Applied Mathematics PhD

The Doctor of Philosophy program in applied mathematics is intended for students with superior computational and mathematical modeling ability. The program emphasizes a solid mathematical foundation and promotes creative scholarship in an application discipline. The School of Mathematical and Statistical Sciences at Arizona State University has faculty in applied mathematics with outstanding interdisciplinary research programs and strong external funding.

Current research interests include mathematical population biology, mathematical neuroscience, mathematical medicine, geophysical and environmental fluid dynamics, stochastic processes in biology, imaging and inverse problems, control and optimization, computational methods and analysis for ordinary and partial differential equations, and the mathematics of complex adaptive systems.

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 colloquiums 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.

Applied mathematicians have opportunities in Arizona, the US and internationally. Typical careers are in research and development in high-tech manufacturing industries like semiconductors, biotech, aircraft, automobile; as data scientists for technology companies like Google, Facebook, Amazon etc.; as consultants for larger and smaller consultant firms (McKinsey, Rand, self-employed); or research scientists in government labs and professors at research universities and liberal arts colleges.

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

Degree Overview

The PhD in applied mathematics emphasizes a solid mathematical foundation and promotes creative scholarship in an application discipline.

The 84-credit program includes five core courses which act as qualifier exams, a written comprehensive exam, an oral prospectus, and a written dissertation. The program encourages interdisciplinary study and 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 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 also on 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.

Paloma Gutierrez CastilloMathematics is marvelous because it can be used, among other things, to understand nature. I work in computational fluid mechanics but the numerical techniques that I have been using are very flexible, and they can be applied to many different fields.


Paloma Gutierrez Castillo
PhD Applied Mathematics - Arizona State University
Arthur J. Krener Assistant Professor of Mathematics at UC Davis


The curriculum builds a strong foundation in applied mathematics and allows the flexibility of interdisciplinary learning and research. The program further encourages interdisciplinary activity by offering students the opportunity to choose dissertation advisors from outside the school. Current members of the graduate faculty in applied mathematics come from the School of Mathematical and Statistical Sciences, electrical, industrial, aerospace and mechanical engineering, and from the biological, physical, chemical and geological sciences.

Students must pass:

  • core courses, which serve in place of qualifying examinations (details below)
  • a written comprehensive exam
  • written and oral components of a dissertation prospectus
  • dissertation defense
Requirements and electivesHours
Core courses15
Courses, Electives and Exams15-30
Total hours required84

Courses and electives

There are three essential components to a Ph.D. in applied mathematics: coursework, comprehensive exam, and thesis.

One of three essential components to a Ph.D. in applied mathematics is your 84 hours (minimum) of coursework.

Year 1:

APM 505 Applied and Numerical Linear Algebra is a required core course. 

The following five applied math (APM) courses are also required:

• APM 501 Differential Equations I - ordinary differential equations 
• APM 502 Differential Equations II - partial differential equations 
• APM 503 Applied Analysis
• APM 504 Applied Probability
• APM 506 Scientific Computing

In their first year, students must complete at least five of these six required courses with an overall GPA of 3.33  and no grade less than B-. It is strongly recommended that all six courses be taken. Completion of five courses with an overall GPA of 3.33 serves in place of qualifying exams for the degree.

For electives you work with your graduate advisor to determine a minimum of 5-10 more courses.

Years 2 and 3 - In the third semester of study, students select a dissertation (thesis) advisor and a bit later, a dissertation committee. In consultation with the advisor, students will select and take two 500-level courses, one of which may be from an area outside of applied math, as the basis for their written comprehensive exam. Students must pass a written Comprehensive Exam before the beginning of the fourth year.

One of three essential components to a Ph.D. in applied mathematics is the comprehensive exam.

Comprehensive Exam – a written exam must be passed by the end of the fifth semester over advanced coursework as part of a plan of study chosen in consultation with the student’s advisor.

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

MAT 591/APM 591 Seminar (3)


One of three essential components to a Ph.D. in applied mathematics is your dissertation.

Dissertation – an original piece of research written by the student under the guidance of an advisor and the dissertation committee. Before starting the dissertation, the student must pass an oral exam based on a written dissertation prospectus, which covers background material in the general area of the thesis work. Students must pass the dissertation prospectus exam by the end of the 8th semester.

APM 792 Research

Years 4 and 5 – Student’s dissertation should be written and successfully defended by the end of Year 5. The dissertation will be reviewed by an external reviewer, approved by the advisor and the graduate director. A goal for every student is to have at least one publication submitted in a peer reviewed research journal (typically with his/her advisor and other collaborators) by graduation. Students are highly encouraged to present their research at ASU seminars and relevant research conferences.

APM/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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