# 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 522 | Computer Algebra |

MA 540 | Uncertainty Quantification |

MA 544 | Computer Experiments in Mathematical Probability |

MA 565 | Graph Theory |

MA 573 | Modeling |

MA 584 | Finite Difference Methods |

MA 587 | Finite Element Methods |

MA 784 | Nonlinear Equations and Optimization |

MA 788 | Numerical Nonlinear Partial Differential Equations |

**Computer science**

CSC 489 | Fundamentals of Computer Science |

CSC 501 | Operating Systems |

CSC 505 | Algorithms |

CSC 506 | Architecture of Parallel Computers |

CSC 471, CE 537 | C, UNIX |

CSC 512 | Compilers |

**Additional computational courses**

PY 525 | Computational Physics |

ECE 513 | Digital Signal Processing |

MAE 560 | Computational Fluid Mechanics and Heat Transfer |

ST 555 | Statistical Programming |

FIM 548 | Monte 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