[alleycat5000]

Check out https://www.chebfun.org/ if you want to see some crazy stuff you can do with polynomials!

Also the book Approximation Theory and Approximation Practice

https://epubs.siam.org/doi/book/10.1137/1.9781611975949

is really great, by the author of Chebfun.

[IIAOPSW]

Approximate approximation theory practice.