Example counter
Sep. 7th, 2010 06:19 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
sniffnoy(UNLOCKED May 17 2017)
Well, I survived the first day of my return to teaching.
Conclusions:
1. I should not use the characteristic function of the rationals as an example of a weird function if not everyone in the class is familiar with the concept of rational numbers.
2. Using the photoelectric effect as an example may not have been the best idea, either.
I'm glad I at least thought of the divisor-counting function as an easy example of a function that only makes sense for integers - somehow I didn't last year... (I was almost tempted to use integer complexity, but that is obviously a terrible, terrible, idea.)
-Harry
Well, I survived the first day of my return to teaching.
Conclusions:
1. I should not use the characteristic function of the rationals as an example of a weird function if not everyone in the class is familiar with the concept of rational numbers.
2. Using the photoelectric effect as an example may not have been the best idea, either.
I'm glad I at least thought of the divisor-counting function as an easy example of a function that only makes sense for integers - somehow I didn't last year... (I was almost tempted to use integer complexity, but that is obviously a terrible, terrible, idea.)
-Harry
no subject
Date: 2010-09-07 10:56 pm (UTC)2- How the heck did this come up as a useful example?
For the only integer defined function- why not use integer complexity? It is pretty easy to explain. I explained it to a not terribly mathy 12 year old a while ago. I also suspect that using that example and then saying something like "I'm picking this example because I'm doing research related to it" might actually make math seem more alive (many college students seem to think that mathematicians "spend their time talking about what Newton and other old guys did"- more or less direct line from a student who was confused when I mentioned casually that I was getting a PhD and that that involved having to have original research.)
no subject
Date: 2010-09-08 06:36 am (UTC)No, precalc, as last year.
If so, and they don't know what a rational number is there's a serious problem.
As a result I made a quick historical digression about the Pythagoreans, but I'm not sure how helpful that was for those who didn't already have a handle on the concept. One kid - [switches original entry to protected] :P - asked if I was saying that √2 wasn't a number...
2- How the heck did this come up as a useful example?
The point of today's first class was "What is a function?" Functions are not formulae, etc. I thought photoelectric effect would be a nice example of a piecewise function occurring in nature. Actually the real point was what I did before that - first I just described without saying how it looked, to point out that it's a perfectly sensible function even if we have no idea how it behaves or how to compute it. Any number of things would have worked for that, of course, but I thought having the result be something piecewise (and which I couldn't even write down due to not knowing the numbers) would help illustrate it further.
For the only integer defined function- why not use integer complexity? It is pretty easy to explain.
Easy, perhaps, but not trivial. I didn't want to have to spend time on that when there was an easier example at hand. And as it happened I ended up taking too long on other things as it was...