Applications of Mathematics to Population Geography

Three levels of application of mathematics are considered in order of increasing complexity. The first level involves measurements of processes and phenomena, the second the derivation of empirical relationships, and the third the construction of deductive models reflecting the basic mechanism of processes and phenomena. Examples of the three levels are given: Boyce's city-shape index illustrates the first; and Clark's formula for population density within cities is given as an example of the second. The second level is also illustrated by Medvedkov's procedure for forecasting the interplay of natural and mechanical movement of population, involving the use of matrix algebra. On the third level, Medvedkov constructs models of flows of pedestrians doing their shopping on their way home from work to determine an optimal distribution of retail outlets.