Applied mathematics research requires a deep understanding of mathematics and broad knowledge of other disciplines. Applied mathematicians must be well-trained in fundamentals of mathematics to model, analyze and compute solutions to real-world problems.

Real-world mathematics problems usually are not amenable to complete abstraction. Therefore, they often do not fall within the admissible set of problems for "pure" mathematics research. Instead, applied mathematicians must work through these issues to respect the connections that any mathematical analysis will have to the application.

Because mathematics serves as the framework for so many different areas in science and engineering, applied mathematicians are continually increasing their breadth of knowledge in other fields.

In fact, applied mathematics research is usually assessed through two criteria: (1) the sophistication of the mathematics used and (2) the novelty of the application. At UC Merced, the faculty and students engage in research in the following areas: