Basic Concepts of Mathematical Geology

The application of mathematical methods such as the metrical matrix, binomial expansion, and set theory to rock-forming minerals integrates Bowen's reaction series and Goldschmidt's ion substitution principles. These methods are particularly relevant when diadochy occurs in crystals undergoing substitution during magma crystallization. This mathematical approach aims to bridge the gap between Bowen's and Goldschmidt's concepts, addressing mineralogical and petrological challenges related to the distribution of chemical elements and elemental substitutions during magma crystallization, while considering thermodynamic principles. This innovation will benefit students of Earth Sciences-including Geology, Geochemistry, Petroleum Geology, and Geophysics-by enhancing their critical thinking skills through a mathematical perspective.