In the branch of probability called "large deviations," rates of convergence (e.g. of the sample mean) are considered. The theory makes use of the moment generating function. So, particularly for sums of independent and identically distributed random variables, the theory can be made accessible to senior undergraduates after a first course in stochastic processes. This paper describes a directed independent study in large deviations offered to a strong senior, providing a sample outline and discussion of resources. Learning points are also highlighted