The excellent Nerd Wisdom website steered me toward a most unusual book about understand classical mechanics (Lagrangian and friends, see contents for details) precisely enough that computers can manipulate the expressions involved. Not numerical values, expressions.
I remember that when I learned about all these stuffs back in college, I was a master of symbol manipulation and automatically assumed or ignored details as necessary to arrive at the final solutions. Many of my friends had more trouble doing this since they were more precise thinkers and never got used to hand-waving arguments involved. This book would be a great boon to them. There’s no ambiguity left in the symbols if computers can understand them.
Young physicists in training might find this useful too.