Comments on: My Favorite Rant From Today

By: Who Invented Calculus: A WebQuest « Continuous Everywhere but Differentiable Nowhere

Wed, 18 Nov 2009 02:21:20 +0000

[...] of limits. They didn’t know anything about derivatives or integrals, or what calculus is, except for my rant. I wanted them to do some research on their own to learn what calculus [...]

By: samjshah

samjshah — Sun, 27 Sep 2009 00:43:52 +0000

Oh, TOTAL TOTAL mock rant. I was jumping up and down, and getting all excited about what we are going to be able to do with the course, now that we’re finally getting started on proper calculus topics…

By: Scott

Scott — Sat, 26 Sep 2009 23:23:29 +0000

Is this a genuine rant or a mock rant you give to your kids?

I wouldn’t expect many high schoolers to know what Calculus is before they have taken the course. You say they’ve signed up for it, well sure… its the “next class”. They’re not exactly choosing it.

I understand that you want to explain what they’re about to be studying and that you want to provide motivation, but do you seriously expect them to be able to give you an answer?

How many kids could answer “What is Algebra?” in week 3 of that class?

By: samjshah

samjshah — Sat, 26 Sep 2009 02:46:10 +0000

True, but I don’t want to give them a treatise on calculus. I just wanted to get them excited about what’s on the horizon. Pieces here and there.

Honestly, I don’t know what I’d do if I were asked to write 1 page on the definition of calculus — the scope, the structure, the philosophical backbone. Maybe one day this year I’ll be so inspired to see what I come up with.

By: Will Farris

Will Farris — Fri, 25 Sep 2009 16:20:51 +0000

Actually, I guess you did sort of hit it with “It’s the study of the very small to learn about the very big .” But that definition also applies to atomic theory, no? :-)

By: Will Farris

Will Farris — Fri, 25 Sep 2009 16:08:31 +0000

Great lead in, but you never did really answer your question. What is your answer to them? My answer is that calculus is about infinite summations and quantities called infinitesimals, or hyperreals, that are “alive” entities, dynamic rather than static things that are always in a process of getting arbitrarily smaller. Limits, of course, are a different perspective. They give structure or definition to the “approaching zero” process. It is the process, not destination, that is of primary interest. See here, class, I hold in my hand an infinitesimal dx. Now, it just buzzed out of sight but it is still there, because when I pop it into denominators, nothing blows up! So now the next philosophical question is: can we consider dy/dx to be a fraction given that it follows all the standard operations of division?

By: Kristen

Kristen — Fri, 25 Sep 2009 03:00:40 +0000

Sam, this is funny… every year I ask my precalc kids what exactly “precalculus” is. I know there’s no good definition, but they always answer “the class before calculus”. So I guess we’re just going around and around!

(At least you can give them a good vision of calculus! Precalc not so much.)