I've said this before to my friends, and it doesn't hurt to repeat it here: I'm glad I'm not a student in my own class. I wouldn't be able to stand myself.
Today I must have been unbearable as an instructor. As I went over an example today, even I found it boring and tiresome. That sucks. Calculus mightn't be the most exciting subject in all of academia, but it shouldn't be that boring.
One of these days I'll remember to keep my lectures short and snappy, and send the kids off to work on problems .. maybe even a worksheet of my own design. Better to keep them active and thinking, and doesn't the UM Teaching Staff always say: "Let the students discover the facts for themselves?"
At any rate, I seem to have lost the ability to ask questions that my students are willing to answer. Maybe they don't know the answers because they didn't do the reading, or maybe I'm simply not asking the right questions or questions that make any sense. Maybe they're just confused.
At any rate, class hasn't been going very well, lately.
I'm trying to remember when I first learned differentiation and integration, and it must have been about .. 6 or 7 years ago, when I was about 17 and still in high school.
Christ. I was that young once, wasn't I?
I barely remember learning it, but it didn't seem that hard at the time. I do remember being scared to death of my Calculus teacher, Mr. Bevelander.
Yet at the same time I always felt at ease asking questions. It was a class of 8-10 students (how that happened, I have no idea) and every time someone had a question, we'd ask. If it didn't make any sense after a moment, our teacher would toss us a nub of chalk, and whoever had asked the question would walk over to the board and elaborate on the matter.
It helped tremendously in the cases that one of us did the problem in a completely different way than Bevelander had imagined. In fact, I wouldn't even say that he taught; rather, he put us to work on problems and critiqued our work. It went in a somewhat formulaic manner, but then again, so did plenty of other things in high school.
I remember rather liking chalkboards after that, and it helped to think right in front of it, adding another line of computation as I wondered where to go next or whether this approach was any good or not.
At any rate, teaching is over until Thursday. I'm not complaining.
Research is going well. I figured out the mystery behind that weird-@$$ exponent (I had mentioned it before, here), and it was a mistake -- just not the one I expected. The proof is still the same and much progress remains, but at least it's slightly saner.
Tuesday, September 27, 2005
Sunday, September 25, 2005
on hope, and the learning process.
Grading upsets me.
I think it's because I am a closet perfectionist, despite my occasional, outwardly relaxed appearance. Details do matter and so does rigor, otherwise I'd be a student philosopher and not a student mathematician. Then again, there are plenty of non-rigorous bits of mathematics done, each and every day. But we're supposed to try for correctness and accurate, logical thinking.
I keep reminding myself that most of my students are about 18 years old, and about 6 years younger than I am. Most of them have just arrived from high school, where mathematics may have been glorified computations, excessive formulae, and few insightful ideas.
They may not have been asked to justify their answers in the way we, as Calculus instructors at UM Mathematics, demand them to justify.
It may be that, aside from logical reasoning when writing essays, they've never been held accountable for this sort of thing. They may not be used to thinking of a generic case, or searching for a pathological situation or worst-case scenario in order to compare with what must "always" be true.
That's a lot of 'may's and it tries my patience. It only convinces me that perhaps I'm not well suited to the life of an educator. I have enough trouble with my own shortcomings, so how do I deal with those of others?
It's not easy to find hope in this line of questioning.
I went to a dinner party last night and to be simplistic about it, the other guests were bourgeoisie-in-training: law students, MBA students, and an Urban Planning and PolySci Ph.D. student each.
There's nothing wrong with these people, mind you, because the world has to keep running. Money is an important commodity to everyone, and I say these people are being exceedingly realistic. I just choose not to be one of them, because the world and its people frustrates me too easily and quickly for my taste; more importantly, I don't have a mind for money.
One of the MBA fellows half-asked/half-told me, "You must be really smart, to study mathematics!"
I replied, half-jokingly, "I wouldn''t say that. Nobody's actually good at mathematics. It's just that mathematicians just never give up. We're just stubborn that way, and we just try and try."
(It's not entirely accurate if you believe that some people are either 'naturally' good at maths or have learned to be "good," but in light of how frustrated mathematicians can be as a result of their exertions, there must be a speck of truth in this.)
Maybe that's it, then. Maybe it's just enough to try, and by trying, to reach some modicum of improvement. It's evident that my students are trying, either for a good grade or for a good understanding of calculus. The end doesn't matter so much, but they are trying.
