Let's learn about wavelets!
October 23, 2002 10:14 PM Subscribe
Let's learn about wavelets! OK, let's not. Notice, however, how differently wavelets are introduced across the web, and how widely authors construe terms like "gentle", "beginner", and "approachable." Do you know a website that clearly and creatively describes some complex topic? How do you teach well with the Internet?
Good job, what a fine post. I wonder if anyone has a 'Wavelets for Dummies' site yet?
posted by crunchburger at 10:18 PM on October 23, 2002
posted by crunchburger at 10:18 PM on October 23, 2002
there's something of a tradition for using terms like "gentle" and "introductory" in maths/physics texts that are anything but (somewhere i have a copy of "introductory nuclear physics", which always makes me smile, and i recently bought "elementary number theory" but am still on the first chapter...).
if you really want introductory, it's best to look for a title that includes "for engineers". in fact, googling for "wavelets for engineers" gets your first link, which is pretty good (if you're actually interested in wavelets, numerical recipes has quite a good brief summary - it's the kind of subject where people can get carried away with obscure details related to particular basis functions when really they're all pretty much the same).
anyway, getting back to your question, your examples show exactly how the internet teaches so well (i think it's an excellent technical resource) - it provides information at widely different levels. all you need to do is google a little to find the level you need.
that might imply that people who want to add tutorials to the 'net should first check to see what is out there and then filled the gaps. however, in my limited experience, explaining things is hard, especially explaining complex things in a simple way - you really have to understand a subject well before that's possible. so maybe it's better for people just to add whatever insight they find and let "meta" services (like search engines) provide structure.
posted by andrew cooke at 10:50 PM on October 23, 2002
if you really want introductory, it's best to look for a title that includes "for engineers". in fact, googling for "wavelets for engineers" gets your first link, which is pretty good (if you're actually interested in wavelets, numerical recipes has quite a good brief summary - it's the kind of subject where people can get carried away with obscure details related to particular basis functions when really they're all pretty much the same).
anyway, getting back to your question, your examples show exactly how the internet teaches so well (i think it's an excellent technical resource) - it provides information at widely different levels. all you need to do is google a little to find the level you need.
that might imply that people who want to add tutorials to the 'net should first check to see what is out there and then filled the gaps. however, in my limited experience, explaining things is hard, especially explaining complex things in a simple way - you really have to understand a subject well before that's possible. so maybe it's better for people just to add whatever insight they find and let "meta" services (like search engines) provide structure.
posted by andrew cooke at 10:50 PM on October 23, 2002
ps on a competely different topic, tss, what's so exciting about your apartment that the images need to be password protected?!
posted by andrew cooke at 10:55 PM on October 23, 2002
posted by andrew cooke at 10:55 PM on October 23, 2002
...what's so exciting about your apartment that the images need to be password protected?!
I'm guessing goats. And porn. And goat porn.
posted by Danelope at 11:31 PM on October 23, 2002
I'm guessing goats. And porn. And goat porn.
posted by Danelope at 11:31 PM on October 23, 2002
MIT's Open Courseware might prove to be a useful resource. It's a bit sparse at the moment (and nothing on wavelet analysis that I could see), but there is great potential there if the various departments really get behind the initiative.
Mmmm... wavelets.
posted by Galvatron at 11:59 PM on October 23, 2002
Mmmm... wavelets.
posted by Galvatron at 11:59 PM on October 23, 2002
A very good site that all students should have bookmarked is the Bureau International des Poids et Mesures (BIPM). It's best to get information straight from the horses mouth. I looked it up back when I didn't believe there was a prefix called Yotta, but there is, and it's 1024.
posted by riffola at 12:22 AM on October 24, 2002
posted by riffola at 12:22 AM on October 24, 2002
Yeah, elementary math texts are great. My favorite is Melvyn B. Nathanson's "Elementary Methods in Number Theory," which is the Springer graduate Text in Mathematics number 195. This book nearly killed all who used it in my program last semester; the second half of the book is one big string of summation signs...
