Archive for August, 2007
Our overlords have caused these damnable devices to take over more and more of our lives and they just keep telling me, “Get out of here, Finchley!”. And what I want to know is: how much trouble would it take for your typical technophile to feel that, say, their cel phone was too much trouble? Because it looks to me like if you had to, say, wrestle an alligator every day before you were allowed to turn the thing on, why then, you’d just have to start honing your alligator-wrestling skills pretty quick, wouldn’t you. And probably start buttonholing everyone about your latest alligator-wrestling tricks before too long in the bargain.
Or maybe, and this is my last thin thread of hope on the topic, a lot more people resent having to wrestle those alligators than I imagine—and they just won’t admit it. Maybe because their living depends on it, say. I guess I could live with that.
My next rant will have something to do with actual math.
Alexandre Borovik has revised his manifesto. I’d sure like to see more such commentary on “the current discourse of university teaching”. But that’s probably asking too much (unless, the obvious, I actually try to contribute something along those lines instead of, what’s much easier, just griping all the time). It’s kind of weird. By sticking to some very particular issue—reopening a school in Turkey, for example—it’s possible to really make a difference in people’s lives. But once you get into “big picture” stuff, forces of the status quo just seem to emerge out of everywhere at once and somehow (almost!) always seem to sideline any interesting ideas far away from whatever audience might benefit from ’em. Anyhow, Prof. B doesn’t let this kind of thing bother him; just goes right ahead and does the work. There’s probably somebody around here who could learn something from that …
Estimate using rectangles and
a. the right hand rule.
b. the left hand rule.
c. the average of a and b.
Solution. The width of each interval is … so we have
Note that the terms of each sum are the reciprocals of the endpoints ; this is of course because our integrand () is the reciprocal function. Finally, since the integral is “obviously” equal to , and , our answer in c is reasonable.
I’m not saying textbook problems have to use real-world data. In fact, as far as I’m concerned, there’s way too much emphasis on “applications” in college maths (and below). But.
For heck sake, when you make stuff up, do it carefully enough that it isn’t obviously impossible. I’ve just come from working with a statistics student. We were supposed to test the claim that a certain population proportion was 10% against a sample proportion of 13%, based on n= 57 data points (at some stated confidence level that I’ve forgotten). But wait a minute. You can’t get 13% from a sample of 57 subjects: (i.e., 12%) and (i.e., 14%). Now, this is from a textbook. You should see some of the nonsense the actual instructors make up. And what I am saying is: quit telling stupid lies. Or become an administrator or something.