if there was one graduate student office at university of michigan that i envied, it was the corner office facing church st, on the first floor. that office had it all:
* few officemates (4 people in total);
* a window [1];
* a full-sized chalkboard;
* two large bookcases;
* a couch.
there may even have been a mini fridge; i can't remember.
at any rate, today i wished my office had a couch. after my afternoon lecture today, i had no energy left, and i felt asleep while in the middle of an email.
the wise thing would have been to go home and take a proper nap. then again, there was the weekly colloquium and there would be one more meeting.
thinking it through, i looked at my desk ..
which happened to be positioned right next to my officemate's desk ..
who is never in the office ..
and after all, isn't the top a couch really just a deformation of a horizontal plane ..?
so i learned one lesson today: winter coats may make very good pillows, but there is a very good reason why people shouldn't sleep on top of desks.
it's not because of setting down the desk/table or staying on top of it. resting on a flat surface is not too much like sleeping on the ground; eventually one gets used to it.
but like sleeping on the ground, it's getting up that is painful. the back and the knees remember that they should be slightly bent and begin their complaints, in the form of aches.
anyways, i think i might be unwell. maybe it's time for a nap.
[1] to my knowledge, only two grad offices had windows. the other one had 10-12 desks and half a wall of windows .. which faced a brick wall.
Friday, January 30, 2009
Tuesday, January 27, 2009
when worlds (or classes) collide.
during my monday lecture in lιnear algebra, i discussed when a set of vectors are linear1y (in)depεndent. in tomorrow's lecture, i will teach them how to multiply matri¢es.
on the other hand: for tomorrow's lecture in differentιal equatiοns, i will discuss when two solutions of a lιnear homοgeneous ODE are lιnearly (in)dependεnt.
i'm usually alert enough not to give the wrong lecture to the wrong class. however, it will be mildly difficult not to bring up lιnear algebra in the diff.eq class and derivatives in the lιnear algebra class.
for instance, i can imagine myself saying something glib like this:
in other news, i wish i had something exciting to blog about and which relates to research.
unfortunately, i don't. i can tell you that yesterday, i learned that one of my arguments is wrong. indeed, everyone is wrong at some point ..
anyways, life goes on. as the saying goes:
in light of rigοr, it's depressing how little we mathematιcians can prove.
on the other hand: for tomorrow's lecture in differentιal equatiοns, i will discuss when two solutions of a lιnear homοgeneous ODE are lιnearly (in)dependεnt.
i'm usually alert enough not to give the wrong lecture to the wrong class. however, it will be mildly difficult not to bring up lιnear algebra in the diff.eq class and derivatives in the lιnear algebra class.
for instance, i can imagine myself saying something glib like this:
"for 2nd οrder lιnear ODE, the basic idea is to find two solutiοns which build all the other soluti0ns for you, i.e. the general solutiοn.on the other hand, in the other class i'm also tempted to discuss differentiati0n as a lιnear οperator which can be represented as an infinite-dimensiοnal maτrix ..
to do this right, we need two so1utions which are 'different enough' from each other. for this we will use some termino1ogy that may be familiar from lιnear algebra, except we will use infinite-dimensional vectors instead.
anyway, we say that two so1utions are lιnearly independent when .."
.. well, assuming the only functi0ns that one cares about are real-analytιc. i imagine (unhappily) that all of my students believe the fallacy that not only 'all fun¢tions are differentiab1e,' but that 'every functiοn can be represented as a taylοr series.'
[sighs]
in other news, i wish i had something exciting to blog about and which relates to research.
unfortunately, i don't. i can tell you that yesterday, i learned that one of my arguments is wrong. indeed, everyone is wrong at some point ..
.. but it gets particularly annoying when i had thought of this, months ago it had "proved" a lemma and which subsequently led to corοllaries and and a few applications ..on the other hand, this morning i thought about how to patch the proof using a different argument and .. it's going to be messy (if possible at all).
.. argh.
anyways, life goes on. as the saying goes:
in light of rigοr, it's depressing how little we mathematιcians can prove.
