Degree Requirements for the PhD in Atmosphere-Ocean Science and Mathematics

Overview of Requirements

The Atmosphere-Ocean Science and Mathematics (AOSM) PhD program follows the rules and procedures for doctoral studies in the Graduate School of Arts and Science (GSAS), and shares most of the requirements for the PhD in Mathematics. Students will be enrolled full-time for the duration of the program, which normally requires 4 to 5 years to complete. The requirements for the AOSM PhD are:

  • Complete 72 course credits (48 credits in Years I and II).
  • Pass (with grade A) the written comprehensive examination (Year I).
  • Pass the oral preliminary examination (Year II or III)
  • Defend preliminary research (Year IV)
  • Defend and submit a PhD dissertation (Year V).

The PhD dissertation should be preceded by at least one publication in a peer-reviewed journal. There is no foreign language exam requirement.


The curriculum for the AOSM PhD program is similar to that for any student focusing on applied mathematics, with the addition of a set of courses on disciplinary topics in atmosphere ocean science. All courses are worth 3 points per term, and the student must complete 72 points in total. The overall total must include 16 “core” courses, including the 7 required core courses (marked with asterisks* below), as well as 9 of the additional core courses. Exceptions to these requirements must be approved by the Director of Graduate Studies (DGS).

Core Courses

  • *Methods of Applied Mathematics (MATH-GA 2701.001 - Fall)
  • *Fluid Dynamics (MATH-GA 2702.001 - Fall)
  • *Geophysical Fluid Dynamics (MATH-GA 3001.001 - Fall)
  • *Ocean Dynamics (MATH-GA 3003.001 - Spring, alternate years)
  • *Atmospheric Dynamics (MATH-GA 3004.001 - Spring, alternate years)
  • *Climate Dynamics (MATH-GA 3005.001 - Spring, alternate years)
  • *Geophysical Turbulence (MATH-GA 3006.001 - Spring, alternate years)
  • Linear Algebra, one-term format (MATH-GA 2111.001 - Fall)
  • Real Variables (MATH-GA 2430.001)
  • Complex Variables, one-term format (MATH-GA 2451.001)
  • Ordinary Differential Equations (MATH-GA 2470.001 - Spring)
  • Partial Differential Equations I (MATH-GA 2490.001 - Fall)
  • Numerical Methods I (MATH-GA 2010.001 - Fall)
  • Numerical Methods II (MATH-GA 2020.001 - Spring)
  • Mechanics (MATH-GA 2710.001 - Spring)
  • Applied Stochastic Analysis (MATH-GA 2704.001 - Spring)
  • Probability and Limit Theorems I (MATH-GA 2911.001 - Fall)

Electives and Advanced Topics Courses

In addition to the above list, the Department of Mathematics offers a wide selection of additional courses, covering the range from fundamental topics to advanced research seminars, known as Advanced Topics courses. Many of the more advanced courses are taught as seminars, requiring only attendance. While the Advanced Topics courses are offered at irregular intervals, AOSM candidates are strongly encouraged to enroll in any that are relevant to AOS subjects, whenever such courses do not interfere with satisfaction of the required core curriculum.

Extra-departmental Courses

It is possible to take courses relevant to the student’s research in other departments at NYU, and at other universities (for example, many AOS-related courses are offered at Columbia University's Graduate School of Earth and Environmental Sciences). A base minimum of 40 credits must be obtained at NYU, and 32 of these credits must be obtained in the Department of Mathematics. Registering for classes in other departments or institutions requires permission of the DGS.

Research Credits

After completion of the preliminary oral examination, PhD students may register for PhD Research (3 points per term), which may satisfy up to 18 points.