That has to count for something: it did when I was such a student and my teachers had to grade my shoddy work.
Hope always lies in possibility. Perhaps my students will make their mistakes now and when their exam comes, they won't make them again. Perhaps they will learn more than simply how to do well on their exams, and appreciate a little mathematics for its own sake, which belies appreciating the fundamental logic and reasoning for its own sake. Perhaps it's worth the frustration of grading.
Those are still a lot of 'perhaps,' so here's to hope. \:
I think it's because I am a closet perfectionist, despite my occasional, outwardly relaxed appearance. Details do matter and so does rigor, otherwise I'd be a student philosopher and not a student mathematician. Then again, there are plenty of non-rigorous bits of mathematics done, each and every day. But we're supposed to try for correctness and accurate, logical thinking.
I keep reminding myself that most of my students are about 18 years old, and about 6 years younger than I am. Most of them have just arrived from high school, where mathematics may have been glorified computations, excessive formulae, and few insightful ideas.
They may not have been asked to justify their answers in the way we, as Calculus instructors at UM Mathematics, demand them to justify.
It may be that, aside from logical reasoning when writing essays, they've never been held accountable for this sort of thing. They may not be used to thinking of a generic case, or searching for a pathological situation or worst-case scenario in order to compare with what must "always" be true.
That's a lot of 'may's and it tries my patience. It only convinces me that perhaps I'm not well suited to the life of an educator. I have enough trouble with my own shortcomings, so how do I deal with those of others?
It's not easy to find hope in this line of questioning.
I went to a dinner party last night and to be simplistic about it, the other guests were bourgeoisie-in-training: law students, MBA students, and an Urban Planning and PolySci Ph.D. student each.
There's nothing wrong with these people, mind you, because the world has to keep running. Money is an important commodity to everyone, and I say these people are being exceedingly realistic. I just choose not to be one of them, because the world and its people frustrates me too easily and quickly for my taste; more importantly, I don't have a mind for money.
One of the MBA fellows half-asked/half-told me, "You must be really smart, to study mathematics!"
I replied, half-jokingly, "I wouldn''t say that. Nobody's actually good at mathematics. It's just that mathematicians just never give up. We're just stubborn that way, and we just try and try."
(It's not entirely accurate if you believe that some people are either 'naturally' good at maths or have learned to be "good," but in light of how frustrated mathematicians can be as a result of their exertions, there must be a speck of truth in this.)
Maybe that's it, then. Maybe it's just enough to try, and by trying, to reach some modicum of improvement. It's evident that my students are trying, either for a good grade or for a good understanding of calculus. The end doesn't matter so much, but they are trying.
That has to count for something: it did when I was such a student and my teachers had to grade my shoddy work.
Hope always lies in possibility. Perhaps my students will make their mistakes now and when their exam comes, they won't make them again. Perhaps they will learn more than simply how to do well on their exams, and appreciate a little mathematics for its own sake, which belies appreciating the fundamental logic and reasoning for its own sake. Perhaps it's worth the frustration of grading.
Those are still a lot of 'perhaps,' so here's to hope. \:
Friday, September 23, 2005
not so much 'new' as 'old' ..
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:
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:
Wednesday, September 21, 2005
strung out on coffee and work.
I've forgotten one of the unsaid rules of doing mathematics:
I've thought about one particular problem for far too long, and now there is too much momentum to stop .. and when I say a problem, I mean a problem. It's a mathematical statement, pure and simple.
I can't tell whether it's true or false.
When I try to prove it, I run into technical difficulties. If you know a little metric topology, the issue involves a lack of control on the diameter of a particular sequence of metric balls. If this is ever settled, then the proof is done.
I can't construct the right counterexample, either. The first things one tries, they don't work. Radial functions f(x) = x * F(|x|)/|x| don't work when F is a power function, and more complicated functions are too complicated and inconclusive.
I still think it's true.
I'm close .. but my estimates are crap, and there's still no proof.
This may as well be a matter of faith. The statement could be false, and maybe I'm missing something.
F*ck. I should leave this alone.
This statement came to mind when I was trying to prove something else, and I don't need this result to continue my research. I should be doing something more productive .. say, working on my Calc II lesson plans or preparing a grading sheet for another week's worth of Team Homeworks ..