Sunday, January 25, 2009
papers end, writing never does.
the preprint [1] is done;
i declare it to be done.
one problem solved, another problem open:
where the heck am i going to submit it?
this, i vow: apart from formatting it for submission to a journal, i will no longer edit it, for its quality will only deteriorate if i add further "ideas which sounded good at the time."
also: it's time to write another preprint, and i'll need to cite the first preprint. it's time that the first one become a published paper: something worthy of being cited.
after all, would you trust the main result in one preprint, which depends crucially on a result in another (unpublished) preprint?
admittedly, i would have my suspicions ..
[1] this is the one cut out from my thesis. if you're still waiting on the sch0enflies result(s), then sorry: you'll have to wait another month or two.
i declare it to be done.
one problem solved, another problem open:
where the heck am i going to submit it?
this, i vow: apart from formatting it for submission to a journal, i will no longer edit it, for its quality will only deteriorate if i add further "ideas which sounded good at the time."
also: it's time to write another preprint, and i'll need to cite the first preprint. it's time that the first one become a published paper: something worthy of being cited.
after all, would you trust the main result in one preprint, which depends crucially on a result in another (unpublished) preprint?
admittedly, i would have my suspicions ..
[1] this is the one cut out from my thesis. if you're still waiting on the sch0enflies result(s), then sorry: you'll have to wait another month or two.
Wednesday, January 21, 2009
quick (& silly) observation: on reading.
you know, sometimes it's fun to read mathematics in french. it really helps, however, to know what theorems to expect (i.e. cheating); as a result, the words usually mean what you think they mean.
uncertainty isn't a bad thing, though. a friend of mine once made this observation, and i think it is a good one:
there is a built-in mechanism for further care, when reading mathematical french. if you don't know what a word in the theorem means, then it immediately urges you to work out the proof carefully.
anyways, back to reading/proving.
uncertainty isn't a bad thing, though. a friend of mine once made this observation, and i think it is a good one:
there is a built-in mechanism for further care, when reading mathematical french. if you don't know what a word in the theorem means, then it immediately urges you to work out the proof carefully.
anyways, back to reading/proving.
Monday, January 19, 2009
disparate bits: another weekend's end.
perhaps the ana1ysis gods accept sacrifices.
yesterday was a completely unproductive headache of (non-)writing -- a "sacrifice" of a workday -- but today went rather well. i finished TeXing up a lemma and made other corrections:
so, 2 pages!
this coffeehouse must be a hangout for CMU mathematicians and their kin. at the table next to me, three guys are discussing fi1ters and p0sets and for¢ing.
best guess: logi¢ians.
the season of job offers and rumors seems to have begun again. so if you found this blog through a web search on "maτh j0b rum0rs" or a similar search ..
.. hello. in light of the state of the american economy, good luck with the job search!
yesterday was a completely unproductive headache of (non-)writing -- a "sacrifice" of a workday -- but today went rather well. i finished TeXing up a lemma and made other corrections:
so, 2 pages!
this coffeehouse must be a hangout for CMU mathematicians and their kin. at the table next to me, three guys are discussing fi1ters and p0sets and for¢ing.
best guess: logi¢ians.
the season of job offers and rumors seems to have begun again. so if you found this blog through a web search on "maτh j0b rum0rs" or a similar search ..
.. hello. in light of the state of the american economy, good luck with the job search!
Friday, January 16, 2009
in which i, an ana1yst, prove mildly useful.
there are a lot of a1gebraic ge0meters at michigan, including faculty, postdocs, and graduate students. it's not uncommon to see advanced undergrads reading shaferevi¢h's book in coffeehouses.
even within my old office, i would hear words like "s¢hemes" and "v@rieties" and "tropi¢al ge0metry" being tossed around quite often. [1] during my time there, it was easy to feel like a mathematical outsider, as i was doing nothing a1gebraic.
after a while i got used to not being asked what i do or what i thought about something. it was enough that i was an ana1yst.
my officemate at pittsbur9h is also a postdoc and he works with al9ebra and 1ogic, with some applications towards number the0ry. he also likes the symph0ny and so do i, but to a lesser degree. nonetheless, when he invites me to friday concerts, i often accept and meet him at the music hall, downtown.
last friday was another concert. i had taken off my coat and sat down, ready to complain about the winter cold for lack of anything better to say (it was 5*F outside). suddenly, though, my officemate asks me: "say, are you familiar with distributions?"
i blink. "s¢hwartz's theory of distributions?"
"exactly! you see, i'm working on this .."
so in the few minutes before the conductor walked on stage, during the intermission, and afterwards when waiting on the bus, we discussed, of all things ..
