Why is probability an under-emphasized subject in most math programs? Why does it seem that the hot topics these days are category theory and algebra? What do you think about the following: A student learns probability (both on the applied side and the pure side) and picks up the real analysis on the way. That way there is a purpose for learning the real analysis.

Can we do this with many mathematical subjects (e.g. first teach from an applied perspective, and learn the pure stuff because it is needed)?

requireprobability at the grad level. – engelbrekt Feb 6 '10 at 20:06