The talk will start with a brief introduction of US NSF's 10 Big Ideas and give an overview of the recent trend of computational mathematics in the US. Then I will present my own research topic which will serve as an example to demonstrate how a problem in composite materials can be studied from the computational mathematics point of view. Furthermore, it will be shown how its link to the function theory can help us develop a mathematically simple and elegant way for solving a complicated problem arising in wave propagation of poroelastoc materials.