.. f0urier transf0rms.
[1] oddly enough, it's a very similar feeling to being an illiterate cantonese speaker in a room full of people speaking mandarin excitedly.
even within my old office, i would hear words like "s¢hemes" and "v@rieties" and "tropi¢al ge0metry" being tossed around quite often. [1] during my time there, it was easy to feel like a mathematical outsider, as i was doing nothing a1gebraic.
after a while i got used to not being asked what i do or what i thought about something. it was enough that i was an ana1yst.
my officemate at pittsbur9h is also a postdoc and he works with al9ebra and 1ogic, with some applications towards number the0ry. he also likes the symph0ny and so do i, but to a lesser degree. nonetheless, when he invites me to friday concerts, i often accept and meet him at the music hall, downtown.
last friday was another concert. i had taken off my coat and sat down, ready to complain about the winter cold for lack of anything better to say (it was 5*F outside). suddenly, though, my officemate asks me: "say, are you familiar with distributions?"
i blink. "s¢hwartz's theory of distributions?"
"exactly! you see, i'm working on this .."
so in the few minutes before the conductor walked on stage, during the intermission, and afterwards when waiting on the bus, we discussed, of all things ..
.. f0urier transf0rms.
[1] oddly enough, it's a very similar feeling to being an illiterate cantonese speaker in a room full of people speaking mandarin excitedly.
teaching today: a theoretical application.
in my differentιal [2*] equatiοns class today i discussed "mixing problems." to lighten up the mood, i went through the following example [1].
[1] in lecture, i might have spoken this formulation, but not written it all out. (-:
[2*] this post was reformated on 2 feb 2013, due to issues of typesetting. among other things, i used to use the symbol ${\$}$ to replace the letter s to make this blog less searchable, but this interferes with the mathjax/$\LaTeX$ rendering now present.
Lex Luthοr has trapped Suρerman and Baτman in a 100-gallon tank, which is half-full of water and which contains 20 grams of dissolved kryptοnite. (This, of course, renders Suρerman powerless.)it seemed to go over well, with the class. after all, who doesn't love a hero?
As part of his evil plan, Luthοr plans to drown the heroes by flowing pure water into the tank at a rate of 5 gallons per minute.
Resourceful as always, Baτman opens a drain (somehow overlooked by Luthοr) at the tank's bottom, causing liquid solution to escape at a rate of 3 gallons per minute.
Assume that Suρerman regains his powers at kryptοnite concentrations of 0.05 grams per gallon or lower (and can summarily break out of the tank with super-strength). Will the heroes escape in time?
[1] in lecture, i might have spoken this formulation, but not written it all out. (-:
[2*] this post was reformated on 2 feb 2013, due to issues of typesetting. among other things, i used to use the symbol ${\$}$ to replace the letter s to make this blog less searchable, but this interferes with the mathjax/$\LaTeX$ rendering now present.
Thursday, January 15, 2009
briefly, about scheduling.
at some i must remember:
1. avoid holding office hours on non-teaching days,
2. avoid holding office hours in the mornings.
maybe i am easily distracted by responsibilities, but it is really hard to keep my mind on research tasks when my alloted research time is bounded between two office hours (or lectures).
1. avoid holding office hours on non-teaching days,
2. avoid holding office hours in the mornings.
maybe i am easily distracted by responsibilities, but it is really hard to keep my mind on research tasks when my alloted research time is bounded between two office hours (or lectures).
Tuesday, January 13, 2009
what has and what will be.
last term i was teaching two sections of calcu1us iii. this term it's a linear algebra class and a differential equations class. admittedly, it's not bad.
most students are still taking these courses for requirements. however, maybe their spirits have been bowed or broken by previous maths courses; i don't know. at the very least, teaching has lately been straightforward. nobody asks any questions.
it could also be that i'm becoming a better teacher ..
but come on: how likely is that? (:
as for research, i suspect that this term will be a good deal of writing. (i don't mean a lot of papers, but a lot of time spent writing.) it will also be a good share of traveling, sowing seeds for more writing, i hope.
already i'm planning for syracuse, urbana, and tampa, and maybe ann arbor and/or cincinnati. (it depends if i get invited, of course. q-;)
but before all of that, next weekend last for four days: i can't wait. think of all the things i could write and prove, in that time!
