School mechanics gives you F = ma and sets you loose. University classical mechanics asks a deeper question: is there a single principle from which all of motion follows? The startling answer is yes — nature moves along the path that makes a quantity called the action stationary, and from that one idea the whole of mechanics reappears, now in a form powerful enough to survive into quantum theory and relativity.

This branch rebuilds mechanics from the top down — the Lagrangian and Hamiltonian formulations, conservation laws and symmetry, central forces and orbits, coupled oscillators and normal modes, rigid-body rotation, and the first glimpse of chaos. It leans hard on the calculus of variations and linear algebra you already have in mathematics.