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.

The USC Department of Mathematics succeeds admirably in both advancing science and extending fundamental knowledge. Research in the department in the fundamental core subjects of algebra, analysis, geometry, and topology is prolific, highly visible and internationally recognized. Our groups in these areas are involved in a number of collaborative efforts with scholars in some of the top math departments in the world. The department has a lively and very highly regarded probability group with connections to medicine, researchers engaged in mathematical biology, well recognized researchers in fluid dynamics and applied and interdisciplinary mathematics in general, an active financial mathematics program, and faculty who are energetically involved in cryptology.  For more information on the members of the department and their particular areas of interest, please visit the web pages listed below for our groups in each of the core areas 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.

In addition to pure research in the fundamental areas of mathematics, USC and the Los Angeles area in general provide an outstanding environment for collaborative interdisciplinary research. Department members pursue joint projects with researchers in other departments in the College, such as Physics and Economics, and in other schools on the USC campus, including the Viterbi School of Engineering, the Keck School of Medicine, and the Marshall School of Business. Members of our faculty are also involved in a number of ongoing research projects with industry and governmental labs including the Air Force and Naval Research Laboratories, The Institute for Defense Analysis (IDA) and the Jet Propulsion Laboratory (JPL). The department is also an academic sponsor of the NSF Mathematical Sciences Research Institute (MSRI) in Berkeley and was chosen as a participating department in the Carnegie Foundation Initiative on the Doctorate (CID).

In addition to the research centers described on this page, USC researchers in mathematics have access to USC’s High Performance Computing and Communications center (HPCC). The HPCC comprises a diverse mix of computing and data resources. Two Linux clusters constitute the principal computing resource. In addition, HPCC has a central facility that provides more than 400 terabytes of combined disk storage and potential access to nearly a petabyte of tape storage, as well as a Condor cluster that uses spare cycles on UNIX workstations in USC's general-access computing rooms. Among supercomputers in an academic setting, HPCC's new supercomputer cluster is the seventh fastest in the United States. Among all supercomputers in the world, it is ranked 61st. It claimed this distinction by achieving a benchmark in fall 2008 of 44.19 teraflops, or 44.19 trillion floating-point calculations per second, on its 768-node, 10-gigabit backbone cluster. The local aspect of HPCC allows USC faculty members free and unfettered access to a world-class facility

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.