Comments on: A brief note on mathematics

By: Luke Pacold

Luke Pacold — Sun, 31 Jan 2010 23:39:00 +0000

I think I saw it in "Images of Infinity" when I was much younger, but didn't really understand it until last semester in M380, c/o Prof. Dadok.

By: Carlo Angiuli

Carlo Angiuli — Wed, 27 Jan 2010 02:06:00 +0000

Lots of elegant, accessible things slip through the cracks like that. Another one is Cantor's diagonal argument, which doesn't seem to come up nearly early enough.

By: Joe Pacold

Joe Pacold — Wed, 27 Jan 2010 01:59:00 +0000

If I end up teaching algebra in high school (or at the 100/200-level in college) I am going to work in elementary number theory somehow. It's elegant, accessible, and historically important, but somehow never shows up in the standard classes.

By: Carlo Angiuli

Carlo Angiuli — Tue, 26 Jan 2010 19:36:00 +0000

Sarah: That's a good way to put it. I definitely agree that "advanced" topics should be taught early on; it's a shame that people don't really see the beauty of it all until at least halfway through an undergraduate degree.John: In some sense, definitions and theorems do naturally fall into a partial order under the "prerequisite" comparator. (Assuming you choose one canonical version of each. For instance, you can't really take analysis unless you're familiar with basic calculus.) But the connectedness of these ideas is highly understated, especially pre-college.Brian: Yes, I have. It's a bit overstated, but has some very good points.

By: Brian Slattery

Brian Slattery — Tue, 26 Jan 2010 18:34:00 +0000

Have you read Lockhart's Lament? http://www.maa.org/devlin/LockhartsLament.pdfMight be of interest

By: John Brown

John Brown — Tue, 26 Jan 2010 15:18:00 +0000

I think that the standard math curriculum (up until the point where you might be planning to do this thing for a living) is structured like a progression. People often have this false idea of going "higher" in math, as if it's this really tall ladder that you ascend until you fall off. "How far did you get in math?" is a question that betrays this false premise. It's not just a matter of teaching things as disconnected. They're also pigeonholed into a strict hierarchy.

By: Sarah Tonin Brodsky

Sarah Tonin Brodsky — Tue, 26 Jan 2010 12:02:00 +0000

I believe math is a language for describing the world around us, giving us a means of taking the ideas and concepts within our own mind and transferring them to another's in a way which best attempts to preserve the initial content. Proofs describe, create, and discover such content. The education system definitely does not illuminate the true nature of mathematics until much later in the game; which is extremely unfortunate. I think if more "advanced" mathematics were taught early on then perhaps more non-mathematicians, in particular, would look at the subject in a different, more useful light.good morning.

By: Sarah Brodsky

Sarah Brodsky — Tue, 26 Jan 2010 11:02:00 +0000

By: Carlo Angiuli

Carlo Angiuli — Tue, 26 Jan 2010 10:14:00 +0000

I don't have a concrete thesis at the moment, except perhaps "mathematics classes should be structured differently."

By: Jerry Vinokurov

Jerry Vinokurov — Tue, 26 Jan 2010 10:07:00 +0000

I wonder what your thesis is here. I would agree that mathematics classes do a poor job of connecting seemingly disparate areas of math, though.