most students are still taking these courses for requirements. however, maybe their spirits have been bowed or broken by previous maths courses; i don't know. at the very least, teaching has lately been straightforward. nobody asks any questions.
it could also be that i'm becoming a better teacher ..
but come on: how likely is that? (:
as for research, i suspect that this term will be a good deal of writing. (i don't mean a lot of papers, but a lot of time spent writing.) it will also be a good share of traveling, sowing seeds for more writing, i hope.
already i'm planning for syracuse, urbana, and tampa, and maybe ann arbor and/or cincinnati. (it depends if i get invited, of course. q-;)
but before all of that, next weekend last for four days: i can't wait. think of all the things i could write and prove, in that time!
apparently i have "the best job in the u.s." ...
... at least, according to the wall street journal:
Doing the Math to Find the Good Jobs
Mathematicians Land Top Spot
in New Ranking of Best and Worst Occupations in the U.S.
By Sarah E. Needleman
an excerpt:
Nineteen years ago, Jennifer Courter set out on a career path that has since provided her with a steady stream of lucrative, low-stress jobs. Now, her occupation -- mathematician -- has landed at the top spot on a new study ranking the best and worst jobs in the U.S.
among the reasons why:
The study also considers pay, which was determined by measuring each job's median income and growth potential. Mathematicians' annual income was pegged at $94,160, but Ms. Courter, 38, says her salary exceeds that amount.
so i think, again, they mean applied mathematicians, which is fine: they are mathematicians too. myself, i don't mind my job as a theorist / researcher / teacher ..
.. but i do wish i were better at my job. \-:
Doing the Math to Find the Good Jobs
Mathematicians Land Top Spot
in New Ranking of Best and Worst Occupations in the U.S.
By Sarah E. Needleman
an excerpt:
Nineteen years ago, Jennifer Courter set out on a career path that has since provided her with a steady stream of lucrative, low-stress jobs. Now, her occupation -- mathematician -- has landed at the top spot on a new study ranking the best and worst jobs in the U.S.
among the reasons why:
The study also considers pay, which was determined by measuring each job's median income and growth potential. Mathematicians' annual income was pegged at $94,160, but Ms. Courter, 38, says her salary exceeds that amount.
so i think, again, they mean applied mathematicians, which is fine: they are mathematicians too. myself, i don't mind my job as a theorist / researcher / teacher ..
.. but i do wish i were better at my job. \-:
Sunday, January 11, 2009
knowing the score AND the clock.
i think that, once again, that i spoke too soon. in regards to an earlier post while i was on holiday, the technical details don't work out after all. so .. no theorem: not yet.
maybe i was spending too much time in the sun, not thinking clearly enough.
more likely i think that i've been focusing too hard on this one conjecture. odd: a year ago, i wouldn't have cared about it or thought much about it. besides worrying about finishing a thesis, at the time i was obsessed about, er ..
.. a different conjecture. [2]
at any rate, maybe i should let it go. at this point i care too much about it, and that affects my objectivity and creativity. i should be working on other things and learning new things.
even if i did prove this thing, so what? in maths just as in sports, it's important to know both the score and the game clock.
i think i've reached a peak in my productivity, in this research area. i don't think i'll get any more good ideas (assuming the ideas that worked are really that good).
soon i'll have worked on all the things that i want to work on. soon i'll have to move on and find something else of interest, something i like enough so that i can work and prove new things and write papers ..
.. because at this point in my career, i really need some more papers.
[2] as for why i switched from one conjecture to another: i think i have a proof for the earlier conjecture.
however, the argument i have in mind is long, technical, and not as interesting as i would like it to be. at some point i'll sit down, write it well, and see if i find any subtle flaws.
maybe i was spending too much time in the sun, not thinking clearly enough.
more likely i think that i've been focusing too hard on this one conjecture. odd: a year ago, i wouldn't have cared about it or thought much about it. besides worrying about finishing a thesis, at the time i was obsessed about, er ..
.. a different conjecture. [2]
at any rate, maybe i should let it go. at this point i care too much about it, and that affects my objectivity and creativity. i should be working on other things and learning new things.
even if i did prove this thing, so what? in maths just as in sports, it's important to know both the score and the game clock.
i think i've reached a peak in my productivity, in this research area. i don't think i'll get any more good ideas (assuming the ideas that worked are really that good).
soon i'll have worked on all the things that i want to work on. soon i'll have to move on and find something else of interest, something i like enough so that i can work and prove new things and write papers ..
