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Doctoral Program

To be admitted to study for the degree of Doctor of Philosophy in Aeronautics and Astronautics, students must have fulfilled the requirements for the department's Master of Science degree or its substantial equivalent.

Applicants who have received their MS from other institutions may apply directly to the PhD program. Students who are currently pursuing the MS in our department and wish to continue for the PhD should submit a graduate program authorization petition form online through Axess at the beginning of their last quarter in the master's program. Current Stanford students in other degree programs who wish to be considered for admission to the Aero/Astro PhD program will also follow the procedures described above, but will need to submit additional supporting materials; check with the Aero/Astro Student Services Office for details.

Qualifying examination procedures(Quals)

Before beginning dissertation research for the PhD degree, a student must pass the departmental qualifying examination. Admission to Stanford University for study beyond the master’s degree does not imply that you have been admitted to candidacy for the PhD — that special designation is reserved for students who have passed the department’s PhD Quals. After passing the exam, the student will then need to submit an approved program of PhD course work on an Application for Candidacy for Doctoral Degree to the Student Services Office.

The purpose of the PhD Quals is to evaluate your capacity to perform outstanding research and that you are adequately prepared to undertake the research. The basis of this examination is a series of oral examinations given in the four fields of dynamics and controls, fluids, structures and applied math/IT. Every student is examined in three of these fields: one field for a major field exam and two other fields for minor field exams. The decision on the qualification of each student for the PhD program is based on the student's:

  • Ability to assimilate knowledge.
  • Aptitude for independent thought.
  • Fundamental understanding of the basic principles.
  • Potential to conduct research.

Eligibility and general advice

Eligibility: A student must meet the following conditions by the appropriate deadline to be able to take the qualifying examination:

  1. 30 units of master's coursework completed. A student who has completed fewer than 30 units may petition to take Quals.
  2. Stanford graduate GPA of 3.5 or higher.
  3. Investigation of a research problem, under the direction of a faculty member who will evaluate this work as evidence of the potential for doctoral research. The minimum requirement for taking Quals is to complete 3 units of AA 290 before the Quals quarter.


A student in the Aero/Astro MS program who wishes to pursue doctoral study must take the qualifying examination in autumn or spring of the second year. A PhD student who did not study in our MS program must take the first available qualifying examination after two quarters of study here. Honors Cooperative students who have enrolled at less-than-fulltime for most of their study should take the qualifying examination within two years after entering the PhD program. All petitions to waive specific Quals conditions or to defer the exams are due the first week of the Quals quarter; they must include advisor signature and appropriate documentation.


The Aero/Astro PhD qualifying exam is given once in the fall quarter and once in the spring, usually in the second week of November and May. The exact dates will be announced several weeks before the exam. Application forms (including the dates and participating faculty for this exam) are made available early each Quals quarter and are due approximately two weeks later; the application serves as the basis for exam scheduling. The application must have the signed approval of the student's advisor and research supervisor.

Recommended courses to prepare for qualification examination

  • The major field exam will be a 60-minute test of knowledge and understanding on topics selected by the committee, based on the student's chosen area, including 15 minutes devoted to pertinent mathematics. It will be conducted by a committee of four examiners, chaired by either the academic or research advisor. Committee members should be from Aero/Astro faculty participating in the exams, from the field closest to the student’s specialty. If the student has done significant research in this area with another faculty member, however, the student may petition to have that professor on the major field exam committee. Also, for applied math/IT, committee members may be faculty from other departments at Stanford who are specialists in these areas.
  • There will be two examinations in each minor field. Each minor examiner will conduct a separate 15-minute oral exam. Questions are usually from materials in courses (ENGR 105, AA242A, AA200, AA210A, AA240A, AA240B, courses listed under Applied Mathematics and IT), or their equivalent at other universities, but may cover fundamentals from earlier (undergraduate) courses as well. Examinations are not intended to evaluate course work, but focus on general understanding, aptitude and assimilation of knowledge. Minor examiners are to be chosen from the faculty participating in the exams in each field.
    • Controls and dynamics
      Engr 105: Feedback Control Design
      AA 242A: Classical Dynamics
    • Fluids
    • AA 200: Applied Aerodynamics
    • AA 210A: Fundamentals of Compressible Flow
    • AA 240A: Analysis of Structures
    • AA 240B: Analysis of Structures
    • Structures
    • CME 204: PDEs in Engineering (ME 300B)
    • CME 303 = MATH 220: PDEs of Applied Mathematics (MATH 220)
    • EE 261: Fourier Theory
    • MS&E 313: Vector Space Optimization
    • EE 263: Intro to Linear Dynamical Systems
    • CME 200 = ME 300a: Linear Algebra with Application to Engineering Computations
    • CME 302: Numerical Linear Algebra
    • CME 306: Numerical Solution of PDEs
    • CS 221: Artificial Intelligence: Principles and Techniques
    • CS 229: Machine Learning
    • MS&E 221: Stochastic Modeling
    • CME 308 = MATH 228: Stochastic Methods in Engineering
    • EE 278: Intro to Statistical Signal Processing
    • ENGR 207b: Linear Control Systems II
    • MS&E 251: Stochastic Decision Models
    • CME 304: Numerical Optimization
    • AA 222: Intro to Multidisciplinary Optimization
    • EE 364a: Convex Optimization
    • Applied math and information technology (IT). Students can choose one sub-area in this field as a choice for a major or minor field exam. The exam will be based on two non-overlapping courses selected from a sub-area below. Additional courses in any sub-area may be proposed with advisor consent, and will be reviewed for approval by the candidacy chair.
    • Mathematics of continuous systems
    • Linear algebra and numerical methods
    • AI / machine learning
    • Stochastic processes and control
    • Optimization
  • AA 290/Research examination

