Probability Theory course is actually an introduction to the study of statistics and probability, but based upon the usage of Calculus to study both discrete and continuous aspects of the subject. The main difference is in how these topics are approached. For example, in a basic stats class, confidence intervals are introduced as a way to describe the distribution of parameters (i.e. how spread out your estimated results are). The focus is on how to make and interpret these intervals. With a calculus based statistics approach, functions are derived for these intervals .