GCM25: Noether's theorem, Noetherian charge, & conserved quantities

We begin gently by discussing the connection between symmetry of time, space translations, and rotations and the corresponding conservation of energy, linear momentum, and angular momentum, respectively. Then we kick into high gear, and discuss the set of all Lie group transformations that leave invariant a certain modified (by exact time differential) action functional invariant, to the full version of Noether's theorem. (In the second part we use basic symplectic geometry notation, but the earlier part is completely elementary and uses only calculus.)