PhD in Computational and Applied Mathematics

Our department fosters a supportive environment through hands-on instruction while promoting the proficiency needed to prepare students for a wide range of career possibilities. Particular strengths as a department include computational and applied mathematics. The department offers M.S. and Ph.D. degrees in computational and applied mathematics.

Current research includes numerical analysis and scientific computation, dynamical systems, fluid dynamics, electromagnetics, data science, mathematical biology, and computational neuroscience.

The Department of Mathematics offers one of the country's leading programs for those who want to pursue graduate studies in computational and applied mathematics. The program specifically emphasizes physical applied mathematics, numerical analysis, and scientific computation.

Students selected for this program will study under a distinguished faculty that consists primarily of numerical analysts and applied mathematicians. In keeping with a long-standing SMU tradition, all faculty members, including our endowed chair holder and other senior professors, are required to teach graduates and undergraduates. With a 1:1 ratio of graduate students to faculty members, graduate students can be assured of individual attention.

SMU also offers excellent computer facilities, an outstanding library collection, competitive financial aid, and the advantage of being located in an area where job prospects for graduates are plentiful.

Research

Faculty members are actively working in the traditional and emerging areas of applied mathematics and scientific computing.

Current research activities in applied mathematics cover electromagnetic phenomena for nonlinear lasers, meta-materials, and fractional materials, uncertainty quantification and stochastics dynamics in the biological and electrical power network, machine learning in data sciences and functional material studies, anomalous diffusion and fractional differential equations in biological and optical systems, electrostatic solvation and interactions in protein physics, free-surface fluid dynamics and foam rheology, 3-D vortex reconnection and magneto-hydrodynamics for plasma physics, dynamics systems and wave turbulence, density functional theory for electronic structures, kinetic theory for quantum transport and Bose-Einstein condensation, and transports in nano-manufacturing through interaction between electron and ion beams with solids, etc.

A wide selection of numerical methods and algorithm development, undertaken by faculty members to address problems in the above-mentioned areas, include deep neural networks, polynomial chaos, high order, and fast integral equation methods, absorbing boundary conditions, finite element, and finite difference and discontinuous Galerkin methods, fast large scale eigensolver, multiphase flow interface modeling, and Monte Carlo methods, etc.