.. nnnaaaargh. Gah. Bleah.
I don't want to think about that .. at least not now.
I should get back to work. Tomorrow's another meeting with my advisor, and there is plenty I want to talk about .. that is, if I ever have it ready.
The other aspects of my life are unimportant right now. They may as well be nonexistent, and if I ever stop again and think too hard about my life, I might become depressed again. Then I'd never get any work done.
Soldier on, then. All I need are rock music, calories and fluids, good paper and pens, and a good dose of luck. That's all I ask.
Never get emotionally involved with your work.
I've thought about one particular problem for far too long, and now there is too much momentum to stop .. and when I say a problem, I mean a problem. It's a mathematical statement, pure and simple.
I can't tell whether it's true or false.
When I try to prove it, I run into technical difficulties. If you know a little metric topology, the issue involves a lack of control on the diameter of a particular sequence of metric balls. If this is ever settled, then the proof is done.
I can't construct the right counterexample, either. The first things one tries, they don't work. Radial functions f(x) = x * F(|x|)/|x| don't work when F is a power function, and more complicated functions are too complicated and inconclusive.
I still think it's true.
I'm close .. but my estimates are crap, and there's still no proof.
This may as well be a matter of faith. The statement could be false, and maybe I'm missing something.
F*ck. I should leave this alone.
This statement came to mind when I was trying to prove something else, and I don't need this result to continue my research. I should be doing something more productive .. say, working on my Calc II lesson plans or preparing a grading sheet for another week's worth of Team Homeworks ..
.. nnnaaaargh. Gah. Bleah.
I don't want to think about that .. at least not now.
I should get back to work. Tomorrow's another meeting with my advisor, and there is plenty I want to talk about .. that is, if I ever have it ready.
The other aspects of my life are unimportant right now. They may as well be nonexistent, and if I ever stop again and think too hard about my life, I might become depressed again. Then I'd never get any work done.
Soldier on, then. All I need are rock music, calories and fluids, good paper and pens, and a good dose of luck. That's all I ask.
Saturday, September 17, 2005
a rant that turned into a post.
Someone posted on LJ: Mathematics Community about the "Reformed" vs "Traditional" Calculus class formats. I ended up writing this opinion about this previous comment by another community member. My response is below.
If you're not going into higher-level, proof-based mathematics courses, then it can be argued that it isn't necessary to know the rigorous definition of a limit.
An interesting point. If you choose to view courses in a basic Calculus sequence (Calc I, II, possibly III and Diff Eq) as general-ed requirements, and if you will never venture into higher-level pure mathematics (where logical arguments and geometric ideas are more important than computational methods) then perhaps there is little to no need for such rigor as the ε-δ definition of a limit.
What bothers me is whether we demand reductions in other general-ed courses.
The ε-δ definition isn't just a description of a limit; that's what a limit is in mathematics. It's not a pretty graph or a table of values, but such methods help us to understand the nature of a limit. A math teacher should emphasize that: if you choose to learn mathematics, then as an important mathematical idea, you should learn this.
If all you need is how to use a limit in practical, day to day life, such as understanding instantaneous velocity or approximating marginal revenue, then that's fine. You don't need to learn it, but if you take a Traditional Calculus course, don't expect a math teacher to cater exclusively to your non-mathematical needs. Its purpose is to teach mathematics and to emphasize mathematical thinking.
Maybe what is needed is "Calculus I for Scientists and Engineers" or "Calculus I for Economists and Sociologists" or "Calculus I for Mathematicians," and this notion of Reformed Calculus is a step towards that direction. Maybe it is "watered down," but if planned correctly, a Reformed Calculus class teaches you what you need in order to work in your own field. It doesn't teach you what mathematics is like, because that is not its purpose.
I say: if you choose to allow Reformed Calculus classes, then you should also keep a few alternative Traditional Calculus classes. It's a specialization of needs: students are different and their studies demand different approaches. The coursework should reflect that.
If you're not going into higher-level, proof-based mathematics courses, then it can be argued that it isn't necessary to know the rigorous definition of a limit.
An interesting point. If you choose to view courses in a basic Calculus sequence (Calc I, II, possibly III and Diff Eq) as general-ed requirements, and if you will never venture into higher-level pure mathematics (where logical arguments and geometric ideas are more important than computational methods) then perhaps there is little to no need for such rigor as the ε-δ definition of a limit.
