## PhD Program

The PhD in mathematics requires:

- A total of 90 credit hours*, including seven core courses and five formal 500 level courses.
- Four written preliminary exams.
- A one credit professional development course, MATH 492, taken during the first fall semester in the PhD program. (Only for classes entering fall 2018 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 22k 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 22k 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 and the Master's degree requirements outlined below are met. Students will be awarded an MA in mathematics once the requirements are met and the master's program form is completed. (See the graduate coordinator 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 credit hours of gradaute courses in the math department are accumulated. Courses with substantial mathematical content from outside of the math department can be used to meet the rest of the 30 credit hour requirement, but they need to be *pre-approved* by the graduate committee. The credits *must* include at least 5 of the 7 core courses. The courses must be passed with a minimum grade of B-.

Getting a pass on a prelim exam exempts a student from taking the corresponding core course, but does not grant credit hours.

Students will be awarded an MA in mathematics once the requirements are met and the master's program form is completed. (See our graduate administrator for the necessary forms.) Students have 2 years for the completion of the Master’s degree requirements.

### 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 seven core courses in their first three years, or demonstrate proficiency by passing the prelims in the respective topics. The seven courses need to be passed with a B- or better grade. 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 403: Probability Theory

MATH 436: Algebra I

MATH 437: Algebra II

MATH 440: General Topology

MATH 453: Differentiable Manifolds

MATH 471: Analysis I

MATH 467: Analysis II

#### 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: Analysis I (4 cr.) | MATH 467: Analysis II (4 cr.) or MATH 403: Probability Theory (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) or MATH 472: Analysis III (4 credits) or A course in your research area | MATH 467: Analysis II (4 cr.) or MATH 403: Probability Theory (4 cr.) |

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 must pass four written preliminary exams (prelims) of their choosing from the prelims corresponding to the 7 core courses. Prelims need to be passed with at least 3/5 problems substantially correct. Prelims are given during the year, as part of the final exams of the corresponding courses, and again in August.

Students are required to pass exams according to the following schedule:

- One exam passed by the end of May in their first year
- Two exams passed by the end of August of after their first year.
- At least three passes by the end of December of their second year. If a student fails to satisfy this or the previous requirement, they can continue in the program, but will separate at the end of the Spring semester.
- All four prelims must be passed by the end of May of the second year.
- Note, that regardless of which courses a student chooses for their prelim exams, they must pass all 7 core courses with the minimum grade of B- by the end of their second year.

Preliminary exams:

- Probability Theory (MATH 403)
- Algebra I (MATH 436)
- Algebra II (MATH 437)
- Analysis I (MATH 471)
- Analysis II (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 is considered a pass for the prelim. Getting a pass on a prelim exam satisfies the requirement of passing the corresponding course as well.

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

- Algebra I prelim topics
- Algebra II prelim topics
- Analysis I prelim topics
- Analysis II prelim topics
- Topology prelim topics
- Geometry prelim topics
- Probability prelim topics

**Past Prelims**

Here are some past prelims in pdf form:

- Algebra I : 2020-August, 2021-Fall, 2022-August
- Algebra II : 2020-Spring, 2021-Spring, 2022-Spring
- Analysis I : 2021-August, 2022-August, 2022-Fall
- Analysis II : 2019-Spring, 2019-August, 2022-Spring
- Topology : 2020-Fall, 2021-Fall, 2022-Fall
- Geometry : 2020-Spring, 2021-Spring, 2022-Spring
- Probability : 2023-Spring, 2023-August

### 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. Students are encouraged to pass their oral exam by the end of their third year in the program. They are required to pass it by the end of their fourth year.

### 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.