# PhD Qualifying Examination and Required Courses

**Qualifying Examination **

One-year sequences for the Written Qualifying

Examination. Select three sequences. This page describes the standard tracks. The Interdisciplinary Tracks are described here.

Full details on scheduling and retake policies are found here.

MA 521 – 721 |
Abstract Algebra |

MA 520 – 720 |
Linear Algebra and Lie Algebra |

MA 522 – 722 |
Computer Algebra II |

MA 523 – 723 |
Applied Matrix Theory |

MA 551 – 753 |
Topology |

MA 580 – 780 |
Numerical Analysis |

MA 515 – 715 |
Analysis |

MA 531 – 731 |
System & Control |

MA 532 – 732 |
Ordinary Differential Equations |

MA 534 – 734 |
Partial Differential Equations |

MA 573 – 574 |
Modeling |

MA 524 – 724 | Combinatorics |

MA 546 – 747 |
Applied Probability and Stochastic Processes |

MA 555 – 755 | Differential Geometry |

Students who have not had the equivalent of MA

405 (Introduction to Linear Algebra and Matrices), MA

407 (Introduction to Modern Algebra), and MA

425 – 426

(Mathematical Analysis I and II) must make up these courses. Students

who have not had the equivalent of MA

426 may take it for graduate credit by registering for MA 591M.

The following courses must be passed with a grade of A or B.

- All students: MA

515 Real Analysis and MA

521 Modern Algebra. - Mathematics students: three from Group 1 and one

from Group 2. - Applied Mathematics students: two from Group 1

and two from Group 2.

**Group 1**

MA 513 |
Complex Variables |

MA 551 | Topology |

MA 518 |
Differential Geometry |

MA 520 | Linear Algebra |

MA 715 |
Functional Analysis |

**Group 2**

MA 580 |
Numerical Analysis |

MA 532 | Ordinary Differential Equations |

MA 534 |
Partial Differential Equations |

MA 546 | Probability |

MA 785, 584, or 587 |
Numerical Differential Equations |

**Concentration
in Computational Mathematics (CMA) **

CMA students must fulfill all the requirements for

the PhD in Applied Mathematics. One of the three subjects for the

qualifying examination must be Numerical Analysis such as MA

580 – 780.

In addition to MA 580 and 780, CMA students must take three courses

from the list of approved CMA courses.

The MAI concentration is available to Ph.D. students

in either Mathematics or Applied Mathematics. It is not available

to Masters students.

MAI students fulfill all the requirements for the

Ph.D in MA or AMA except that they have the option of substituting

a qualifier in another field for one of the three required math

PhD qualifying examinations. This substitution requires prior approval

of the Director of Graduate Programs (DGP) or Graduate Program

Administrator (GPA). The substituted exam does not have to be on

the same date as the two math qualifying examinations. The taking

of the two math qualifying examinations and the substituted exam

will be considered as one set of examinations and the usual departmental

retest policies will hold.

In addition to the MA or AMA PhD requirements the

IMA student would be required to demonstrate evidence of interdisciplinary

work. This would be done as follows:

Required of all MAI students

- Member of committee from other discipline.

- At least 2 courses in the other discipline, at least one of

which is not cross-listed with mathematics.

- A formal research proposal to be presented at the preliminary

oral exam. The proposal could be as much as several fully developed

chapters of the final thesis or as little as a few pages. The

proposal would clearly explain the interdisciplinary research

plan. A copy would be filed with the Math Dept Graduate Program

Office.

MAI Students are required to do at least two of:

- Attend and present at a conference in the other discipline.

- Attend and present at a conference in the other discipline.
- Publish in the literature of the other discipline.

- Have a Summer internship.

- Take a Preliminary examination in the other discipline.