We consider the basic trends in mathematical geography and discuss quantitative laws in this field and methods of analysis. Proposed was the so called 'quantum' theory of settlement formation. It proceeds from a number of simplest hypotheses about interaction of towns and the results of self-organization theory. The model includes 2m nonlinear parabolic equations and one integral equation, which describe the process of growth of roads. The value of m coincides with the number of hierarchical levels of central places analyzed. We discuss the correspondence of this model to the classical Kristaller theory, V.A.Shuper relativistic theory of central places and modern 'fractal' theories of settlement.
Mathematical modelling in actual problems of science and technics