Greg Stanton

Wouldn't it be great if beginners could easily program #math animations directly in the browser, share them, and *interact* with them? Well... youtu.be/Br40z-lpC3o

@CoryMSimon There's a precise connection between the discrete generating functions from de Moivre (they solve recurrence relations, i.e. difference equations) and the continuous Laplace transform (it solves differential equations). Very cool story, but that's for another day!

@CoryMSimon So there you have it. You now have the short version (in a single tweet), and a longer version haha. I hope you don't mind the extra detail. That's not the full story, of course. What about other uses of the Laplace transform, like solving differential equations?

finally got around to learning about moment-generating functions (MGFs) for dealing with probability distributions. the MGF for a random variable is just a flipped, two-sided Laplace transform of its probability density. take a derivative of the MGF and evaluate at zero, voilà, we get a moment of the distribution, explaining the name. web.ma.utexas.edu/users/gordanz/…