ABSTRACT
Mathematical modeling is simply the process of formulating real-world problems or processes into mathematical equations whose behavior mimics the key features of those systems. The model may then be used qualitatively to gain further insight into the behavior of the system or, more quantitatively, for hypothesis testing. In either case, a comparison of the behavior of the model with that of the experimental system tests the appropriateness of the model. The behaviors of the model may also suggest further experiments to explore the system under study (and to further test the correspondence between the model and reality). Some of these may not have been previously considered. Indeed, it can be argued that without a mathematical formulation, it is not possible to test rigorously whether a scientific theory is consistent with experimental observations. The modeling process is, of course, iterative with observations driving refinement of the mathematical model and new behaviors of the model potentially suggesting further experimental avenues.
