Since the first footprint was at the end of the lunar-lander ladder, the same ladder that was used to get out and get in the Eagle again by Aldrin and Armstrong, my guess is that the very first footprint was already pretty messed up, even before they left the place...

And don't forget the blast from the rocket engine at take of.. that one was sure to wipe it of the face of the moon...

You wanted to know how math applies to physical situations. I had the exact opposite thing. We were told to just use differential equations and not worry about the theoretical foundations. The math we catched up a year later, so we had enough experience with practical situations. While studying Chemical Enigineering we used Atkins "Physical Chemistry" for a dense introduction to thermodynamics and how it applies to chemistry (it also has some mechanics and quantumtheory): http://www.whfreeman.com/pchem7/

Do we live in the same 'Europe'? My Europe (or rather the little part of it that I live in) has a max speed of 120 KM/h. And our friendly neighbour (Germany) has an even better rule: No max speed (unless said otherwise). So I guess you define Europe to end at the borders of your country, which is kind of _not_ the idea.