i mean, it's just a constant ..

9 times out of 10, in analysis all one needs is an inequality, of some kind. usually the multiplicative constants are unimportant.

today is that one day, of all things,
that the actual constants matter ..

[sighs]

blog suggestion: opinionator.

i don't read the new york times regularly, at least not in print form.

for me, the density of its prose takes a few weeks of readjustment; i'm never patient enough to make the commitment. [1]

on the other hand, there are a host of NYT blogs that are tremendous fun. of these, one is particularly gears for us mathmos and techies:

"opinionator" by steνen strοgatz

personal anecdote. in my first year of grad school, i ran supplementary problem sessions for a linear algebra class, and even subbed for one or two of its lectures, during hallowe'en [2]. one economics student was particularly interested in the subject, though she had taken little/no mathematics since her calculus days. we became pleasant acquaintances.

one day there was a distinguished mathematical lecture by strοgatz, who was an unknown to me at the time. we had snuck into the reception tea earlier. when the crowd started towards the lecture room, i suggested that we attend. in retrospect i think she agreed out of guilt -- cookies can do that to you -- but we enjoyed the talk immensely. it mixed well physical intuitions from nature and a little maths from beyond the classroom.

"this is great!" she said, "are all the mathematics colloquia this interesting?"

ummm .. (-:

at any rate, strοgatz is a fine expositor. he has this way of taking something simple but, in a seamless process, pointing out its depths.

for instance, consider arithmetic .. which is also considered in "rock groups." trivial stuff, right?

each of us can imagine arithmetic in the form of making patterns with little stones. however, a neat little pattern, such as

[image borrowed from NYT]

serves as a wonderful intuition: why sums of odd numbers give perfect squares.

sure, it's trivial when you have the picture. it's not research-level maths ..but still, it makes me smile. it makes me feel like a boy again, realising a little depth, learning these facts for the first time.

then there is empathy. some representations don't make sense, initially, because we may encounter matters beyond our intuition. for example, in "division and its discontents," strοgatz writes:

The bafflement began when Ms. Stanton pointed out that if you triple both sides of the simple equation

$\frac{1}{3} \;=\; 0.33333\ldots$

you’re forced to conclude that $1$ must equal $.9999\ldots$

At the time I protested that they couldn’t be equal. No matter how many 9’s she wrote, I could write just as many 0’s in $1.0000\ldots$ and then if we subtracted her number from mine, there would be a teeny bit left over, something like $.0000\ldots01$.

i remember experiencing the same sense of mystery, as well as trying to explain it to my calculu∫ 2 students.

"the reason why it was confusing back then is that, as children, we were ignorant of geοmetric series," i offered.

"put another way, it's probably the first time you were exposed to the notion of a limit, which isn't quite fair. for most of us, we learned decimals in grade school, whereas we learned about limits in our first calculus class."

anyway, i like the exposition in "opinionator." i like (re)discovering the depths in seemingly simple ideas.

[1] for the same reason, i don't often read novels. lately the only ones i've read are (i) suggestions from friends and (ii) those, upon inspection of their spines, i estimated would take at most one sitting to read.

[2] it's not hard to remember that day. somehow i procured some orange chalk for the occasion. (-:

on being a "young researcher" ..

it's odd, being one of a few postdocs in a mathematics department .. at least, from my own biased experience.

you see, when i was a student, my department ran rife with postdocs.

before the economic woes of fall 2008, there were at least a dozen hires, every year. [0]

in the research group that i joined, in one year there were 4, all in varying stages of a job. it made for well-attended research seminars .. and lively discussions afterwards, over mediocre pizza and drinks.

here, there are about a half-dozen postdocs. of them, only two are non-applied; i am one and the other is, roughly speaking, a logician/algebraist. we haven't so much in common, except we are few.

one could liken the change in departments to, say, becoming among the few remaining νulcans in a rebooted star trek universe.

luckily, i have plenty of people to talk to. i meet regularly with two faculty, my postdoctoral mentors. their students are promising; occasionally i meet with them, too.

sometimes, though, i miss talking to mathematicians that are my own "age."

• when i speak with tenured faculty, i am the slow, plodding one: i learn a lot, but it's a race to catch up with what they already know well.


• when i speak with graduate students, somehow i am the knowledgeable, patient one. [1] it becomes important to pace matters accordingly, ask them pre-questions before questions, sharpen the discussion ..

so regularly i feel woefully young and inexperienced, and other times, i am surprisingly seasoned and "old."

sometimes, for a change in scene and an exchange of ideas, i travel. i meet colleagues and friends. [2] i try to figure out who i still am, who i can be.

in this aspect, it is good to be young. it is easier to find travel funds, as a young researcher. i know this time will be short, so i may as well enjoy the perks!

