The Fast Fourier transform is one of my favorites. Aside from its usual place in signal analysis, it’s useful for performing convolutions (see convolution theorem), computing derivatives, and other things. Plus, it’s super satisfying to walk through the derivation from the mathematics and see the Cooley-Tukey algorithm pop out at the end. That was one of my favorite sections to teach when I taught a data analysis class a decade and a half ago.
