Mappings/Applied mathematics/Motivation/Section

Suppose that a particle is moving in space. This process is described by assigning to every point in time ${}t\in \mathbb {R}$ the point in space ${}z(t)\in \mathbb {R} ^{3}$ where the particle is at that time. The running of a computer program that uses altogether ${}s$ memory units can be described by saying for every computing step (which means the execution of a program line) what the content of the memory units is. So to the number ${}n$ counting the computing steps, we assign the tuple

${}(b_{1}(n),\ldots ,b_{s}(n))\in \mathbb {N} ^{s}\,.$

In an election, every voter has to decide for exactly one party ( or for not voting). The temperature profile on the earth is described by assigning to every point in time and every point on the surface its temperature. Such and many other situations are captured by the concept of a mapping.