Explain "what is math" to non-math person
...and how they can learn.
What's the point?
- patterns
[beautiful basic structure]
arithmetic = spelling;
there's a *poetry*.
It's an unknown beauty.
...like poetry in another language, wagashi/kaiseki, etc.
Much of beauty in science is math!
what's basically taught are computations:
arithmetic algorithms,
and some in calc
...b/c useful to do/learn other subjects.
It takes a *huge* amount of time.
Think of it like learning to play the piano.
Lotta combinatorics is not technical,
but still requires rigorous thinking;
if want a taste, that's a good place to go.
[Concrete math?]
Good goals would be:
- Galois theory
- Fourier theory
- Lie theory
other stuff v. beautiful but more technical
(Lie algebras)
really, really want feedback
*group theory / basic algebra class is the key one*
it's *new* and *different*
Artin's "Algebra" / Dummit and Foote
Key things to learn:
- math thinking: rigor, high abstraction
- repertoir/breadth