In this talk, I review the mathematical results of the
dynamcis of Bose-Einstein condensate (BEC) and present
some efficient and stable numerical methods to compute ground states
and dynamics of BEC. As preparatory steps,
we take the 3D Gross-Pitaevskii equation (GPE) with an angular
momentum rotation, scale it to obtain a four-parameter model
and show how to reduce it to 2D GPE in certain limiting regimes.
Then we study numerically and asymptotically the
ground states, excited states and quantized vortex
states as well as their energy and chemical potential diagram
in rotating BEC. Some very interesting numerical results are
observed. Finally, we study numerically stability and interaction
of quantized vortices in rotating BEC. Some interesting interaction
patterns will be reported.