The Shadowy World of Umbral Calculus

An introduction to a famously enigmatic area of math, for calculus students of all levels ↓ Info and Timestamps ↓ In this video we use a primer on discrete calculus to motivate an exploration of the idea you saw in the thumbnail, deriving 2 summation methods along the way! This was made for the 2022 Summer of Math Exposition (#SoME2), an annual jam encouraging new creators like me to make content like this. It’s been a really satisfying project to complete, and I’ll definitely be making more in the future! Discord Server: Patreon: 0:00 Intro 1:28 Forward Differences 2:49 Summation 5:59 Falling Powers 7:23 Umbral Calculus 9:53 Stirling Numbers 11:39 Umbral Exponentials 13:27 Newton’s Forward Difference Formula 14:31 Thanks for watching! Music: Chris Haugen - Glacier Chris Haugen - Northern Lights #umbral #calculus Corrections: 7:13 denominator should be (x 1)(x 2)...(x n 1) - Jose V 13:13 and so ϕ(1/x) = 1/(x 1) - Jose V 13:22 ϕe^-x is undefined, and the other “curious equation“ shown means that implicitly applying ϕ to a circle gives a logarithmic spiral - Discord community