.. because at this point in my career, i really need some more papers.
[2] as for why i switched from one conjecture to another: i think i have a proof for the earlier conjecture.
however, the argument i have in mind is long, technical, and not as interesting as i would like it to be. at some point i'll sit down, write it well, and see if i find any subtle flaws.
Friday, January 09, 2009
the early bird gets the research done.
in regards to an earlier comment, lately i have been experiencing the joys of mathematics in the early morning.
take this morning: i woke up at 5:30am, decided that i wouldn't be able to fall asleep again, and then proceeded to coffee and breakfast. by 6am i was leafing through books in fun¢tiona1 ana1ysi$.
(as it happens, i defined an ad-hoc bana¢h space yesterday,
and it would be very helpful if it were also ref1exive.)
there is one drawback, though. i'm the sort of person who likes his reward after his work. (that's why i prefer to go running in the afternoons and evenings, and not in the mornings.) by "work" or responsibilities, i am referring to teaching. this term,
10-11am: differentia1 equati0ns
2-3pm: (basic) 1inear a1gebra [1]
it's hard for me to sit down and think unhindered when i have further responsibilities to meet later. my thoughts are not:
great! i have 2-3 hours to think about research.
but instead,
crap. i have to teach at 10am;
i only have a few hours for research.
i suppose that suggests a few things about me: that (1) i am a pessimist at heart, and (2) if i can be a slacker, then i shall. there is also the dread of murphy's law: inevitably when one has a good idea, then it's at the last possible second and one has no further time to entertain it.
then again, this early morning math might be a better strategy. i often prefer research to teaching [2] and let's face it: time always runs out, and after teaching, i've less energy left for thinking than i would prefer to have.
as long as there is time available for new theorems, who am i to complain? in this life, we take what we can get.
on a slightly related note, i'm getting more fickle with age, at least when it comes to books and sources. while leafing through functional analysis texts, it was hard to find exactly the right one.
note to self: maybe i should invest in a copy of y0sida's book, and for that matter, a copy of ev@ns and 9ariepy's book on mea$ure the0ry and some books of e. $tein. the book list goes on.
anyways, i leafed through rud!n and went through his idiosyncracies,
i thumbed through r0yden (the middle part) and read lists of facts about bana¢h spaces ..
.. and in the end, the one source that really spoke to me were the lecture notes that my advisor wrote some years ago, when he was teaching a functi0nal ana1ysis course. [3] he always did explain mathematics well.
so like everyone else, i guess i'm partial to my own mathematica1 upbringing. (:
[1] in the course, we'll cover so1utions to systems of 1inear equati0ns, some basic facts about basis and 1inear dependen¢e and determinants, how to diagonalize symmetri¢ maτrices, and how to compute ei9envectors. there are some applications too, but i can't remember them right now.
so i'm just saying what this course is: the first lessons one learns in 1inear a1gebra. it's not like we're going to prove the $pectral theorem or anything.
[2] unless, of course, the research really isn't going well.
[3] my postdoctoral mentor is currently drafting notes in latex, which he makes available on his homepage. however, at the time i couldn't access and use them.
call me a luddite, but i still haven't acquired high-speed internet at home.
take this morning: i woke up at 5:30am, decided that i wouldn't be able to fall asleep again, and then proceeded to coffee and breakfast. by 6am i was leafing through books in fun¢tiona1 ana1ysi$.
(as it happens, i defined an ad-hoc bana¢h space yesterday,
and it would be very helpful if it were also ref1exive.)
there is one drawback, though. i'm the sort of person who likes his reward after his work. (that's why i prefer to go running in the afternoons and evenings, and not in the mornings.) by "work" or responsibilities, i am referring to teaching. this term,
10-11am: differentia1 equati0ns
2-3pm: (basic) 1inear a1gebra [1]
it's hard for me to sit down and think unhindered when i have further responsibilities to meet later. my thoughts are not:
great! i have 2-3 hours to think about research.
but instead,
crap. i have to teach at 10am;
i only have a few hours for research.
i suppose that suggests a few things about me: that (1) i am a pessimist at heart, and (2) if i can be a slacker, then i shall. there is also the dread of murphy's law: inevitably when one has a good idea, then it's at the last possible second and one has no further time to entertain it.