---

[0] the pace of hiring may have remained the same; i don't know. since i left for my postdoc, i haven't returned there.

[1] yeah, i know: me, of all people. can you believe it? (-:

[2] maybe i should call people more often. in fact, i was on skype today, to talk to a collaborator. now i wonder what collaborations were like, before VoIP.

flight plans | collaborations vs. solo works.

every time i board a plane, i forget something. this time, it included toothpaste, contact lens solution, and a copy of one particular paper that i was planning to read.

frustrating!

i brought a secondary reference, a copy of my preprint in progress, and even two papers that were for "fun" .. that is, in case i felt like thinking about maths, but not about any of my own projects ..

but the one paper that really mattered: it had to be that one that i would forget.

over the first leg of my flight i tried to reconstruct the proof. i remembered to include one particular step, but couldn't remember exactly why it was necessary.

by the second leg of my flight, i had grown curious enough to look up the PDF version in my maths_papers folder of my laptop. with only 30 minutes left of battery power, there was enough time to read the proof and think it over. the LaTeXing would have to wait.

good enough. odds are that i wouldn't be able to write it well at the time, anyway.

---

on a related note, if all goes well i'll have four more collaborations in the works. that is good.

then again, it's been a while since i wrote a paper on my own.

in my recent work on schοenflies extensions, i can't separate which were my ideas and which were the advisor's.

i'm also loathe to count the paper i cut from my thesis [1]; i can say with honesty that though the advisor pointed me to that direction of study, the driving ideas were almost all mine. i remember the advisor being confused at first, probably thinking i was crazy.. and one day, his eyes widened when he realised why exactly it would work.

you see, he was a hard man to surprise. i never thought that i'd be able to. (-:

anyways: been there, done that, what have i done lately, on my own? the question is still relevant: can i be successful, by myself?

i still feel like i don't know anything. i'm still not good at formulating problems. maybe that explains the collaborations. i'm nearsighted with details, and someone has to point me in a direction to start. \-:

maybe i'll try my hand at (geοmetric) measurε theοry again. i don't know much about it, but it's an area in which i can work alone, comfortably. if i prove something interesting enough [2], then maybe i'll finally write that paper about curreηts.

[1] in retrospect, maybe it would have been a good idea to break it up into two papers. it ended up being 35 pages long, and in two rough parts: (1) building some machinery and some euclidean results, and (2) answering a special case of a conjecture that everyone already knows is true, but with a different proof in mind.

it's been a year since i sent it to a journal, and supposedly it's gone to the referee. is it really that taxing to read? admittedly i needed three distinct theories to make it work, but .. come on. if (s)he thinks it's crap, then at least let me know now so that i can re-submit it!

[2] for now, i have a few theorems, but .. they're somewhat obvious. if i were a referee, i would reject a paper with only those contents.

holidays, of several sorts.

spring break commences. i'll be working and traveling .. perhaps even both at once, so i mightn't be updating for a few days.

---

so before i forget, let me repeat my mild distaste for pi day.

i simply cannot explain it rationally. admittedly, if i had to choose between e and π, then i'd choose the latter.

then again, this happens to be a day when all the math groupies gather together and geek out ..

.. and i've never been good in crowds;
they make me uneasy. [1]

some holidays are remembrances of important historic events, that characterise our identity.

i would not object to celebrating hιlbert's birthday, for example. the undergraduate math club actually celebrated cantοr's birthday [2] recently; props to them!

most of them, however, are just excuses to have a party. besides, i have always been a contrarian and a strange one;

i'll gladly throw a toga party on 15 march;

when i was in charge of the geο calendar, i would always try and sneak in festivus under the list of holidays and observances .. to no avail.

someone always took it out. \-:

so this year, let me announce it again: why not celebrate $\sqrt{10}$ day -- march 16th, instead? (-:

[1] this might well explain my erratic behavior at conferences: i don't talk to as many people as i should. i've been trying to improve on that.

[2] oddly enough, this coincides with golden ratio day, which is "january 62nd" (or march 3, in funny arithmetic).

blind spots.

i think my analysιs midterm today caused trauma to my students. afterwards, they asked me about part A of one problem:

"can you give us the counterexample?" they asked.

"sure," i said. "take the closed interνal $[0,\infty)$ and then .."

