With respect to "Fermi Problem" two things. First MIT is offering "Street-Fighting Math <http://www.edx.org/course/mitx/mitx-6-sfmx-street-fighting-math-1501>: Teaches, as the antidote to rigor mortis, the art of educated guessing and opportunistic problem solving." as a MOOC (free!) starting in March.
Second, my favorite dimensional analysis problem: you presumably know that the fuel efficiency of a car is often expressed as litres of petrol per 100km, right? Well, litres of petrol are a volume measure, and 100km is a length measure. Volume is length^3, so litres of petrol per 100km is length^3/length = length^2 What might the "real world" significance of this area be? (Answer later if no one gets/spoils it.) -- Charles