What bothers me is whether we demand reductions in other general-ed courses.
- Take a freshman writing class - if you're not going to be a Lit or humanities major, then does it mean that you don't have to analyze your readings as deeply? Does it mean that your essays don't have to be as circumspect and readable?
- Consider a first course in programming, say in C or in JAVA - does it mean that you don't have to learn to comment your code?
The ε-δ definition isn't just a description of a limit; that's what a limit is in mathematics. It's not a pretty graph or a table of values, but such methods help us to understand the nature of a limit. A math teacher should emphasize that: if you choose to learn mathematics, then as an important mathematical idea, you should learn this.
If all you need is how to use a limit in practical, day to day life, such as understanding instantaneous velocity or approximating marginal revenue, then that's fine. You don't need to learn it, but if you take a Traditional Calculus course, don't expect a math teacher to cater exclusively to your non-mathematical needs. Its purpose is to teach mathematics and to emphasize mathematical thinking.
Maybe what is needed is "Calculus I for Scientists and Engineers" or "Calculus I for Economists and Sociologists" or "Calculus I for Mathematicians," and this notion of Reformed Calculus is a step towards that direction. Maybe it is "watered down," but if planned correctly, a Reformed Calculus class teaches you what you need in order to work in your own field. It doesn't teach you what mathematics is like, because that is not its purpose.
I say: if you choose to allow Reformed Calculus classes, then you should also keep a few alternative Traditional Calculus classes. It's a specialization of needs: students are different and their studies demand different approaches. The coursework should reflect that.
Wednesday, September 14, 2005
embracing the mundane ..
EDIT (AS OF 15 SEPT 2005, 5:30 PM): About the "More Mathematical" part: never mind. I made a mistake while trying to find a mistake, so there are no old mistakes, only new ones.
Despite my worries, which were silly and without much point, the advisor meeting went reasonably well. I get the feeling I should write up some results, and prove new things to further the theory.
Aside from my last post (and before that, an article post, which is negligible), I haven't posted very regularly on this weblog. More than anything, my posts seem to occur in blitzes, and I have a hypothesis on why: it's because my life, even my mathematical one [1], is hardly exciting. Perhaps it takes about a fortnight before something noteworthy happens.
So how do I combat this temporal affliction? I can think of one simple answer, right away: don't wait for the noteworthy stuff; just write a lot of trivial posts! I will embrace and extoll the mundane! It's not like my weblog is really good entertainment, anyways. q:
So today I will tell two bits of news, and one is more mathematical than the other:
[1] Some would argue that my mathematical life is my only life, which could be justified: during a semester I might spend north of eight (8) hours in my office in the Department for six (6) days of the week. The parties I attend are mathmo parties, and aside from a few friends and former housemates, I know very few non-mathmos in Ann Arbor. (;
[2] I suppose this betrays a latent sense of vanity in me.
Despite my worries, which were silly and without much point, the advisor meeting went reasonably well. I get the feeling I should write up some results, and prove new things to further the theory.
Aside from my last post (and before that, an article post, which is negligible), I haven't posted very regularly on this weblog. More than anything, my posts seem to occur in blitzes, and I have a hypothesis on why: it's because my life, even my mathematical one [1], is hardly exciting. Perhaps it takes about a fortnight before something noteworthy happens.
So how do I combat this temporal affliction? I can think of one simple answer, right away: don't wait for the noteworthy stuff; just write a lot of trivial posts! I will embrace and extoll the mundane! It's not like my weblog is really good entertainment, anyways. q:
So today I will tell two bits of news, and one is more mathematical than the other:
- More Mathematical
- I think I made a computational mistake in the last proof I showed to my advisor, which is both bad and good. It's bad because .. well, errors are inherently bad in academia and in particular, mathematics: they detract from the foundation of rigor and fact that comprises our body of knowledge.
However, it's good because the three of us (a visiting prof was also observing our discussion) were kept mystified at this strange exponent from my Lebesgue theory argument. If you know about this sort of thing - Hölder conjugates and Sobolev conjugates, for instance - then they often take a certain form. This exponent of mine was really out there.
Of course, I have to check again that my mistake is, in fact, a mistake, and that I didn't make a mistake while searching for a mistake.
Zounds! This could be worse than compiling computer programs!
