The Mathematical Association of America recently published a number of promotional videos showing various mathematics can be used in “the real world.” Here’s the first pair of videos describing the process of mathematical modeling. From the YouTube descriptions:
Dr. Genetha Gray talks about her path and about a research problem that she worked on at Sandia National Laboratories. Using quite limited geological data, they had to create a groundwater flow computational model, with parameters to be determined, so that they could study the feasibility and safety of prospective subsurface nuclear waste storage sites.
Prof. Gwen Spencer of Smith College introduces the mathematics behind optimization, calibration, and the quantification of uncertainty in models and in the results that they give.