You're lucky to understand this so well and to get (i) for calculus. I always thought big-O was used more to teach about algorithms (their efficiency), which is where I first encountered it. So maybe Knuth's calls for calculus reform were heeded after all and I'm just behind the times.
On another topic: should we tell Channel 6 that Guido is right here on edu-sig. I think we should help hide him. I saw that documentary about Britney Spears yesterday. Paparazzi have made her life somewhat more difficult than it needs to be, even though she's a karate kid. http://www.channel6tvnews.com/story/agc2dHZuZXdzcgsLEgRjYXJkGPEkDA Kirby On Wed, Dec 10, 2008 at 10:04 PM, DiPierro, Massimo <mdipie...@cs.depaul.edu> wrote: > The problem is that calculus tends to deal with the concept of > infinitesimally small and O(eps) is used for small eps. Computer Science > tends to deal with complexity and O(n) is used for large n. The Big-Oh > definitions are different: > > i) In calculus f(x) in O(g(x)) iff lim_{x\rightarrow 0} f(x)/g(x) < \infty > > ii) In CS f(x) in O(g(x)) iff lim_{x\rightarrow\infty} f(x)/g(x) < \infty > > It is common to use (i) to teach calculus (I was thought that way) but it is > not common to use (ii) to teach algorithms. I do so in my notes for Design > and Analysis of Algorithms [1] > and students like it but many computer scientists believe that using limits > is just an extra step. > > Massimo > > [1]http://bazaar.launchpad.net/%7Emdipierro/algorithms-animator/devel/download/3/csc321notes.pdf-20080914191632-ofooevmsoqqnkrpz-6/csc321notes.pdf?file_id=csc321notes.pdf-20080914191632-ofooevmsoqqnkrpz-6 > > > > > ________________________________________ > From: edu-sig-bounces+mdipierro=cs.depaul....@python.org > [edu-sig-bounces+mdipierro=cs.depaul....@python.org] On Behalf Of kirby urner > [kirby.ur...@gmail.com] > Sent: Wednesday, December 10, 2008 10:39 PM > To: edu-sig@python.org > Subject: Re: [Edu-sig] computer algebra > > On Wed, Dec 10, 2008 at 8:27 PM, Guido van Rossum <gu...@python.org> wrote: > > << SNIP >> > >> There are different schools of thought about this actually. I don't >> think pride comes into it. > > Well, *my* school is quite pompous about it. We think "open oh" is for > sissies. > > But that's just us (quirky). Others more sobering. > > << GOOD STUFF >> > >>> Note that by "open oh" I'm not talking about "big oh", a different >>> notation that I don't think is redundant, agree with Knuth that if >>> your calculus book doesn't include it, you're probably in one of those >>> computer illiterate schools (ETS slave, whatever). >> >> I think that comment is a little out of line. BTW big Oh is not part >> of calculus, it's part of complexity theory, a totally different field >> (more relevant to computers than calculus though). >> > > Not part of calculus as commonly taught today, but *would* be if > Donald Knuth had his way: > > http://micromath.wordpress.com/2008/04/14/donald-knuth-calculus-via-o-notation/ > > Kirby > >> -- >> --Guido van Rossum (home page: http://www.python.org/~guido/) >> > _______________________________________________ > Edu-sig mailing list > Edu-sig@python.org > http://mail.python.org/mailman/listinfo/edu-sig > _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
