Every first-year Ph.D. student must take the diagnostic placement exam prior to their first semester at Tulane.

• Structure & Scope: A 4-hour written exam covering undergraduate Linear Algebra and Vector Calculus, administered during the week before Fall classes begin. The syllabus is available on the department website.
• Remote Testing: Incoming students unable to take the exam in person must arrange to take it remotely on or around the scheduled day. Failure to take the exam remotely or in person requires registration in all relevant undergraduate prerequisite courses.
• Academic Pathway on Failure: Students who do not pass the placement exam are required to enroll in select upper-division undergraduate courses (such as Linear Algebra or Real Analysis) to build proficiency. These prerequisite courses do not count toward graduate credit, and the student must earn a grade of A− or higher.
• Dismissal Risk: Progress is reviewed at the end of each semester. Students who fail to earn an A− in these courses will be considered for dismissal from the Ph.D. program (unless they show strong progress in other coursework, in which case the GSC may permit them to take further prerequisite courses).

Summer Graduate Communication Program

Following School of Science and Engineering (SSE) policy, all international graduate students (including native English speakers) supported by a Teaching Assistantship (TA) must take the Summer Graduate Communication Program. Exemption requests for students holding degrees from U.S. institutions are reviewed case-by-case.

Based on program performance, TAs may be required to take additional linguistic coursework: SCEN 7650 (Advanced Professional Speech) in the Fall, and SCEN 7660 (Advanced Professional Writing) in the Spring.

Start Date and Relocation

Incoming students must provide proof of relocation to New Orleans by the university's course-add deadline. Failure to do so may result in their start date being deferred to the next semester.

Ph.D. coursework is structured to establish a solid mathematical foundation while transitioning students into active doctoral research.

• In-House Credit Requirement: Students must complete 33 credit hours (11 graduate courses) approved by the Graduate Studies Committee (GSC). All 7000-level math courses count toward this limit.
• 6000-Level Course Restrictions: By default, the only 6000-level courses that count toward the 33 credits are Math 6210 (Differential Geometry) and Math 6300 (Complex Analysis). Exceptional pre-approval for other 6000-level courses is granted by the GSC only when no 7000-level equivalent exists at Tulane.
• Bridging the SSE 48-Credit Gap: The School of Science and Engineering (SSE) requires 48 credit hours for graduation. Once the department's 33 credits are completed, the remaining 15 credits are met by registering for Math 7980 (Reading and Research) on a pro forma basis or Math 9990 (Dissertation Research) under the advisor. Alternatively, students can take extra elective graduate courses pending advisor and GSC approval. Both the student and their advisor share the responsibility to ensure the 48-credit limit is reached prior to graduation.
• Reading & Research Courses (Math 7980): Reading courses are limited to students who have passed both Qualifying Exams and secured an advisor. At most 6 credit hours (2 courses) of Math 7980 can count toward the in-house 33 credit-hour requirement. Registration requires advisor and GSC approval via the Independent Study Registration form and a one-paragraph justification.
• External Credits: Up to 6 credit hours (2 courses) may be taken in other departments at Tulane, subject to advance GSC approval. Pre-quals students are generally not permitted to take external courses.
• Transfer Credits: A maximum of 6 credit hours (2 courses) may be transferred from another institution with GSC approval. Transfer courses must show substantial overlap with Tulane offerings, and the student must have received a grade of B or higher. Discuss with the DGS and submit the request form.
• Learning Seminar Courses (LSCs): Officially announced as Special Topics courses (Math 7710–7790), LSCs count toward the 33 credits and are open to 2nd-year+ students (first-year students require GSC approval). They meet 75 minutes weekly, are voluntary for faculty, and help prepare students for oral exams.

Doctoral students are expected to maintain high academic standards throughout their tenure.

• Minimum QPR: All SSE graduate students must maintain a cumulative Quality Point Ratio (GPA) of 3.0 (B) or higher.
• Probation Rules: Receiving a single grade of B− immediately triggers a review for academic probation by the SSE Associate Dean in consultation with the GSC.
• Dismissal for Low Grades: Earning two grades of B−, or one grade below B− (such as C+ or lower), will result in the student being placed on academic probation and considered for dismissal from the program.
• Probation Terms: The specific terms are negotiated by the department and the Associate Dean, typically requiring the student to receive grades of B+ or higher in all classes in the subsequent semester.
• No Prerequisite/Core Credit: Graduate students will not receive credit toward any program requirement for a course in which they receive a grade lower than B−.

Doctoral students must pass two comprehensive 4-hour written qualifying exams in two different areas of mathematics to demonstrate broad academic competency. Exams are offered twice a year, in August (before the Fall semester) and January (before the Spring semester).

Offered Subjects

The exams offered depend on the first-year sequences taught, based on direct syllabi which align with course content but are subject to rotation:

• Algebra
• Analysis
• Applied Mathematics
• Differential Geometry*
• Partial Differential Equations*
• Probability and Statistics
• Scientific Computation
• Topology
• Algebraic Geometry*

*Offered in accordance with course rotations.

