Read Edwin Jaynes.
The problem with most Probability and Statistics courses is the axiomatic approach. Purely formalism. Here are the rules - you can play by them if you want to.
Jaynes was such a revelation for me, because he starts with something you want, not arbitrary rules and conventions. He builds probability theory on basic desiredata of reason that you that make sense. He had reasons for my "whys?".
Also, standard statistics classes always seemed a bit perverse to me - logically backward. They always just felt wrong. Jaynes approach replac... (read more)
I think this is a most awesome mistype of desiderata.