Concentrations

Computational Mathematics (CMA)

Ph.D. students in applied mathematics opting for the concentration in computational mathematics must meet the requirements for the applied mathematics Ph.D. In addition, they must take numerical analysis as one of their three qualifying exams, and they must select three courses from the following list of computational courses.


Computational mathematics

MA 522Computer Algebra
MA 540Uncertainty Quantification
MA 544Computer Experiments in Mathematical Probability
MA 565Graph Theory
MA 573Modeling
MA 584Finite Difference Methods
MA 587Finite Element Methods
MA 784Nonlinear Equations and Optimization
MA 788Numerical Nonlinear Partial Differential Equations

Computer science

CSC 489Fundamentals of Computer Science
CSC 501Operating Systems
CSC 505Algorithms
CSC 506Architecture of Parallel Computers
CSC 471, CE 537C, UNIX
CSC 512 Compilers

Additional computational courses

PY 525Computational Physics
ECE 513Digital Signal Processing
MAE 560Computational Fluid Mechanics and Heat Transfer
ST 555Statistical Programming
FIM 548Monte Carlo Methods for Financial Mathematics

Other courses may be acceptable, subject to approval by the student’s advisory committee and the director of graduate programs.

Interdisciplinary Mathematics (MAI)

MAI students must fulfill all the requirements for either the mathematics or the applied mathematics Ph.D. They have the option of substituting a qualifying exam in another field for one of the three required math Ph.D. qualifying exams.

This substitution requires prior approval from the director of graduate programs. The substituted exam does not have to be on the same date as the two math qualifying exams. The two math qualifying exams and the substituted exam will be considered as one set of examinations, and the usual departmental retest policies will hold.

MAI students are required to demonstrate evidence of interdisciplinary work as follows.

Required of all MAI students:

  • have a committee member from the other discipline
  • take at least two courses in the other discipline, at least one of which is not cross-listed with mathematics
  • present a formal research proposal at the preliminary oral exam

The proposal can be as much as several fully developed chapters of the final dissertation or as little as a few pages. It should clearly explain the interdisciplinary research plan. A copy will be filed with the Mathematics Department graduate program office.

In addition, MAI students are required to do at least two of the following:

  • attend and present at a conference in the other discipline
  • publish in the literature of the other discipline
  • have a summer internship
  • pass a preliminary examination in the other discipline