BenCrowder.net » Math http://bencrowder.net I make stuff. Wed, 17 Mar 2010 23:47:48 +0000 http://wordpress.org/?v=2.9.2 en hourly 1 Inside out http://bencrowder.net/blog/2006/09/inside-out/ http://bencrowder.net/blog/2006/09/inside-out/#comments Tue, 19 Sep 2006 13:52:54 +0000 Ben http://www.topofthemountains.net/2006/09/19/inside-out/ From Thought Provoking Message of the Day, I read about the “Worm Whisperer” this morning. Quite interesting — Kelly Dorgan “has challenged a century-old theory, endorsed by none other than Charles Darwin, about how worms move.” Everyone used to think that worms (and other burrowing creatures) would actually eat the mud, ingest it, and then excrete it. Not anymore:

By studying the stress fields around the worms, Dorgan discovered that they actually launch their mouths inside out like a wedge to pry open the mud. Then they ease into the space opened by the crack. To keep moving, they just keep leveraging the crack.

That’s cool. :)

There are nine other people profiled in the Popular Science article, including Nima Arkani-Hamed (fifth dimension, multiple universes), Melody Swartz (growing organs), Omar Yaghi (hydrogen nanoscaffolds), and Terry Tao (cleaning up jumbled signals mathematically). Fascinating stuff, really — I recommend reading through all of the articles.

[tags]Popular Science, Kelly Dorgan, Nima Arkani-Hamed, Melody Swartz, Omar Yaghi, Terry Tao[/tags]

]]> http://bencrowder.net/blog/2006/09/inside-out/feed/ 0 (cons calculus (cdr ‘(eating is fun))) http://bencrowder.net/blog/2006/08/cons-calculus-cdr-eating-is-fun/ http://bencrowder.net/blog/2006/08/cons-calculus-cdr-eating-is-fun/#comments Wed, 16 Aug 2006 16:03:26 +0000 Ben http://outsidethebox.blankslate.net/2006/08/16/cons-calculus-cdr-eating-is-fun/ Last night I spent an hour or so working through Calculus and Pizza: A Cookbook for the Hungry Mind. While I don’t care so much for all the pizza/food stuff (extra fluff that gets in the way of what I’m after), the math is good. I’ve relearned how to do derivatives, find local minima and maxima, use the chain rule and extended power rule, and so on. Still haven’t gotten to integrals yet, though. The calculus is pretty easy, I must admit; the only thing that keeps hanging me up is the algebra. Most of the algebra is a piece of cake, of course, but there are little bits and pieces here and there that I keep forgetting. But it’s coming back.

After that, I picked up The Little Schemer and spent a most enjoyable two hours working through the first 80 pages. At first I didn’t intend to actually write all of the little functions you’re expected to write, but I’m glad I did. And to my small surprise, I was able to write all of them without too much trouble. We’re talking functions like +, -, >, and < , folks. Simple stuff. It’s like writing the language from scratch yourself. (Yes, I know there’s more truth to that than there may seem at first. :))

The coolest thing is learning how to solve problems recursively rather than iteratively. Sure, some of this stuff would be far easier using a for loop, but using recursion like this means no side effects (at least if I understand correctly), and that’s sweet. I can’t wait to finish the rest of the book and move on to The Seasoned Schemer. (And I’ll be glad when we move on to higher-level programs, too.)

Oh, the parentheses in Scheme don’t bother me at all — in fact, I rather like them. :)

[tags]calculus, Scheme[/tags]

]]> http://bencrowder.net/blog/2006/08/cons-calculus-cdr-eating-is-fun/feed/ 0 Binomials and cubic splines and such http://bencrowder.net/blog/2006/08/binomials-and-cubic-splines-and-such/ http://bencrowder.net/blog/2006/08/binomials-and-cubic-splines-and-such/#comments Tue, 15 Aug 2006 23:14:53 +0000 Ben http://www.topofthemountains.net/2006/08/15/binomials-and-cubic-splines-and-such/ Last night I started reading Calculus and Pizza, going through the first four or five chapters (along with the exercises). I love calculus! Derivatives have come back from the misty hollow of my memory with lightning speed, and the other bits (the chain rule, etc.) are hot on their heels. It’s tremendously fun. As for algebra, I’d completely forgotten about the binomial theorem (namely, (a+b)2 = a2 + 2ab + b2), and a lot of the exponential rules were a bit rusty (square root of x is the same as x1/2). It’s nice to remember what I once knew. And before long I’ll have enough of it under my belt that I’ll be able to go on and learn all the cool stuff I never got to. Mmm. :)

And all this means I finally get to use my trusty old TI-86 again…

[tags]calculus[/tags]

]]> http://bencrowder.net/blog/2006/08/binomials-and-cubic-splines-and-such/feed/ 3 Proofs and stuff http://bencrowder.net/blog/2006/08/proofs-and-stuff/ http://bencrowder.net/blog/2006/08/proofs-and-stuff/#comments Sun, 13 Aug 2006 02:47:52 +0000 Ben http://outsidethebox.blankslate.net/2006/08/12/proofs-and-stuff/ I read Stevey’s Math Every Day post, and darn it all, I need to start brushing up on my math! It’s been ages since I studied it (five years, to be precise), and while a fair amount is still with me (like addition and subtraction ;)), it’d be nice to re-master everything I once knew. And then I’ll be able to start learning all the really cool stuff in math. Mmm.

Problem is, I’m not quite sure how to go about doing it. Pick up a textbook and work through the problems, one by one? Find some other kind of math book? Wikipedia? MathWorld? I don’t know. I’m not even exactly sure what order I should study things in. I do know that calculus was last, though. :)

I think I’m going to do what Stevey did — “math every day.” Ten minutes a day will be good for starters, and on days when I have the time, I’ll be able to do more. Mmm, I miss math.

[tags]math[/tags]

]]> http://bencrowder.net/blog/2006/08/proofs-and-stuff/feed/ 2 It’s Greek to me http://bencrowder.net/blog/2006/03/its-greek-to-me/ http://bencrowder.net/blog/2006/03/its-greek-to-me/#comments Thu, 02 Mar 2006 04:51:38 +0000 Ben http://digitalbridge.blankslate.net/2006/03/01/its-greek-to-me/ Last night I spent the evening reading Paul Graham essays (and thus wanting to learn Lisp :)). Also read Eric Raymond’s How to Become a Hacker. Interestingly enough, the brief discussions of math therein were like drops of water to a parched tongue, making me salivate for more. The last math I really did was AP Calculus back five years ago in high school, and all I can remember of that is the word “integral,” the word “derivative,” and something about dy over dx (I think). So I pulled out my copy of Euclid’s The Elements (the three-volume Dover set) and started reading through the propositions. (Disclaimer: despite the following sentence, I still think I’m a normal, healthy human being.) It was fun. :) Today I stopped in at the library after lunch and picked up a neat book called The Nature and Power of Mathematics. I’ve only read 13 pages of it so far, but the two forces at work are readily apparent: the first is a strong desire to re-learn what I’ve forgotten and then to push the boundaries of my knowledge and burst out into new, glorious horizons of mathematical beauty; the second is a befuddled cloud that sits on my head and reminds me just how little I know about math nowadays, and that’s why half of what I read is hard to understand. But obstacles are meant to be overcome, so I’ll press on until I can comprehend multivariable calculus and all that. To infinity (wait, don’t limits have something to do with infinity? It’s starting to come back…) and beyond! :)

[tags]math, Paul Graham, Euclid[/tags]

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