It is a mathematically rich field, with very elegant geometric interpretations of observed phenomena. Has been applied to everything from the motion of the planets to the motions of the stock market. Some information is discrete, and readily represented on finite machines. Other information is not discrete, like the position of the planets, or the temperature in a room, or is too large to deal with, so it is approximated and represented by a smaller set of information. It also sometimes happens that we know that the information is not discrete, but we have discrete samples.
Interpolation is the problem of reconstructing the continuous information from the sample.
An important optimization problem consisting of a linear objective and linear constraints. Molecular dynamics We observe the motion of large collections of molecules as the physical properties of gases, liquids and solids. Molecular dynamics tracks these individual motions to predict bulk properties of matter. Typical simulations involve millions of interacting particles, and are extremely intensive computations. The solution of a problem consisting of some objective whose value is to be maximized or minimized, subject to a set of constraints.