    The qualifying exam includes a 30-minute research examination consisting of a 20-minute presentation and 10 minutes of questions and answers. The research presentation committee will be selected from your major exam area, and will include at least three Aero/Astro faculty members, counting the advisor. We will sometimes also reach out to other Stanford departments for additional examiners. The content of the presentation should be based on a minimum of 3 units of completed AA 290 work, focus on what the student has done, and demonstrate an understanding of how to approach a research problem.

You should consider the following outline when preparing your Qualifying Examination research presentation:

1.      What is the research problem? Why is it hard? Who does it impact?

2.      How is it solved today? What are the limits of current practice?

3.      What is the new technical idea? Why we can succeed now?

4.      Are there others dedicated to finding a solution to the problem?

5.      What is the impact if successful?

  • General advice for Quals research
    Be sure that the faculty member understands you are doing Quals research — the type of project and level of interaction may differ from a simple: "Let-me-try-this-field" AA290. If the supervising faculty member is not in the Aero/Astro department, you should consult in advance with the Aero/Astro Student Services Office and your Aero/Astro advisor to ensure that this research will meet the Quals requirement.

Qualification decision

Following the qualifying examination, the results will be discussed by the department faculty in a closed meeting. In addition to performance on the examination, the student's research potential and academic performance are considered. FINAL DECISIONS WILL BE RELAYED TO THE STUDENT BY THE ADVISOR.

Students who fail to qualify may remain in (or be admitted to) the PhD program only if they pass the next available qualifying examination. The qualifying examination may not be taken more than twice. A student who fails to qualify after two attempts may remain in the AA-PhD program for one additional quarter. After this additional quarter, a student will be formally dismissed from the PhD program by the Aero/Astro Faculty Committee. In this quarter, the department will not approve a leave of absence or any form of reduced tuition.

If students elect to formally enter the engineer degree, they must discontinue the PhD at the same time they add the engineer degree via the graduate program authorization petition.

Entering candidacy

At Stanford, PhD students must complete the candidacy process and be admitted to candidacy by their second year of doctoral study. Students must first pass the departmental qualifying exam (for detailed deadlines, see the section on PhD qualification, above), and must then submit an official Application for Candidacy for Doctoral Degree. The department-specific candidacy form can be found at the Aero/Astro Student Services Office, and lists the courses the student will take to fulfill the requirements for the degree. The candidacy form must include the full 90 non-MS units required for the PhD; it should be signed by the advisor and submitted to the Aero/Astro Student Services Office for the candidacy chairman's signature before the end of the quarter in which you pass the qualifying examination. Changes can be filed at any time by submitting a revised candidacy form. To graduate or go TGR (Terminal Graduate Registration), you must have completed all the units listed on your current candidacy form. Candidacy is valid for five years; this term is not affected by leaves of absence.