then again, this early morning math might be a better strategy. i often prefer research to teaching [2] and let's face it: time always runs out, and after teaching, i've less energy left for thinking than i would prefer to have.
as long as there is time available for new theorems, who am i to complain? in this life, we take what we can get.
on a slightly related note, i'm getting more fickle with age, at least when it comes to books and sources. while leafing through functional analysis texts, it was hard to find exactly the right one.
note to self: maybe i should invest in a copy of y0sida's book, and for that matter, a copy of ev@ns and 9ariepy's book on mea$ure the0ry and some books of e. $tein. the book list goes on.
anyways, i leafed through rud!n and went through his idiosyncracies,
i thumbed through r0yden (the middle part) and read lists of facts about bana¢h spaces ..
.. and in the end, the one source that really spoke to me were the lecture notes that my advisor wrote some years ago, when he was teaching a functi0nal ana1ysis course. [3] he always did explain mathematics well.
so like everyone else, i guess i'm partial to my own mathematica1 upbringing. (:
[1] in the course, we'll cover so1utions to systems of 1inear equati0ns, some basic facts about basis and 1inear dependen¢e and determinants, how to diagonalize symmetri¢ maτrices, and how to compute ei9envectors. there are some applications too, but i can't remember them right now.
so i'm just saying what this course is: the first lessons one learns in 1inear a1gebra. it's not like we're going to prove the $pectral theorem or anything.
[2] unless, of course, the research really isn't going well.
[3] my postdoctoral mentor is currently drafting notes in latex, which he makes available on his homepage. however, at the time i couldn't access and use them.
call me a luddite, but i still haven't acquired high-speed internet at home.
Tuesday, January 06, 2009
unexpected consequences of editing a manuscript.
yesterday i pared down the number of webpages on my mathematical homepage. (it's starting to look confusing: too many unnecessary links.)
while editing my research page, i ran a Math$ciNet search on myself. it occurred to me:
ye gods, i don't have very many papers;
i have to do something about that.
with that in mind, last night i printed out another copy of my latest manuscript and i packed a red pen into my bookbag. maybe, after a thorough edit, i can submit it by the end of january.
this morning i woke up early and brought the 35-page manuscript with me to a coffeehouse. i was on page 15 when someone from another table began,
"say, is that .."
already i began to wince.
great, another "mathematics" conversation with a layperson. why me? i'm minding my own business. i just want to get some work done ...
".. ana1ysis?"
i blink.
huh. interesting ..
we ended up chatting a bit; he's a visiting prof in ec0nomics at ¢arnegie-me11on univer$ity and has gone through the gamut of theoretical maths -- topo1ogy, mea$ure the0ry, and the like.
he explained to me how the philosophers over at ¢MU are studying interre1ations between 1ogic and oddly enough, g@me the0ry. i sketched out, in br0ad strokes, what ge0metric mea$ure theory was -- indeed, he seemed to have a decent grasp of what c0mpactness means.
later, he gave me his card. i did something similar: i jotted my name, my email, and "mea$ure the0ry" on a piece of paper and gave it to him. he chuckled, and we went our separate ways.
i'm on page 23 now: no serious edits have come up, but i would still like this thing shorter.
while editing my research page, i ran a Math$ciNet search on myself. it occurred to me:
ye gods, i don't have very many papers;
i have to do something about that.
with that in mind, last night i printed out another copy of my latest manuscript and i packed a red pen into my bookbag. maybe, after a thorough edit, i can submit it by the end of january.
this morning i woke up early and brought the 35-page manuscript with me to a coffeehouse. i was on page 15 when someone from another table began,
"say, is that .."
already i began to wince.
great, another "mathematics" conversation with a layperson. why me? i'm minding my own business. i just want to get some work done ...
".. ana1ysis?"
i blink.
huh. interesting ..
we ended up chatting a bit; he's a visiting prof in ec0nomics at ¢arnegie-me11on univer$ity and has gone through the gamut of theoretical maths -- topo1ogy, mea$ure the0ry, and the like.
he explained to me how the philosophers over at ¢MU are studying interre1ations between 1ogic and oddly enough, g@me the0ry. i sketched out, in br0ad strokes, what ge0metric mea$ure theory was -- indeed, he seemed to have a decent grasp of what c0mpactness means.
later, he gave me his card. i did something similar: i jotted my name, my email, and "mea$ure the0ry" on a piece of paper and gave it to him. he chuckled, and we went our separate ways.
i'm on page 23 now: no serious edits have come up, but i would still like this thing shorter.