".. wait, that's a closed interval?" one asked, shrilly.

i blinked; oh no ..

so i said yes. they inquired further, and we looked it up in the textbook.

"so is $\mathbf{R}$ an open interval?" another asked.

"actually, it's both open and closed," i pointed out. "there are no endpoints to test, so it has to be both."

"what?!?"

[sighs]

i thought that was one of the first things that anyone ever teaches students: open vs. closed, neither or both ..

oh well. i'll just grade the exams generously.

a day in the life.

many things happened to me today, which was unusual.

1. i worked for a few hours on a joint preprint [0];


2. i held three office hours and administered 1 makeup exam;


3. i had two separate research meetings with members of my research group;


4. i decided not to go to india for the ICM, and accept the logical consequences.


5. i sat on a panel on a "life after graduate school" workshop, in which the subjects were how to apply for postdocs and write grants [1];


6. i was invited to give a colloquium!!!

---

[0] technically, a day consists of 24 hours. suffice it to say that i didn't get much sleep, last night.

[1] this time, i avoided sounding like an idiot. on the other hand, i think i ended up sounding paranoid and bitter.

names.

some of my analysιs students are finally calling me by my first name, which is a relief.

it's who i am,
how i imagine myself.

---

being called "dr. so-and-so" makes me sound either old or distinguished or a medical doctor, all of which seem .. wrong, to me.

"prof. so-and-so" is worse. i feel like a fraud, having convinced someone that i'm on the tenure track somewhere.

on a related note, being called "mr. so-and-so" feels businesslike.

i imagine some sort of imminent business transaction, like check-in at the airport counter or a credit card offer!

"You either die a hero or you live long enough to see yourself become the villain."

earlier today one of my TAs stopped by my office to discuss a mishap during recitation.

immediately i thought of the ending to the dark knight.

i should probably now interpolate between those two sentences.

---

last week one of my quiz questions was numerically painful for the students, due to a typo or two: suddenly they had to take the sum of squares of two 2-digits numbers instead of two 1-digit numbers, and then some. [1]

subsequently a majority of the class was unable to complete the quiz in the allotted time.

i think most of them still haven't forgiven me.

---

so in some show of fairness, i wrote another quiz that same thursday, and told the students that they'll get another chance to take it again for a better grade.

on friday, i spotted a new typo; most of the steps would remain intact, but they wouldn't be able to reach a final answer. so i fixed it and emailed the new copy to the TAs ...

..
..

yeah, you can guess what happened.

actually, it gets better:
that one TA made the photocopies for another TA as well.

---

so i told the TA,

"look, my name is mud already.
you remember last week, right?

i'll just tell them that it was my mistake.
they're mad at me anyway."

sometimes it's not about being a hero. sometimes we make mistakes, sometimes we don't, but someone has to deal with the pieces .. be the object of scorn .. say, a dark knight. \-:

[1] if you must know, it was something like $\sqrt{28^2 + 33^2}$.

when a lecture has no worth, say what you want [EPILOGUE ADDED].

i'm hard-pressed to think of what to discuss today, in my analysιs class. we've covered what i wanted out of chapter 5 already. running time backwards,

next week: spring break
friday: midterm / "spring break eve"
wednesday: review session

so .. today?!?

---

if i start chapter 6, then i'll just have to review half of it after break .. which will over-test my patience.

if i give a pre-review session, then that might help. then again, review sessions are already enough teeth-pulling ..

in that everyone has questions,
but nobody ever asks anything

so why have two of them?

i don't want to cancel class either;
that sets a tricky precedent for future pre-exam weeks .. \-:

---

ultimately, today's lecture isn't worth anything, in terms of the syllabus. maybe i'll just talk about what i want to talk about --

a supplementary lecture, like unifοrn convergence,
power series as continuous functions,
and why sine and cosine are continuous, after all

-- and just tell the students that they are not responsible for remembering it, i.e. that it will never come up on any homeworks, quizzes, or exams.

at least that would stop them from worrying. heck, with the stress off, they might even listen more attentively than usual .. (-:

---

- added: 2 mar '10 -- 12:55am -

well, on the whole that that was a foolish idea. i don't think the students got much out of it. i should have held an impromptu review session, instead.

my greatest gaffe was telling the students that they didn't need to take notes. it didn't occur to me how quickly it would take them to lose interest.

on a related but disturbing note, my students had the same looks on their faces as my audiences, when i give conference talks. maybe i have this effect on everyone.. \-: