# Overview of the Ph.D. Program

Our Ph.D. program provides a rigorous and thorough education, under a very dynamic and interactive environment, aimed at preparing our students to assume leadership positions as researchers in academia, industry, government labs and similar settings. Our students conduct research on one of the several areas that represent the diversity and scope of our faculty's expertise:

Algebra | Algebraic Geometry | Applied Mathematics |

Approximation Theory | Combinatorics | Complex Analysis |

Control Theory | Differential Equations | Differential Geometry |

Functional Analysis | Fluid Dynamics | Geometric Group Th. |

Math. Material Sciences | Mathematical Physics | Mathematical Biology |

Number Theory | Numerical Analysis | Operator Theory |

Probability Theory | Representation Theory | Topology/Alg. Topology |

Program requirements are based upon the premise that Ph.D. students should have a broad exposure to graduate level mathematics, as well as experience doing mathematical research in an area of specialization. To achieve this goal, we offer a wide spectrum of courses each semester from our extensive Curriculum.

Our program
has developed an *Interdisciplinary
Track* for the Ph.D. degree, which originated from the
various active collaborations between our department and other
academic units at Texas A&M University, many of which involve
faculty members with joint appointments in these units. Students in
this option will obtain the same rigorous training in mathematics
as any student in the Ph.D. program, but this track places
responsibility upon a student’s advisory committee to devise
a course of study with sufficient depth and breadth to prepare the
student for an interdisciplinary mathematical career. The advisory
committee must include a co-mentor in the department
representing the related discipline.

In order to obtain the doctoral degree, a student must comply with the following set of requirements.

#### Requirements:

##### Ph.D. degree in Mathematics

- Qualifying & Breadth Requirements
- Preliminary Exam and Candidacy Requirements
- Dissertation Requirement

##### Ph.D. degree in Mathematics - Interdisciplinary Track

- Qualifying & Breadth Requirements
- Preliminary Exam and Candidacy Requirements
- Dissertation Requirement

#### Steps to the Ph.D. Degree

The steps
necessary to obtain the Ph.D. degree are summarized below.

Click **here** for a fully detailed timetable with useful
links.

- In the first two years of studies, a typical student engages in coursework designed to support the fulfillment of the Qualifying Requirements (a combination of qualifying exams and course sequences) and the fulfillment of the Subject Area Breadth Requirements. If a student has decided to follow the Interdisciplinary Track, they should make an informal declaration of this to the Graduate Office so that exam and breadth fulfillment can be tracked accordingly.
- Then the student should form a Ph.D. advisory committee (4 members: 3 in math, 1 outside of math),
submit a degree plan
(at this point, they should formally declare which Ph.D. track they
are pursuing) and
engage in a combination of coursework, seminars and directed
studies aimed at preparing the student for the Preliminary Exam and
for conducting research towards the dissertation.
- After passing the Preliminary Exam, completing the formal
coursework and submitting a Research Proposal, the student is
admitted to candidacy.
- At this point the only task left is the completion of the Dissertation and its Final Defense (note: there must be at least 14 weeks between the Preliminary Exam and the Final Defense).