Sample Course Schedule

Course schedules should be approved by the student’s advisor and the DGS. In any given semester, students must register for all core AOS courses they have not yet completed. An example course of study for Years I and II follows:

       Fall Term        Spring Term
Year I
  • Linear Algebra I
  • Methods of Applied Mathematics
  • Fluid Dynamics
  • Geophysical Fluid Dynamics
  • Applied Stochastic Analysis
  • Ordinary Differential Equations
  • Atmospheric Dynamics
  • Geophysical Turbulence
Year II
  • Numerical Methods I
  • Partial Differential Equations I
  • Real Variables
  • Advanced Topics in AOS
  • Numerical Methods II
  • Mechanics
  • Ocean Dynamics
  • Climate Dynamics

In Years III through V, the student will register for PhD Research, Advanced Topics in AOS, and other electives. Students are expected to maintain continuous enrollment by registering for at least one graduate course per semester, until completion of the degree.


Written Comprehensive Examination

The written examination tests the basic knowledge required to begin PhD study in Atmosphere Ocean Science and Mathematics. It consists of sections in Linear Algebra (LA), Advanced Calculus (AC), and Geophysical Fluid Dynamics (GFD). The LA and AC exams are the same as those taken by Mathematics PhD students, while the GFD exam is specific to the AOSM program. The exams are scheduled on two consecutive days, in early September or early January, with three hours allotted to each subject. All students must take the examination in order to be allowed to register for coursework beyond 36 points of credit; it is recommended that students attempt the examination during Year I, well before this deadline.

Students are required to apply for the September examination by the end of the previous spring term, and for the January examination by the end of the previous fall term; specific application deadlines, pertaining to each academic year, are found in the departmental Academic Year Calendar, distributed to students prior to each fall term (and also available at both fall and spring registration periods). Application forms are available at the Mathematics Department Office.

In the fall term, the Department offers a series of workshops to help students prepare for the LA and AC exams, while the required first-semester GFD course will prepare students for the GFD exam. Students may attempt to pass the exams twice without special permission, but a third attempt will require approval by the DGS. Copies of previous examinations may be obtained from the Assistant Director for Student Affairs (Tamar Arnon, WWH 623). Students may also wish to consult the Courant Math Wiki.

All PhD students must achieve a grade of A on written examinations in order to register for the Oral Preliminary Examination.

Oral Preliminary Examination

The purpose of the oral examination is to determine if the candidate has acquired sufficient knowledge and maturity to commence dissertation research. The oral examination is comprised of a General section and a Special section, each lasting one hour, and conducted by two different panels of three faculty members. The exam sections are usually taken together during the spring of Year II, but are offered each fall, mid-winter and late spring.

  • The General Exam is based on five topics chosen by the student from a list of fundamental topics in applied mathematics and atmosphere-ocean-climate science. The list should be formed in conjunction with, and approved by the student’s advisor.
  • The Special Exam is based on specific topics relating to the student's planned thesis research. The format of this exam is similar to that of the general exam, but may include some form of research presentation as well. The schedule and format details for this exam will be determined in conjunction with the student's thesis advisor and the DGS.

PhD students must achieve a grade of Pass on both exam sections in order to continue in the program.

Research and Advisement

Choosing a Thesis Advisor

Upon entering the AOSM PhD program, each student is assigned an academic advisor, who will help the student choose courses, and offer consultation about choosing a research area and research advisor. During the fall of Year I, the student should make individual appointments to discuss research opportunities with each of the faculty affiliated with CAOS. Ideally, the choice of research advisor would be based solely upon mutual agreement between the faculty and student. However, two additional factors must be taken into consideration: (i) research funding for graduate student support must be available to the potential faculty advisor, and (ii) students should be equitably distributed among the faculty affiliated with CAOS. To ensure that these requirements are satisfied, the choice of advisor must be approved by the AOSM DGS.

Thesis Committee

Within six months of completion of the oral examinations, the student, in conjunction with his or her advisor, will choose a three-member thesis committee, consisting of the student’s advisor, one additional CAOS faculty member, and one member from an academic institution beyond NYU. The final committee will consist of two additional non-readers who may be chosen closer to the time of the final dissertation defense.

