I'm attempting to put together a list of topics for a general education course centered around "great ideas in mathematics," and I'm looking for input. Ultimately, I would like topics to be approachable for those with a background only up through precalculus.
Things I've thought of so far include the following:
- Numeral systems
- Graph theory
- Infinite sums
- Noneuclidean geometry
- And much more!
Note: I'm interested in especially influential or revolutionary ideas that tend to fall on the purer side of math. Measures of fun and/or practicality are of secondary importance to me, as I tend to be better at convincing students that something is interesting, rather than entertaining or useful.
Something like RSA cryptography is great, because it's somewhat fun/practical while also having a really robust theoretical underpinning that allows me to discuss primes, modular arithmetic, etc.
What do you all think? I'd love to hear any additional ideas.