# Qualifying and Breadth Requirements

Interdisciplinary Track

The Department of Mathematics offers 5 distinct qualifying exams in the following subjects:

- Algebra (Math 653/654)
- Complex Analysis (Math 617/618)
- Geometry/Topology (Math 622/636)
- Numerical/Applied Analysis (Math 610/641)
- Real Analysis (Math 607/608)

Each qualifying exam has a duration of 4 hours, and is offered twice a year (January and August). The syllabi and schedules can be found in the Qualifying Exam section of the Graduate Program web page.

- The Qualifying Exams are designed to assess students' competence in basic mathematical skills and knowledge in the corresponding outside area of interest, at the level of the core courses.
- The Breadth Requirement for the Interdisciplinary Track is designed to ensure that students acquire both a broad education and a solid background in mathematics and depth of knowledge in the outside area of interest, thus requiring that they demonstrate basic knowledge in the various areas displayed in the table below and in the corresponding interdisciplinary area outside mathematics.

## Core Mathematics Courses:

Set I |
Set II |
Set III |
Set IV |

Algebra Math 653/Math 654 |
Real Analysis Math 607/Math 608 |
Diff. Geometry Math 622/Math623 |
Applied Analysis Math 641/Math 642 |

Discrete Math/Number Theory Math 613/Math 630/Math 627 |
Complex Analysis Math 617/Math 618 |
Topology Math 636/Math 637 |
Numerical Analysis Math 609/Math 610 |

## Qualifying Exam Requirement:

- Students must pass at least 1 qualifying exam by the end of 3rd semester of enrollment (not counting Summers) and 2 qualifying exams by the end of the second year of enrollment.
- One exam must be a regular mathematics qualifying exam and one exam must be in the outside area of interest. The outside mentor (co-advisor) should write and grade the qualifying exam based upon the course work the student has completed in the outside area. The exam should have a level comparable to the outside department's qualifying (or preliminary) exams but should focus on the knowledge base necessary for the interdisciplinary program. It can not be a take home exam. It should consist of a rigorous examination that verifies that the student understands the important concepts of the area. The student's advisory committee should see the graded written exam and a copy of it with the official graded results should be filed with the Mathematics Graduate Office. A project will not be accepted in lieu of a written exam.

## Breadth Requirement:

- Students must take at least 3 regular mathematics courses at a level greater or equal to the core courses and obtain a B or higher in each course.
- Students must take at least 1 regular course in the outside discipline at a level greater or equal to their corresponding core courses and obtain a B or higher in the course.
- The choices of mathematics courses and qualifying exams must include subjects from at least 3 distinct sets of subjects displayed in the table above.
- A typical student is expected to have fulfilled these requirements by the end of the fourth year of enrollment.

## * Courses for Breadth Requirement:

The following courses can be used to fulfill the breadth requirements in the indicated mathematics areas. Additional courses may be used with the approval of the Graduate Committee. Courses used to fulfill the breadth requirement in the outside discipline are determined by the student's thesis committee.

Subject |
Courses |

Algebra |
Math 653, Math 654 |

Discrete Math/Number Theory |
Math 613, Math 630, Math 626, Math 627 |

Real Analysis |
Math 607, Math 608, Math 655, Math
656 |

Complex Analysis |
Math 617, Math 618, Math
650 |

Differential Geometry |
Math 622, Math 623 |

Topology |
Math 636, Math 637, Math 643, Math
644 |

Applied Analysis |
Math 611, Math 612, Math 641, Math 642, Math 658, Math
670 |

Numerical Analysis |
Math 609, Math 610, Math
661 |