Committee Meetings

The student should consult regularly with all members of the committee, and must meet to discuss his/her progress with the committee every 6-12 months. The outside committee member should be included by teleconference, unless funds are available to cover the member’s travel to Courant.

Thesis Topic Defense

In Year IV, the student will give a formal presentation to the members of CAOS and the student’s thesis committee. The presentation will cover the planned focus of the PhD thesis, and support the proposed topic with preliminary research. Upon completion of the formal presentation, the committee will meet alone with the student to give extended critical feedback on the student’s progress.

Dissertation Defense

The written dissertation should be based primarily on research published in peer-reviewed journals (at least one should be accepted before defending). The Graduate School of Arts and Sciences at NYU sets requirements for all NYU PhD dissertations; these may be found at the Doctoral Dissertation Submission Guidelines page. Note in particular that students must register for graduation on Albert at least five months prior to the defense.

The oral defense is the final examination of the student’s dissertation. The defense is conducted by five faculty, including the three thesis committee “readers” and two additional “non-readers.” The candidate presents his/her thesis research to both the committee and a general audience, followed by a lengthy question-and-answer period, conducted primarily by the thesis committee.

The following schedule is required:

  • Two months before defense: The additional two “non-reader” members of the committee should be chosen by the student and advisor.
  • One month before defense: The completed written dissertation should be distributed to all five members of the committee.
  • Within two weeks after defense: The final version of the written dissertation, including corrections and changes requested by the committee, must be submitted.

Additional Program Policies and Information

Financial Support

All AOSM PhD students are supported by MacCracken Fellowships, which cover tuition, registration fees and the NYU individual comprehensive health insurance plan. MacCracken funding is renewable for a period of up to five years, contingent upon good progress toward the degree. Students will receive a stipend for the nine-month academic year, covered by the MacCracken Fellowship, support from faculty research grants, and/or external fellowships. A list of external fellowships and other support may be found at the Department of Mathematics Financial Aid Policies page.

Teaching Opportunities

There are ample opportunities for all supported PhD students in the Department of Mathematics to assist in teaching undergraduate mathematics courses. Teaching is optional, and compensation for teaching is provided in addition to the student's nine-month academic year stipend. Students may not teach during the first year of study, and may serve only as graders in the second year of study. During Years III through IV, students have the opportunity to act as Teaching Assistants (TA), for a maximum of four semesters in total.

Summer Support and Opportunities

While the department cannot explicitly guarantee financial support for graduate students during summer months, all past AOSM students who have sought support have received research assistantships while engaged in research with a faculty advisor. In addition, past students have attended summer schools on advanced topics, taken research internships at national labs, or participated in field projects. In lieu of other options, a limited number of teaching positions are available to all PhD students in the department.


Admitted PhD students are eligible for the MacCracken Housing Program, which provides subsidized housing in Stuyvesant Town for the first year of study. After the first year, students typically move to off-campus housing. The NYU Off-Campus Housing Office may be of some assistance in this process.

Master's Degree

The AOSM program does not offer a master’s degree. However, those students who choose not to complete their PhD may opt to receive a Master of Science (MS) in Mathematics. To obtain the MS in Mathematics, the student must (i) pass the written examinations for the Mathematics PhD program with an overall grade of B or better, and (ii) complete at least 36 points of course work. Additional policies and details for the MS in Mathematics may be found at the Mathematics MS page.

Transfers Between the AOSM and Mathematics PhD Programs

Students pursuing the PhD in Mathematics may transfer to the AOSM program, contingent upon satisfaction of the special requirements of the program, and approval by the AOSM Admissions Committee. Conversely, students in the AOSM program wishing to switch to the Mathematics PhD will be treated exactly as a mathematics MS student wishing to enter the mathematics PhD program.

Visa Requirements for International Students

It is important that all foreign students keep their visa status with the United States accurate and up-to-date. Please consult the Office of International Students and Scholars for pertinent details.

How to Apply?

Start at the Apply to the AOSM Program page