The Department of Mathematics at USC offers a Ph.D. track in mathematics with concentration in applied and computational mathematics. This track was approved in the fall of 2009 as the result of an initiative to expand applied and computational mathematics into interdisciplinary areas. Students enrolled in the program can concentrate on either Applied Math, or Computational Math, or interdisciplinary mathematics during the course of their studies. The aims of this track are

- to implement modern applied and computational mathematics curriculum into the graduate training,
- to support science and engineering education and research on the campus of USC,
- to foster interdisciplinary research across various disciplines in science, engineering and medicine.

The applied and computational mathematics faculty maintains a strong and vigorous research program in the following areas:

- applied analysis and asymptotic analysis,
- applied harmonic analysis, approximation theory, and applications of wavelets,
- computational algorithm development and analysis,
- computational fluid dynamics and rheology of complex fluids, computational nanoscience,
- computational biology and cell dynamics,
- fluid dynamics, multiphase flows, and fluid flow in porous media,
- energy research, electron transport, thermal transport,
- high performance computing and simulation of fluid flows and interfacial phenomena,
- mathematical modeling, multiscale modeling of biological and nano materials,
- mathematical biology, cellular dynamics,
- partial differential equations and wave propagations,
- signal and image processing, 3-D visualization and pattern recognition,
- combinatorics, computational combinatorics and stochastic combinatorics,
- network theory, graph theory, discrete algorithms.

Many faculty members are engaged in interdisciplinary research activities and are affiliated with the Interdisciplinary Mathematics Institute and the NanoCenter at USC. The research of faculty and students is supported by the state-of-the-art high performance computing and visualization facilities in the department, IMI and the NanoCenter. These include a high performance Linux cluster (256 processors) equipped with high powered Graphic Processing Units (Tesla cards), a visualization cluster (72 processors) of a tiled display wall, and a host of servers and workstations.

### ACM Faculty Members and Their Research Interests

Peter Binev - Professor

Ph.D., Sofia University, 1985

Research Interests: scientific computing, approximation theory, numerical analysis, nonlinear approximation, learning theory, high dimensional problems, numerical methods for PDEs, computer graphics, image, and surface processing.

Colin Bennett - Distinguished Professor Emeritus

Ph.D, University of Newcastle upon Tyne, 1971

Research Interests: harmonic analysis, interpolation of operators, wavelets, history of mathematics.

Eva Czabarka - Associate Professor

Ph.D. University of South Carolina, 1998

Research Interests: extremal set theory, extremal graph theory, graph drawing, biological applications, statistical evaluation of retrieval algorithm.

Wolfgang Dahmen -SmartState Endowed Chair in Data Analysis, Simulation, Imaging and Visualization,
Williams-Hedberg-Hedberg Chair in Mathematics

Ph.D., RWTH Aachen, 1976

Research Interests: applied and numerical analysis, approximation theory, and interdisciplinary applications.

Daniel Dix - Associate Professor

Ph.D., University of Chicago, 1988

Research Interests: analysis, initial value problems for partial differential equations governing the evolution of nonlinear waves, asymptotic behavior of solutions, solutions with special symmetry, completely integrable equations, and solitons.

Ronald DeVore - Robert L. Sumwalt Distinguished Professor Emeritus

Ph.D., Ohio State University, 1967

Research Interests: approximation theory, applied harmonic analysis, image processing, and wavelets.

Jerry Griggs - Carolina Distinguished Professor

Ph.D., Massachusetts Institute of Technology, 1977

Research Interests: combinatorics, extremal set theory, extremal graph theory, graph coloring, and applications of discrete math to biology, number theory, analysis of algorithms, and communications.

Xinfeng Liu - Associate Professor

Ph.D., State University of New York at Stonybrook, 2006

Research Interests: scientific computing, high performance computing, interfacial phenomena, multiphase flows, computational biology, cellular dynamics.

Lincoln (Linyuan) Lu - Professor

Ph.D., University of California at San Diego, 2004

Research Interests: Random graph theory, computational combinatorics.

Douglas Meade - Associate Professor

Ph.D., Carnegie Mellon University, 1989

Research Interests: applied mathematics, numerical methods for wave propagation on unbounded domains, non-overlapping domain decomposition methods, and computer algebra systems.

Lili Ju - Professor

Ph.D., Iowa State University, 2002

Research Interests: scientific computation and numerical analysis, exact boundary controllability problems for the wave equation, parallel algorithms and high-performance computing, and human brain imaging.

Pencho Petrushev - Professor

Ph.D., Sofia University, 1977

Research Interests: approximation theory, harmonic analysis, numerical methods with current focus on localized nonlinear approximation by wavelet-like bases with applications to image processing, earth gravity models, and multi-scale analysis of very large data.

Robert Sharpley - Distinguished Professor Emeritus

Ph.D., University of Texas at Austin, 1973

Research Interests: classical analysis, approximation theory, multi-resolution analysis,
signal and image processing, numerical analysis, visualization, and autonomous navigation.

Yi Sun - Associate Professor

Ph.D., Princeton University, 2006

Research Interests: Multiscale analysis, modeling and simulation in solids, fluid mechanics, chemistry and biology

László Székely - Professor

Ph.D., Eötvös University, 1983

Research Interests: combinatorial geometry, graph drawing, phylogeny reconstruction, discrete probability, design and analysis of algorithms, combinatorial optimization, extremal problems (graphs and set systems).

Paula Vasquez - Assistant Professor

Ph.D., University of Delaware 2007

Research Interests: Applied and computational mathematics, Multiscale modeling and simulation of viscoelastic fluid flows, Viscoelastic and diffusive transport processes in pulmonary mucus and mucus simulants, Computational and mathematical biology

Hong Wang - Professor

Ph.D., University of Wyoming, 1992

Research Interests: numerical analysis and differential equations, numerical approximation to differential/integral equations, and scientific computations.

Qi Wang - Distinguished Professor

Ph.D., Ohio State University, 1991

Research Interests: applied and computational mathematics, computational fluid dynamics and rheology of complex fluids, continuum mechanics and kinetic theories, multiscale modeling and computation of soft matter and complex fluids of anisotropic microstructures, biofluids and biomaterials, cell dynamics, parallel and high performance computing.

Xiaofeng Yang - Associate Professor

Ph.D., Purdue University, 2007

Research Interests: numerical analysis, high performance computing, multiphase flows, spectral methods for partial differential equations, phase-field methods.

Zhu Wang - Assistant Professor

Ph.D., Virginia Tech, 2012

Research Interests: Reduced Order Modeling, Climate Modeling, Numerical Analysis

### ACM Research Instructors, Assistant Professors and Postdoctoral Associates

L. Scott Johnson -- Assistant Research Director

M.S. University of South Carolina, 2004

Tong Zhang -- Visiting Research Assistant Professor

Ph.D., Chinese Academy of Sciences, 2013

### Applied and Computational Mathematics Related Links

#### Societies:

- SIAM : Society for Industrial and Applied Mathematics;
- AMS : American Mathematical Society;
- APS : American Physical Society;
- ACS : American Chemical Society;
- AICHE : American Institute of Chemical Engineers;

#### Institutes and Centers:

- AIM: American Institute of Mathematics
- IMA: Institute for Mathematics and Its Applications
- IMI: Interdisciplinary Mathematics Institute
- IPAM: Institute for Pure and Applied Mathematics
- MBI: Mathematical Biosciences Institute
- SAMSI: Statistical and Applied Mathematical Sciences Institute