Mathematics PhD

The Doctor of Philosophy program in mathematics is intended for students with superior mathematical ability. It emphasizes a solid mathematical foundation. The School of Mathematical and Statistical Sciences at Arizona State University has active research groups in analysis, number theory, geometry, and discrete mathematics.

Current research interests include: analysis – real, functional and harmonic; discrete mathematics – discrete structures, and enumerative combinatorics including graph theory and algebra; geometry and topology – manifolds and related spaces; and number theory – study of integers and their generalizations.

The school has more than 50 full-time faculty members and 13 postdoctoral faculty and is housed largely in Charles Wexler Hall, near the center of campus. Of the approximately 150 doctoral students, more than half are fully supported as teaching or research assistants. Our graduate students enjoy a collaborative atmosphere and a full schedule of research seminars and colloquiua each week. About 40% of our PhD students are women, and we support an active chapter of the Association for Women in Mathematics (AWM), as well as a student chapter of American Mathematics Society (AMS), and the Graduate Statistics Club. The school hosts an annual Math and Stats Career Day and graduate students explore multiple career paths in science and industry, as well as academia.

Mathematicians have opportunities in Arizona, the US and internationally. Typical careers are as research mathematicians in government labs and professors at research universities and liberal arts colleges. Recent examples include positions as a data scientist at American Express and an actuarial analyst at Segal Consulting.

5 years to degree
> 70 TAs
50 full-time faculty

Degree Overview

The PhD in mathematics emphasizes a solid mathematical foundation.

The 84-credit program includes coursework, two qualifier exams, a written comprehensive exam, an oral prospectus, and a written dissertation. The program has a strong research focus. Students are able to choose from a wide range of electives and topics in order to customize the degree to their interests.

How to apply

The School of Mathematical and Statistical Sciences offers about 20 new teaching assistantships each year.

PhD application deadline is July 1, if you are applying for admission only and are not competing for TA support.

PhD application deadline is December 10, if you want to compete for a teaching assistant position.

Applications are accepted for fall admission only. We do not accept applications for spring admission. The graduate review committee will begin reviewing completed applications for admission and teaching assistantship positions beginning after December 10 for fall admission. The first round of offers for TA support will be made by late January.

Applications still considered incomplete by the School of Mathematical & Statistical Sciences after July 1 will likely not be evaluated by the graduate review committee in time to be considered for admission for that current year. International applicants may want to allow an additional 4-6 weeks for I-20 and visa processing and should pay careful attention to the I-20/DS-2019 important deadlines.

See Graduate Admissions for additional information on non-refundable application fees and the late processing fee.

Application evaluation

Each applicant is evaluated not only on their grades, but their personal statement and letters of recommendation. Only completed applications submitted through the on-line process will be reviewed.

We receive many inquiries asking for a pre-evaluation to see if an applicant would be eligible to apply or make suggestions on their credentials. Unfortunately we are not able to review any application information sent to us.

More specifics can be found on the How To Apply page.

Joe WellsNancy Childress and Julien Paupert are perhaps the two biggest influences that I’ve had in graduate school. Both have been constant sources of encouragement and inspiration. Dr. Childress’ teaching method motivated me to think critically and abstractly, and she rallied for me to get into the graduate program. Dr. Paupert has been a wonderful and compassionate research advisor; he’s been very supportive of my conference travel, promoted me and my work to his colleagues, and has always been very quick to respond to even my most ignorant questions.

Joe Wells
Current doctoral student in mathematics
Arizona State University


The curriculum builds a strong foundation in mathematics. Current members of the graduate faculty in mathematics come from the School of Mathematical and Statistical Sciences.

Requirements and electivesHours
Required courses / Qualifier exams12
Courses, electives and comprehensive exams15-30
Total hours required84

Courses and electives

The Pure Math PhD program has four distinct groups of specialization:

  • Analysis
  • Discrete Math
  • Geometry/Topology
  • Number Theory

which have mostly the same program requirements, except for minor variations in the way that exams are run (see below).

The Pure Math PhD program has five major milestones: qualifying exams, plan of study, comprehensive exam, dissertation prospectus, and dissertation defense.

Year 1

  • Prepare for qualifiers. Ideally, pass both qualifiers by May of year 1.
  • Start search for a dissertation advisor..

Pure Math PhD students must have passed two qualifying exams by the end of the second year.

Each exam is based upon a 2-semester sequence of courses, taken in the first year, in a fundamental area of graduate-level math.

The qualifier sequences go together with the four groups, and there is some variation in the policies for the four qualifying exams:

Analysis: The exam is on Real Analysis, consists of a single 4-hour exam on MAT 570–571, and is given in May and August.

Discrete Math: The exam is on Combinatorics and Graph Theory, consists of two 3-hour parts, with the first part on MAT 512 given in January, the second part on MAT 513 given in May, and both parts given in August.

Geometry/Topology: The exam is on Geometry and Topology, consists of a single 4-hour exam on MAT 501–502, and is given in May and August.

Number Theory: The exam is on Abstract Algebra, consists of two 3-hour parts, both on the same day, the first part on MAT 543 and the second part on MAT 544, and is given in May and August.

It is possible to take a qualifying exam without registering for the course.

Past Qualifier Exams
(this link to Past Qualifier Exams is restricted to current graduate students and faculty)

Year 2

  • Choose a dissertation advisor in semester 3 if this has not been done already.
  • Choose four more dissertation committee members.
  • Plan your comprehensive exam. The comprehensive exam is based upon material that includes the content of at least two 500-level courses, chosen with the advice of the student’s dissertation committee. In particular, the student must choose a dissertation advisor and four other dissertation committee members before scheduling the comprehensive exam.

Year 3

  • File a program of study in semester 5 if this has not been done already. This must be done before taking the comprehensive exam.
  • Pass the comprehensive exam.
  • Choose a dissertation topic.
  • Pass the dissertation prospectus.

All PhD graduate students should sign up for 3 hours of seminars.

MAT 591 Seminar (3)

Year 4

Do dissertation research. Students must pass a dissertation prospectus exam by the end of the 8th semester. While the comprehensive exam shows that the student has the necessary knowledge to conduct research in a specialization area, the dissertation prospectus demonstrates mastery of the methods needed to identify, formulate, and plan research.

MAT 792 Research

Year 5
  • Finish research and write dissertation.
  • Defend dissertation by end of semester 10.

The dissertation is the culmination of the doctoral program. By writing and defending a dissertation the student demonstrates readiness to conduct independent research in a specialization area.

There will be a public oral defense following the completion of the dissertation. It is the student’s responsibility to schedule the dissertation defense, and the student must distribute the dissertation to the dissertation commit- tee and to an external reviewer at least four weeks prior to the defense. The external reviewer must be approved by the dissertation committee.


MAT 799 Dissertation

Students may transfer up to 30 credit hours from a masters in mathematics, or similar degree, into our PhD programs.

Up to 12 additional credit hours may transfer into a Plan of Study (iPOS). Courses applied to a previously awarded degree cannot be included on an iPOS. Details can be found in the graduate college policies.

Masters in Passing

If you satisfy certain master's requirements, you can acquire a master's degree on your way to a PhD. More information can be found in the graduate college policies.

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