(BTW: the second link is my favorite webtest of all time.)
posted by kaibutsu at 4:15 AM on October 24, 2002
(BTW: the second link is my favorite webtest of all time.)
posted by kaibutsu at 4:15 AM on October 24, 2002
Good explanations on the web:
How stuff works
Mathworld
Scienceworld (with separate sections for physics, chemistry, and astronomy).
posted by whatzit at 4:42 AM on October 24, 2002
How stuff works
Mathworld
Scienceworld (with separate sections for physics, chemistry, and astronomy).
posted by whatzit at 4:42 AM on October 24, 2002
Well, the best explanation I've ever had (it wasn't online though, but if thats really a problem I promise to flagellate myself with a wet noodle, or possibly even write it up and put it on my web site) for a somewhat complicated topic was for the Fourier Transform. All waveforms, and sound is an example of a waveform, can be broken up into a series of frequencies that when added together produce the original waveform. In the Fourier Transform each of these waveforms is a sin wave.
So, my poor description out of the way I'll bring up the way this professor brought it up for the slower people in my electrical engineering class. He drew a square wave on the blackboard, and within the square wave drew a sin wave of the same frequency. He showed us it was a pretty good fit, if you looked at the area beneath the two curves it was positive.
Then he drew in a waveform of twice the frequency and showed that, at least as accurately as he was drawing, the areas cancelled out. This isn't a good approximation for a square wave. He continued on and drew a sin wave three times the frequency of the square wave. He showed us that the area was positive but less than the first sin wave.
He then took the two waveforms and visually added them up and showed that it made an even better approximation of the sin wave.
I thought this was a pretty elegant demonstration that didn't require any math, no calculus and convolutions etc. You couldn't go out and apply it, but you could at least understand what it meant.
posted by substrate at 5:14 AM on October 24, 2002
So, my poor description out of the way I'll bring up the way this professor brought it up for the slower people in my electrical engineering class. He drew a square wave on the blackboard, and within the square wave drew a sin wave of the same frequency. He showed us it was a pretty good fit, if you looked at the area beneath the two curves it was positive.
Then he drew in a waveform of twice the frequency and showed that, at least as accurately as he was drawing, the areas cancelled out. This isn't a good approximation for a square wave. He continued on and drew a sin wave three times the frequency of the square wave. He showed us that the area was positive but less than the first sin wave.
He then took the two waveforms and visually added them up and showed that it made an even better approximation of the sin wave.
I thought this was a pretty elegant demonstration that didn't require any math, no calculus and convolutions etc. You couldn't go out and apply it, but you could at least understand what it meant.
posted by substrate at 5:14 AM on October 24, 2002
I'm fond of Wayne Hu's introduction to the cosmic microwave background.
posted by ptermit at 6:54 AM on October 24, 2002
posted by ptermit at 6:54 AM on October 24, 2002
Great post, Tom (if I may use your actual name)! I used to be a math major in another life, but I never did like applied math, so this stuff may be too chewy for me, but I love the presentation and general idea.
posted by languagehat at 9:23 AM on October 24, 2002
posted by languagehat at 9:23 AM on October 24, 2002
Thanks for the responses, everyone...
My apartment photos are protected because I live on the first floor of my building. I don't want to advertise how easy it would be for someone to make off with my goats^H^H^H^H^H computer, digital camera, etc.
posted by tss at 9:59 AM on October 24, 2002
My apartment photos are protected because I live on the first floor of my building. I don't want to advertise how easy it would be for someone to make off with my goats^H^H^H^H^H computer, digital camera, etc.
posted by tss at 9:59 AM on October 24, 2002
Thanks for the great links. I'm glad Whatzit posted Mathworld, of which I have been a fan since back in its pre-CRC days. Somehow, though, I didn't know about Scienceworld, and am very glad to know of it!
posted by Songdog at 10:07 AM on October 24, 2002
posted by Songdog at 10:07 AM on October 24, 2002
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posted by tss at 10:16 PM on October 23, 2002