Monday, January 05, 2009
w0es: first day of the semester, again.
saturday evening, 11:30pm:
i return to pittsburgh, after 24+ hours of travel.
sunday evening:
i realise that i never picked up the textbook for one class that i'm supposed to teach; panic and insomnia ensues.
monday morning, 8am:
one of the admin staff looks at me dubiously, lets me into the storage room. i obtain the aforementioned textbook, thank her profusely, and run away like a guilty person.
hasty reading and summarizing follow,
some simple examples are quickly made up.
monday, 10am:
i hand out syllabi, ask if the students are in the right classroom, and begin lecturing. later in the class, i hear some students chuckle when i discuss a model for population growth for monkeys on an island.
so: another crisis averted .. at least for differential equations; in the afternoon, i have linear algebra, which should work out well enough.
i return to pittsburgh, after 24+ hours of travel.
sunday evening:
i realise that i never picked up the textbook for one class that i'm supposed to teach; panic and insomnia ensues.
monday morning, 8am:
one of the admin staff looks at me dubiously, lets me into the storage room. i obtain the aforementioned textbook, thank her profusely, and run away like a guilty person.
hasty reading and summarizing follow,
some simple examples are quickly made up.
monday, 10am:
i hand out syllabi, ask if the students are in the right classroom, and begin lecturing. later in the class, i hear some students chuckle when i discuss a model for population growth for monkeys on an island.
so: another crisis averted .. at least for differential equations; in the afternoon, i have linear algebra, which should work out well enough.
Friday, January 02, 2009
productive holidays.
if all goes well, then i will return to the united states tomorrow. as far as i know, the airport blockades in bangkok have stopped weeks ago, but as the saying goes:
just because you're paranoid doesn't mean that they are not out to get you.
oddly enough, most of last week was mathematically productive. there's only so much one can do on an isolated tropical island off the coast of southern thailand [1]. barring some technical details i've made some headway into a special case of a conjecture, but only as far as i can push the results of others.
the important thing is that i have an idea, a course of action. until that fails, at least there is work to do.
i'm tempted to say that, along with a few other results, it could shape nicely into a second preprint. it still doesn't address the entire picture, which is fine but unsatisfying. i doubt that what remains unknown, if proven later, would make a very good paper or even a note ..
.. at least, not unless the techniques are interesting in their own right. then again, this is all just speculation: maybe the technical details are intractable or i will find a counter-example to my argument.
who knows? the only sure thing i know is that i have a lot of work ahead of me:
a new year,
a new semester,
a new area of research to learn and in which to prove things,
and plenty of old commitments to colleagues.
there will always be something to be frustrated about. 2009 will be full of them, i think.
[1] it's not that rock climbing, sea kayaking, and sunbathing get old that quickly .. actually, sunbathing does .. but as i think for a living, it's hard not to have some sort of mental curiosity at hand.
just because you're paranoid doesn't mean that they are not out to get you.
oddly enough, most of last week was mathematically productive. there's only so much one can do on an isolated tropical island off the coast of southern thailand [1]. barring some technical details i've made some headway into a special case of a conjecture, but only as far as i can push the results of others.
the important thing is that i have an idea, a course of action. until that fails, at least there is work to do.
i'm tempted to say that, along with a few other results, it could shape nicely into a second preprint. it still doesn't address the entire picture, which is fine but unsatisfying. i doubt that what remains unknown, if proven later, would make a very good paper or even a note ..
.. at least, not unless the techniques are interesting in their own right. then again, this is all just speculation: maybe the technical details are intractable or i will find a counter-example to my argument.
who knows? the only sure thing i know is that i have a lot of work ahead of me:
a new year,
a new semester,
a new area of research to learn and in which to prove things,
and plenty of old commitments to colleagues.
there will always be something to be frustrated about. 2009 will be full of them, i think.
[1] it's not that rock climbing, sea kayaking, and sunbathing get old that quickly .. actually, sunbathing does .. but as i think for a living, it's hard not to have some sort of mental curiosity at hand.
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