Mathematics has been correctly called "the Queen of Science": all of modern science has become increasingly reliant on mathematical methods and discoveries. To wit, the most recent developments in physics, economics, and finance, to name just a few disciplines, are all highly mathematical in nature. Moreover, mathematics is one of the central human intellectual disciplines, with a history extending almost three millennia.

Research in the department has been carried out in the following fundamental core subjects of Mathematics:

In addition, the USC Department of Mathematics is home to a number of interdisciplinary organized research units involving faculty both from within the Department of Mathematics and whose home departments are elsewhere in the College and University.

By any measure, our faculty is a distinguished group of scientists and researchers. A number of our faculty either are or were members of the National Academy of Sciences, several have held prestigious Sloan Fellowships and National Science Foundation (NSF) Career Awards, and many are on the editorial boards of the leading scholarly journals in their fields. Members of our department hold a number of important offices in the American Mathematical Society (AMS).

The quality of the research, applied, applicable and fundamental, carried out by the faculty in the Mathematics Department is evidenced by the fact that a remarkable percentage of them are supported by federal grants, a percentage equal to, or greater than, the average of the top ten departments nationwide. In addition to the fact that the department has been home to a number of Multidisciplinary University Research Initiative (MURI) awards from the Department of Defense (DoD), most of the research being carried out in the department is funded by grants or contracts from the NSF, the National Institutes of Health (NIH), the National Security Agency (NSA), the National Aeronautics and Space Administration (NASA), and DoD.

The USC Department of Mathematics also supports a computing facility that is freely accessible to all members of the Math Department. This facility contains a newly purchased MAC PRO Two Quart-Core server with 10 TB disk space and a 30 workstation computing user laboratory. The Modeling and Simulation Laboratory, the Department of Mathematics, and USC Information Technology Services (ITS) maintain either individual or site licenses for Matlab (including numerous special purpose Toolboxes), Mathematica, and C++ and FORTRAN compilers and developer suites.