As an example of an application of Mathematics to finance, we will look at Hurst exponents, omitting the technical details. Given a time series, the Hurst exponent (H) of the mathematical object is a single number between 0 and 1. What can a single number tell us about the series? It can be interpreted in many ways, one of them is that it measures the jaggedness or smoothness of the series. It helps us classify time series. For example, one of the basic questions, is whether a time series is purely random (a random walk or Brownian movement) or not. Many people have suggested that financial data such as stock prices are random, Hurst exponent helps explain that it is not. H = 1/2 is a random walk with no memory of past states, H between 1/2 and 1 is a persistent time series, where the series has long term memory, and H between 0 and 1/2 is an anti-persistent time series (the persistence works in a negative way). A mean reverting series for example is anti-persistent, but the conver...