- Less Mathematical (but somewhat pertinent)
- I was surfing through the Slashdot website and reading idly, I chanced upon this new facet of Google: Google Blog Search!
Impressed, I did the first thing I could think of [2]: I ran a search under my own name. This website was the 38th hit, which humbled me .. and for the record, the first 37 hits are from a UK blog: blog.fatality.co.uk.
So I have a British weblog doppelganger. Huh. From reading a few random posts in May 2005, his also embraces the mundane .. (;
[1] Some would argue that my mathematical life is my only life, which could be justified: during a semester I might spend north of eight (8) hours in my office in the Department for six (6) days of the week. The parties I attend are mathmo parties, and aside from a few friends and former housemates, I know very few non-mathmos in Ann Arbor. (;
[2] I suppose this betrays a latent sense of vanity in me.
Tuesday, September 13, 2005
Fall Term Life.
Teaching is taking more time than I had thought.
Students actually show up during my office hours, and yesterday when I had no office hours, I was barraged with questions about Team Homework [1] after class. Some of them even followed me to my office, and so did the questions.
Thinking about it, if not for the quiz I administered, the same thing could have happened today. The results aren't going to be terribly pretty, I fear.
There's nothing like a steady job to make you long for those uninterrupted workdays during the summer. Never mind the fact that I barely accomplished anything ..
.. but to be honest, I was living under an illusion: that when fall came, life would be better. I'd become a more responsible person, manage my time more effectively, and it would be more likely that I'd accomplish my daily and weekly goals.
Oddly enough, almost all of those came true ..
.. except the "life would be better" part.
I'm accomplishing much, but it leaves me drained and I crash at 1 am on most nights, if not before. Mathematics doesn't get me eager and excited, as before. I get my work done, but just barely: there seem like so many little things I should be doing for research and thesis work that it's hard enough just to get started .. and at some point, I need to remember to talk with my advisor about a syllabus for my Prelim Exam, which would hopefully happen this December.
Thinking about it now, I'm not sure what "better" means, or should mean. I envisioned myself happy, but let's face it: that's never going to happen. I'm too good at being pessimistic to leave things well enough alone.
Maybe it's enough to be productive and have work to do, and in that way, have a purpose. Those younger days of summer were bits of fun, but they were also empty and unfulfilled .. and a bit lonely, since everyone would be leaving at different times for home or for conferences.
It could be worse. At least I don't have written homework anymore. \:
[1] Over here we do have cooperative mathematics assignments for PreCalc, Calc I, and Calc II; they're much like lab reports and often involve word problems and a fair bit of frustration -- for the students AND the instructors ..
Students actually show up during my office hours, and yesterday when I had no office hours, I was barraged with questions about Team Homework [1] after class. Some of them even followed me to my office, and so did the questions.
Thinking about it, if not for the quiz I administered, the same thing could have happened today. The results aren't going to be terribly pretty, I fear.
There's nothing like a steady job to make you long for those uninterrupted workdays during the summer. Never mind the fact that I barely accomplished anything ..
(proved a few computational lemmas, but hardly anything to shout at)
.. but to be honest, I was living under an illusion: that when fall came, life would be better. I'd become a more responsible person, manage my time more effectively, and it would be more likely that I'd accomplish my daily and weekly goals.
Oddly enough, almost all of those came true ..
.. except the "life would be better" part.
I'm accomplishing much, but it leaves me drained and I crash at 1 am on most nights, if not before. Mathematics doesn't get me eager and excited, as before. I get my work done, but just barely: there seem like so many little things I should be doing for research and thesis work that it's hard enough just to get started .. and at some point, I need to remember to talk with my advisor about a syllabus for my Prelim Exam, which would hopefully happen this December.
Thinking about it now, I'm not sure what "better" means, or should mean. I envisioned myself happy, but let's face it: that's never going to happen. I'm too good at being pessimistic to leave things well enough alone.
Maybe it's enough to be productive and have work to do, and in that way, have a purpose. Those younger days of summer were bits of fun, but they were also empty and unfulfilled .. and a bit lonely, since everyone would be leaving at different times for home or for conferences.
It could be worse. At least I don't have written homework anymore. \:
[1] Over here we do have cooperative mathematics assignments for PreCalc, Calc I, and Calc II; they're much like lab reports and often involve word problems and a fair bit of frustration -- for the students AND the instructors ..
