Why Study Upper-Level Math?

Hi Brandon,

Maybe the place to start is by asking yourself this question. Why are
_you_ taking pre-calculus? Probably so you can take calculus. And why
do you want to take calculus? Probably because you want to get a
degree in something that will require you to understand calculus. And
what kinds of degrees require you to understand calculus? Pretty much
any kind of science or engineering, including quasi-sciences like
economics.

But there is also this: In Japan, if you want to study Zen Buddhism,
you don't do it by talking about Zen Buddhism. You do it by learning
to do something else, like arrange flowers, or perform a tea ceremony,
or shoot arrows, or draw and strike with a sword. The activity
provides a medium in which the lessons of Zen Buddhism can be explored
and mastered.

Similarly, if you want to learn to become more effective at solving
problems, you don't do it by talking about solving problems. You do it
by solving problems! And math, it turns out, is a particularly good
medium for constructing and solving problems.

Finally, there is a kind of beauty to mathematics that rivals the
beauty that people find in paintings and sculptures and music. But
this beauty doesn't really become apparent until you reach a certain
level of proficiency in the subject. In that sense, making students
take upper-level math courses is a way to try to expose them to that
beauty, for fear that they won't be exposed to it without that kind of
coercion. It's a little like forcing them to learn to play musical
instruments, or participate in sports, whether they want to or not.

Write back if you'd like to talk about this some more, or if you have
any other questions.