Course requirements

Each individual program, designed by the student in consultation with the advisor, should represent a strong and cohesive program reflecting the student's major field of interest. A total of 90 units of credit is required beyond the MS. Of these 90 units, a minimum of 27 must be formal coursework (excluding research, directed study and seminars), consisting primarily of graduate courses in engineering and the pertinent sciences. The remainder of the 90 units may be in the form of either PhD dissertation units or free electives. Units applied toward the MS degree cannot be used again. For students who elect a minor in another department, a maximum of 9 units from the minor program may be included in the 27 units of formal coursework; the remaining minor units may be considered free electives and are included within the 90 unit total required for the Aero/Astro PhD.

Mathematics: Students working toward the doctoral degree in Aeronautics and Astronautics must take 9 units of mathematics courses, with at least 6 of these units taken from courses with numbers over 200. A preapproved list of Mathematics Requirements in Aero/Astro is in the department's handbook, and includes all courses in Mathematics numbered 200 or above, but there are many others that may be acceptable. Please consult with your advisor and the Aero/Astro Student Services Office before assuming that a particular course will be accepted in your own program.

Grade Point Average

A minimum grade point average (GPA) of 3.0 is required to fulfill the department’s Ph.D. It is incumbent upon Ph.D. students to request letter grades in all courses listed on the Application for Candidacy form.

Dissertation reading committee

Each PhD candidate is required to establish a reading committee for the doctoral dissertation within six months after passing the department's PhD qualifying exam. Thereafter, the student should consult frequently with all members of the committee about the direction and progress of the dissertation research.

A dissertation reading committee consists of the principal dissertation advisor and at least two other readers. (If the principal advisor is emeritus, there should be a non-emeritus co-advisor.) If the principal research advisor is not within the Aero/Astro department, then the student's Aero/Astro academic advisor should also be a member of the reading committee. It is expected that at least two members of the Aero/Astro faculty will be on the reading committee.

Although all readers are usually members of the Stanford Academic Council, the department chair may approve one non-Academic Council reader if the person brings unusual and necessary expertise to the dissertation research. Generally, this non-Academic Council reader will be a fourth reader, in addition to three Academic Council members.

The student must submit a doctoral dissertation reading committee form, signed by each of the readers, to the Aero/Astro Student Services Office for approval by the department chair. Approval of a non-Academic Council reader requires submission of an additional petition. The initial committee should be officially approved within six months of passing Quals. Any subsequent changes to the reading committee must be submitted to the Aero/Astro Student Services Office for approval by the department chair prior to submission of the dissertation. [The “change of advisor or reading committee” form requires the signature of anyone who is added to the committee; advisors/readers who signed the original form do not need to sign again.]

University oral examination

Each PhD candidate is required to take the university oral examination after the dissertation is substantially completed (with dissertation draft in writing) but before final approval of the dissertation. The examination consists of a public presentation of dissertation research, often during a seminar, followed by substantive private questioning on the dissertation and related fields by the University Orals Committee. This committee comprises four faculty examiners plus a chairman. The examiners usually include the three members of the student's PhD Reading Committee. The chairman must not be in the same department as the student or the advisor. (For students who elect a PhD minor, the minor department may require representation on the Orals Committee.) Once the oral examination has been passed, the student finalizes the thesis for Reading Committee review and final approval.

Forms for the University Orals Scheduling are available in the Aero/Astro Student Services Office. These forms must be submitted with a thesis abstract to the Aero/Astro Student Services Office at least three weeks prior to the date arranged for the oral. (Please refer to "student procedures for scheduling university oral examinations.") Note: Students must be enrolled during the quarter when they take their university orals. If the orals take place during the vacation time between quarters, the student must be enrolled in the prior quarter.

Doctoral dissertation

Please refer to the Directions for Preparing Doctoral Dissertation, which outlines the university guidelines for preparing a PhD dissertation. When you are ready for a final draft of your dissertation, make an appointment to consult with the graduate degree progress officer there to go over a review of the completion of your PhD program and the strict formatting requirements for the dissertation. Submit the final version of your dissertation to the Registrar's Office no later than the posted deadline. Note: All members of the Reading Committee must sign the dissertation before the filing deadline.

Mid-year degrees are not officially conferred until the first week of the quarter after degree completion, and actual diplomas are printed only once a year for distribution at the university's Commencement in June. However, students who have submitted the dissertation and have no outstanding Stanford obligations (financial or academic) may obtain an official University "certificate of completion" from the Graduate Degree Progress Office.

Note: Students who have passed their University Oral Exams in a prior quarter may be eligible to petition for a graduation quarter. For details, contact the Aero/Astro Student Services Office. International students should consult carefully with the International Center before selecting specialized registration status because their visas may prohibit it.