Saturday, September 10, 2005
something to read if you're bored
I typically try to avoid article posts on this weblog, but I thought these few paragraphs were interesting, if only as a stimulus towards thought. It's from an article in the electronic version of the magazine, the Economist.
What, if anything, can be done? Techno-utopians believe that higher education is ripe for revolution. The university, they say, is a hopelessly antiquated institution, wedded to outdated practices such as tenure and lectures, and incapable of serving a new world of mass audiences and just-in-time information. “Thirty years from now the big university campuses will be relics,” says Peter Drucker, a veteran management guru. “I consider the American research university of the past 40 years to be a failure.” Fortunately, in his view, help is on the way in the form of internet tuition and for-profit universities.
Cultural conservatives, on the other hand, believe that the best way forward is backward. The two ruling principles of modern higher-education policy—democracy and utility—are “degradations of the academic dogma”, to borrow a phrase from the late Robert Nisbet, another sociologist. They think it is foolish to waste higher education on people who would rather study “Seinfeld” than Socrates, and disingenuous to confuse the pursuit of truth with the pursuit of profit.
The conservative argument falls at the first hurdle: practicality. Higher education is rapidly going the way of secondary education: it is becoming a universal aspiration. The techno-utopian position is superficially more attractive. The internet will surely influence teaching, and for-profit companies are bound to shake up a moribund marketplace. But there are limits.
Apart from suggesting ideas and shooting them down, this article does try to isolate an important issue. Surprisingly enough, the author has good things to say about American university education:
The problem for policymakers is how to create a system of higher education that balances the twin demands of excellence and mass access, that makes room for global elite universities while also catering for large numbers of average students, that exploits the opportunities provided by new technology while also recognising that education requires a human touch.
As it happens, we already possess a successful model of how to organise higher education: America's. That country has almost a monopoly on the world's best universities (see table 1), but also provides access to higher education for the bulk of those who deserve it. The success of American higher education is not just a result of money (though that helps); it is the result of organisation. American universities are much less dependent on the state than are their competitors abroad. They derive their income from a wide variety of sources, from fee-paying students to nostalgic alumni, from hard-headed businessmen to generous philanthropists. And they come in a wide variety of shapes and sizes, from Princeton and Yale to Kalamazoo community college.
What, if anything, can be done? Techno-utopians believe that higher education is ripe for revolution. The university, they say, is a hopelessly antiquated institution, wedded to outdated practices such as tenure and lectures, and incapable of serving a new world of mass audiences and just-in-time information. “Thirty years from now the big university campuses will be relics,” says Peter Drucker, a veteran management guru. “I consider the American research university of the past 40 years to be a failure.” Fortunately, in his view, help is on the way in the form of internet tuition and for-profit universities.
Cultural conservatives, on the other hand, believe that the best way forward is backward. The two ruling principles of modern higher-education policy—democracy and utility—are “degradations of the academic dogma”, to borrow a phrase from the late Robert Nisbet, another sociologist. They think it is foolish to waste higher education on people who would rather study “Seinfeld” than Socrates, and disingenuous to confuse the pursuit of truth with the pursuit of profit.
The conservative argument falls at the first hurdle: practicality. Higher education is rapidly going the way of secondary education: it is becoming a universal aspiration. The techno-utopian position is superficially more attractive. The internet will surely influence teaching, and for-profit companies are bound to shake up a moribund marketplace. But there are limits.
Apart from suggesting ideas and shooting them down, this article does try to isolate an important issue. Surprisingly enough, the author has good things to say about American university education:
The problem for policymakers is how to create a system of higher education that balances the twin demands of excellence and mass access, that makes room for global elite universities while also catering for large numbers of average students, that exploits the opportunities provided by new technology while also recognising that education requires a human touch.
As it happens, we already possess a successful model of how to organise higher education: America's. That country has almost a monopoly on the world's best universities (see table 1), but also provides access to higher education for the bulk of those who deserve it. The success of American higher education is not just a result of money (though that helps); it is the result of organisation. American universities are much less dependent on the state than are their competitors abroad. They derive their income from a wide variety of sources, from fee-paying students to nostalgic alumni, from hard-headed businessmen to generous philanthropists. And they come in a wide variety of shapes and sizes, from Princeton and Yale to Kalamazoo community college.
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