Differentiation: the good, the bad, and the ugly [slides available]

Abstract

For most (sufficiently simple) smooth functions, most high school calculus students can compute its derivative by repeated application of calculus identities (derivatives of simple functions, chain rule, etc.). In this talk I aim to convince you that this simple topic leads to some surprisingly difficult and interesting mathematical problems. I will discuss how derivatives are calculated in real-world settings, and show that without proper care, you can get catastrophically bad results. I will then introduce some advanced techniques that overcome these issues.

Lindon Roberts

Lecturer

My research is in numerical analysis and data science, particularly nonconvex and derivative-free optimization.