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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, MTH492, taken during the first fall semester in the Ph.D. program. (Only for classes entering Fall 2018 and later.)
  • A 1 credit current topics in math course, MTH493, taken during the second fall semester in the Ph.D. 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.

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.


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.

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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.

First year
MTH 436: Algebra IMTH 437: Algebra II
MTH 471: Real AnalysisMTH 467: Complex Analysis
MTH 440: General TopologyMTH 453: Differentiable Manifolds
MTH 492: Professional Development Sem.
Second year
MTH 443: Algebraic TopologyMTH 472: Functional Analysis
MTH 493: Current Topics in Math
Courses in your research area, start research when ready.
Third and Fourth years
Fifth year
Write your thesis, apply for jobs. A paper or two will greatly boost your job chances

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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

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:

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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.

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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.

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