I dug this out of my desk, and it was written about two weeks ago, when the Fall Term just started and I had a free moment to jot down a few stray thoughts.
For the record, this was the Friday that I held an Office Hour instead of a Math Lab tutoring hour, had tempura at Totoro, and read comic books at Borders Books & Music.
It's been a rather pleasant evening. I didn't do very much today -- unless you count fielding a volley of questions from my eager students at Office Hours. My 1-credit Physics seminar didn't meet today, but I only found out after sitting in a half-empty classroom for fifteen minutes. It wasn't a total waste of time, though.
Other students -- these being Physics grad students -- were also in the room, chatting idly, and I caught more than my share of their Department's gossip. I suppose the scene is much as a Mathematics class would be to the non-mathematics student: academically accessible but ultimately socially insular.
Let me not seek any general meaning from this.
Sitting in my advisor's class reminds me of how different we analysis students are [1], or perhaps how different I am from everyone else. For instance, I seem incapable of saying much during lectures, if I say or contribute anything at all. Somewhere along the way of becoming a maths student I became obsessed with good notetaking.
I use different pen colors and flow tips and everything. I write down as much of the discussion as possible .. what's on the board, which comments the lecturer made, and what comments or questions the audience brings up, and what answers ensue.
I might as well be archiving the experience of that lecture, rather than just its topical contents. It feels like I switch to a Record mode, and while I'm in this mode it seems I can do little else, which is problematic when in my advisor's class. He likes class involvement, you see, and asks plenty of non-rhetorical questions.
He teaches quite well, in fact: motivation, examples, ideas behind the proof .. all the good stuff. It's too bad that my notetaking style is so inconducive to his lecturing style, but happily, this is where the differences between we student analysts can prove valuable.
One of my student peers is really good with questions; some of you know him as Kevin, guardian of the Quasi-World. He takes on questions with detail and delight, and he asks many of his own. My former flatmate Jose' is quick to pick up on clues and is quite clever; he has remarkable intuition. There is Marie, my academic sib [2], who has the gift of clarity: being able to ask the right questions, she sorts out the occasional confusion and is another source of intuition.
Me? I just write it all down.
Maybe in the process of college and the early years of graduate school, I've neglected the ability to process information quickly and to use it effectively. New ideas and concepts take me a great deal of time to work into my thinking. Worse yet, my short-term memory seems to be diminishing and diminishing fast, and I could swear that the time I spend trying ideas and sorting out details takes far longer than I'd like ..
.. say an o(n2) runtime, whatever n is. q:
[1] .. though I prefer the term: "student analyst." It answers two questions in immediate succession:
"What sort of mathematics do you study?"
"What's your academic status?"
[2] In case it wasn't clear, an academic sibling is another student of your thesis advisor. M and I happen to be in the same year in grad school, so more often than not I feel like the evil twin. q:
2 comments:
Hi Jasun--
I have to agree--your notes are beautiful. Thanks again for the set you gave me before I dropped that class. I wish I had enough background understanding to be in there. I like how you describe everyone complementing each other with individual talents--it's like you're all X-men with various superpowers :)
Lately I've been appreciating the protean nature of math. I like it all beautiful written down, but it also exists in lectures and conversation, and of course in the mind. How very alive. I've other metaphors: it's a kind of magic that's not trickery; it's something authentic. And I feel lucky to be in the presence of practictioners.
--Johanna
No problem about the notes, Jo. Glad you liked them. It's a far kinder response than when my sister once looked at my notebooks and said that "I wrote like a girl." I never knew how to react to that. \:
for the set you gave me before I dropped that class. I wish I had enough background understanding to be in there.
Some of that background I remember from coursework, such as Functional Analysis last fall. Other bits, like notions of measure, are familiar but I can't remember where I learned them.
Here's the funny thing: I did take a Topics (700-level) course with our same prof in the Winter of my first year at UM, and I remember being rather confused most of the time.
I ended up becoming something of a pest during Office Hours, and had it not been for these semi-regular conversations with Juha, the advisor search would have been a lot harder and far less certain.
At any rate, don't get overwhelmed with all the things that you don't know, because nobody will ever solve the problem of omniscience. Sometimes the most important skill is being able to ask questions about the things you don't know; I mightn't be able to do it during lectures, but I try to get around to it somehow ..
.. say, during Office Hours. q:
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