# Graduate Program

## 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.
- A 1 credit professional development course, MATH 492, taken during the first fall semester in the PhD program. (Only for classes entering fall 2018 and later.)
- A 1 credit current topics in math course, MATH 483, taken during the second fall semester in the PhD program. (Only for classes entering fall 2017 and later.)
- 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. Currently most grad students who do not have a special fellowship get a 18k annual living stipend and free tuition which is contingent on about 10 hours of teaching work per week during the fall and spring semesters. This teaching component often includes a combination of teaching of recitations, workshops and/or grading homework assignments—those with good evaluations can sometimes get assigned to teach a section of a course which results in additional pay beyond the 18k stipend. No summer duties are associated with the stipend but student's wishing to earn some extra money can apply to teach summer courses for the department also.

PhD students should apply for a master’s degree when 30 credits are accumulated. The credits must include the following: MATH 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 Cynthia Spencer for the necessary forms.)

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

Typically students complete the PhD in four to six years.

**Earning a Masters degree along the way to a PhD**

PhD students should apply for a master’s degree when 30 credits are accumulated. The credits must include the following: MATH 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 our graduate administrator for the necessary forms.)

### 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 per year (12 credits per semester).

Once a PhD student has completed 90 credits during the PhD program, all remaining credits must be taken via the continuation status placeholder course MATH 999. At this stage no further courses appear on your graduate transcript though you may continue to take courses on any topics you desire as you work to complete your PhD research. Typically students transition to the placeholder MATH 999 only sometime in the middle of their 5th year and stay at that status until completion of degree.

Students in continuation status get charged an approximately U.S. 1000 fee per semester in their 6th year and onwards. This fee is subtracted from their stipend.

### 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

MATH 436: Algebra I

MATH 437: Algebra II

MATH 440: General Topology

MATH 453: Differentiable Manifolds

MATH 443: Algebraic Topology I

MATH 471: Real Analysis

MATH 467: Theory of Analytic Functions

MATH 472: 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 |
---|---|

MATH 436: Algebra I (4 credits) | MATH 437: Algebra II (4 credits) |

MATH 471: Real Analysis (4 cr.) | MATH 467: Complex Analysis (4 cr.) |

MATH 440: General Topology (4 cr.) | MATH 453: Differentiable Manifolds (4cr.) |

MATH 492: Professional Development Sem (1 cr). |

fall | Spring |
---|---|

MATH 443: Algebraic Topology (4 credits) | MATH 472: Functional Analysis (4 credits) |

MATH 483: Current Topics in Math (1 cr.) | |

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 (MATH 436)
- Algebra II (MATH 437)
- Real Analysis (MATH 471)
- Complex Analysis (MATH 467)
- Topology (MATH 440)
- Geometry (MATH 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:**

- Algebra I prelim topics
- Algebra 2 prelim topics
- Real Analysis prelim topics
- Complex Analysis prelim topics
- Topology prelim topics
- Geometry 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.