I work as a research scientist at Schlumberger, an oilfield services company that provides measurements of the Earth acquired while prospecting for oil and developing oilfields. A good example of these measurements are seismic surveys where seismic waves are propagated into the Earth's surface, their reflections are recorded, and then these recorded reflections are turned into structural images showing various rock layers and fluids under the Earth's surface. A lot of physics is needed to understand how waves propagate through rocks of various types (sandstone, limestone, clay, salt,…) that may or may not be filled with fluids (water, oil, gas), but a lot of mathematics is needed to take the seismic measurements and the physics equations and turn them into usable images which can be used by people drilling oil wells and trying to produce oil in an economically and environmentally sensible way.

Computing these images accurately and efficiently requires learning how to implement the linear algebra, geometry, and calculus one learns in school on the computer. As a simple example, one can represent the Earth's subsurface as a layered model where each layer is given a number describing how fast sound can propagate through the layer: call this list of say 250 numbers m.