## PhD Program

The PhD in mathematics requires:

- A total of 90 credit hours*, including eight core courses and five formal 500 level courses.
- Six written preliminary exams
- An oral preliminary exam
- A doctoral thesis

*Students can transfer up to 30 credits for a master's degree earned elsewhere.

Students must also satisfy a three-year teaching requirement, fulfilled by teaching assistantships.

PhD students should apply for a master’s degree when 30 credits are accumulated. The credits must include the following: MTH 436, 440, 467, 471, or their equivalent. The written prelims serve as the final exam for the MA.

Students will be awarded an MA in mathematics once prelims are passed and the master's program form is completed. (See Joan for the necessary forms)

Students may also be asked to participate in the graduate students seminars.

### Registration

Graduate students who are teaching assistants must register for a minimum of 18 credits for the academic year (9 credits per semester).

Graduate students who are not teaching assistants must register for a minimum of 24 credits.

### Courses

Students must take all eight core courses in their first two years, or demonstrate proficiency. If possible, students should take advanced courses in their chosen area in the second year. Students are required to maintain a B average or better.

#### Core Courses

MTH436: Algebra I

MTH437: Algebra II

MTH440: General Topology

MTH453: Differentiable Manifolds

MTH443: Algebraic Topology I

MTH471: Real Analysis

MTH467: Theory of Analytic Functions

MTH472: Functional Analysis

#### Sample Schedule

The following schedule allows students to pass the prelims by August at the end of their first year, and start research quickly.

Fall | Spring |
---|---|

MTH 436: Algebra I | MTH 437: Algebra II |

MTH 471: Real Analysis | MTH 467: Complex Analysis |

MTH 440: General Topology | MTH 453: Differentiable Manifolds |

Fall | Spring |
---|---|

MTH 443: Algebraic Topology | MTH 472: Functional Analysis |

Courses in your research area, start research when ready. |

Research |

Write your thesis, apply for jobs. A paper or two will greatly boost your job chances |

### Prelims

Students are expected to pass six written preliminary exams (prelims). Prelims are given during the year, as part of the final exams of the corresponding courses, and again in August. Students will receive a PhD pass, a master’s pass, or a fail.

Students are expected to pass exams at the following level by the date noted:

- One exam at the PhD level by the end of May in their first year
- Two exams at the PhD level by the end of August after their first year
- Four at the PhD level, and the remain two at the master’s or PhD level by the end of May of their second year

Preliminary Exams:

- Algebra I (MTH 436)
- Algebra II (MTH 437)
- Real Analysis (MTH 471)
- Complex Analysis (MTH 467)
- Topology (MTH 440)
- Geometry (MTH 453)

Each prelim has five problems, and grades are based on the number of questions which are substantially correct. A score of three or higher will earn a PhD pass, and a score of two will earn a master’s pass.

**Topics covered on Prelims and list of study books**

Complex Analysis prelim topics

**Past Prelims**

Here are some past prelims in pdf form:

### Oral Preliminary Exam

The oral preliminary exam should be taken within six months of passing the written prelims. The exam is on a substantial paper, generally in the thesis area, selected in consultation with the thesis advisor. This exam must be passed at least six months before the thesis defense.

### Doctoral Thesis

The main requirement for the PhD is completion of a doctoral thesis, written under supervision of an adviser. Upon completion of the thesis, students must schedule a thesis defense.

Students will need to find a thesis adviser after they pass the prelims.