A bit of a side note, but you caught my eye with the phase-space/Lagrangian/Hamiltonian methods. I always loved those methods (including Fourier Transforms).. but that seems to make me an oddity for having both struggled to pass Calculus 2 (as in with a B) while aceing the Classical Mechanics math for Hamiltonian and Lagrange methods and all those phase space problem domains. Makes me suspect that people tend to comprehend certain subsets of math better than others. Still those mathematical methods are going to beyond most first year undergrads.