This is lecture 21 in the series "Introduction to the Mathematics of Climate" offered at the University of Minnesota in 2014 with the support of MCRN and The Institute for Mathematics and its Applications.
This lecture introduces the concept of chaos in light of the question "can we predict the future?". It begins by translating a series of coin flips into a shift map on binary numbers, then explores the dynamics of a tent map and logistic growth map. In concludes with the observations that (1) deterministic systems can behave randomly and (2) it can be impossible to tell whether a time series results from a stochastic process or a deterministic system.
Colin James Grudzien