How to solve the stochastic partial differential equation that gives a Mat\'ern random field using the finite element method

This tutorial teaches parts of the finite element method (FEM), and solves a stochastic partial differential equation (SPDE). The contents herein are considered "known" in the numerics literature, but for statisticians it is very difficult to find a resource for learning these ideas in a timely manner (without doing a year's worth of courses in numerics). The goal of this tutorial is to be pedagogical and explain the computations/theory to a statistician. This is not a practical tutorial, there is little computer code, and no data analysis.