maturity," whatever that means.

reflections after an analysιs class, part 2 of N (so N ≥ 2).

out of 14 students, two failed the class.

for one of them, i couldn't pick him out of a lineup if i tried. (in contrast, i can recognise the other 13 on sight.)

this one was a ghost.

after the first week, i remember him appearing on the day of the midterm, then vanishing for the rest of the term without a trace. [0]

the other student had a similar story, almost a sequel:

he was doing fine, and his intuition wasn't bad. after the midterm, though, he disappeared. i saw him at the final exam, graded his work ..

.. & to quote paulι, his answers weren't even wrong. being a non-cumulative final, this was particularly damaging to him.

to be fair, when i was an undergrad, there were a few courses whose lectures i often skipped.

in fact, there was one that i showed up for fewer than 1/3 of the classes. [1] then again, i spent a lot of time in cafes, reading the textbook .. and disliking it, leafing through other texts in the mathematics library until i found one that made any sense at all.

so i suspect that my own students didn't quite do the same. maybe they're not coffee drinkers? \-:

---

[0] to be honest, i wonder if he thought he withdrew from the course, but forgot to settle the paperwork.

[1] i'm also mis-representing the facts, here. that semester i was enrolled for two courses that met at exactly the same days and times. knowing one prof better than the other, i asked him if i could read the book, attend his office hours regularly, and show up for exams only.

he actually said yes.

so that's how i learned basic measure theοry. to this day, i understand that stuff far better than cοmplex analysιs, despite having dutifully attended all of the lectures for the latter class.

(writing interlude)

this business of degiοrgi classes is rather technical.

today, in order to check details,
i had to turn the paper sideways ..

(that is, long side across)

.. in order to fit all the terms of a particular inequality.

[sighs]

i already have the feeling that there will be some errors that i will never catch. the best i can do, i suppose, is minimize them before submitting the thing. l-:

oh well.

at least i'm no longer teaching, and can spend all day doing this .. which is, in fact, a good thing. (-:

reflections after an analysis class, part 1 of .. um .. N? (N ≥ 1)

grading finals today, i became introspective. between papers, i asked myself:

i had always wondered what teaching an analysιs class would be like. now the semester's over.

well? how did it go?
have i learned anything? [1]

i started thinking of analogies.

1. it's not unlike teaching someone tennis. often the student swings awkwardly, sometimes effectively. you can't help but wince.
   
   sometimes the ball is in play, the shot is bad, and the student knows right away .. but not every student chooses to learn why .. and so we keep on wincing.


2. it's not unlike teaching someone how to code (computer programming). the basics are, yes, basic.
   
   some students quickly become bored, and only bother you when they can't get something to compile. others are frantic, even ask you for your own code ..
   
   [sighs]
   
   .. and sometimes when you do, they still can't figure out how it works.


3. it's not unlike teaching someone a language. unless the student is fluent or has learned a similar tongue, (s)he may have no idea whether something sounds right.
   
   some students really want to speak well, and they'll ask you vocabulary unrelated to textbook stuff. they will meet you outside of class on occasion, and it won't even be about homework.
   
   during one of these chats, a student will say something which makes perfect sense, only you never thought about it that way, before ..
   
   .. and it will remind you of how cool you thought this stuff was, when you first learned it. (-:

[1] that is, other than the basic analysis that i had forgotten, when i first took such a course. (-:

endings & beginnings.

the preprint is out of my hands now;
i've passed it to my co-authors, who are trustworthy people.

this means, of course,
that i should start writing the next preprint.

[sighs]

i wish someone had told me, back in graduate school, that the writing never stops, and that the thesis is only the beginning.

heck, i wish i proved more theorems,
wrote more papers in graduate school.

it's not easy to learn and work on new things when you're (some kind of) faculty with the standard teaching load. it amazes me how others can do it so well.