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Newtonian mechanics
Harmonics
Orbits, Galileo's laws, Copernicus's laws
Gravity and the two-body problem
Paths
Symmetry
Fields
Electromagnetism, waves, action on a field, least action on a field and gauge theory
Noether's theorem
Using the Lagrangian and the principle of least action to derive the Euler-Lagrange equations
Hamiltonian
Music
symmetries and conservation laws and noether’s theorem (time -> energy; space -> momentum; rotation -> angular momentum)