Exam Policies & Restrictions

• Total Attempt Limit: A student has a maximum of 4 total attempts to clear both exams.
• Subject Limit: A student can attempt a single subject exam at most 3 times (leaving only one attempt for the second exam).
• No-Switching Subject Rule: Once a student attempts a qualifying exam in a specific subject, if they fail, they must continue to take the exam in that same subject. Switching is only permitted if the student has completed the corresponding graduate sequence and earned a grade of B or higher in both courses, or by special DGS authorization.
• Round Limits: A student cannot sign up for more exams in a round than they still need to pass (e.g., a maximum of 2 exams in a round. Once 1 exam is passed, they can only attempt 1 exam in a round).
• August "Freebies": Incoming first-year students may attempt up to two qualifying exams in August prior to their first semester. A pass counts toward the requirement, while a failure is voided and does not count toward the 4-attempt limit or the no-switch restriction.
• Deadline & Dismissal: Students must pass both exams by the beginning (January) of the Spring semester of their second year. Failure to do so results in dismissal from the Ph.D. program (students may transition to a terminal M.S. and continue as a TA for the rest of their second year, provided they satisfy all M.S. requirements).
• Extenuating Circumstances: If unable to sit for a scheduled exam, the student must notify the DGS immediately and submit an appeal to the GSC to be considered for testing in a later round.

Registering for Math 9990

Students who clear their quals by August of Year 2 can register for Math 9990 (Dissertation Research) pending advisor/DGS approval. Those clearing by January of Year 2 register temporarily for Math 9990 as DGS advisees while searching for an advisor.

Finding a research advisor is a critical milestone for transitioning from coursework to independent research.

• Pre-Quals Status: Pre-quals students are advised by the Director of Graduate Studies (DGS) by default. They are encouraged to informally discuss research interests with faculty.
• Selection Deadline: The absolute deadline for securing a dissertation advisor is the end of April of the second year in the program.
• Early Selection: Students who clear their quals early (by August of Year 2) are strongly encouraged to secure an advisor by December of Year 2.

The purpose of the oral exam is for the student to learn and communicate advanced material specific to their dissertation research in more depth than qualifying exams.

• Prerequisites: Students must pass the placement exam and both qualifying exams, and must have a secured advisor. Coursework completion is recommended but not required.
• Committee Size & Composition: Set up in consultation with the advisor, the committee consists of the advisor and at least 3 (usually 4) faculty members. Under SSE rules, a majority of the committee must be tenured/tenure-track Tulane faculty. Postdocs may participate as non-faculty.
• Format & Syllabus: The student and advisor construct a narrow syllabus of topics and references. The exam lasts 1 to 2 hours and consists of direct questions asked by the committee based on the syllabus. No presentation is necessary or permitted.
• Deadline: It is strongly recommended that students pass the oral exam by the beginning of Fall of Year 3. They are required to pass by the beginning of Spring of Year 3 (January).
• Consequences of Failure: A student who fails the oral exam twice will be dismissed from the Ph.D. program. A student who has not passed by the January deadline will be considered for dismissal.

Admission to candidacy marks the completion of all Ph.D. requirements except the dissertation itself.

• Requirements: Completed once coursework is finished and placement, qualifying, and oral exams are passed.
• Prospectus Exception: In the Mathematics Department, the prospectus is not a prerequisite for admission to candidacy.
• Timeline: Following SSE rules, candidacy must be completed and approved at least 6 months prior to graduation. Students must fill out the SSE Admission to Candidacy form, obtain the Department Chair's signature, and submit it to the SSE Dean's office.

The written prospectus outlines the student's research agenda and demonstrates its feasibility to their dissertation committee.

• Deadline: Students must successfully defend their prospectus by the end of the Fall semester of the fourth year.
• Format: A 4–8 page double-spaced written document, followed by a 20-minute oral presentation to the dissertation committee, then discussion and questions.
• Required 6-Part Structure:
  1. Cover Sheet: States student's name, program, title of proposed dissertation, advisor, and committee members.
  2. Introduction: A summary of earlier work on the problem, containing substantial literature references.
  3. Statement of the Dissertation Problem: Defines the goals of the thesis, sub-problems, and their importance.
  4. Investigation Plan: An orderly description of the major steps of the research and why they are likely to succeed.
  5. Expected Results: Expected partial or complete results for each phase of the plan.
  6. References: Selective bibliography of major sources of information.
• Pass/Fail & Submission: The committee decides immediately after the defense. If passed, the prospectus and signed prospectus approval form must be submitted to the SSE Graduate Programs office.

The dissertation is the culmination and primary purpose of the Ph.D. degree, demonstrating independent research and a genuine contribution to Mathematics.

• Advisor Meetings: Students are expected to meet with their advisors frequently—at least once per week—to ensure steady progress.
• Continuous Registration: Post-coursework students must register for Math 9990 (Dissertation Research) every semester, including Summer, to remain in good standing.
• Co-advisors: Working with a co-advisor outside the Math Department requires permission from the student's Math advisor and the DGS.
• Dissertation Committee: Consists of the advisor plus at least 3 (usually 4) members. Under SSE rules, a majority of the committee must be tenured/tenure-track Tulane faculty. Professors of Practice, Research Professors, and external faculty are allowed; postdocs may participate as non-faculty.
• LaTeX Formatting: The dissertation must use the official SSE LaTeX template, which is available at the LaTeX Resources page.
• Draft Submission Deadline: A completed draft of the dissertation must be submitted to all committee members at least one month prior to the scheduled oral defense.
• Oral Defense Format: Scheduled in coordination with the committee, but no later than the SSE graduation deadline. The defense begins with a 40 to 50-minute presentation of research results, followed by questions from the committee. Immediately after, the committee decides on pass/fail and notifies the DGS.
• Publications: While publications are not a strict graduation requirement, students are strongly encouraged (with advisor approval) to submit research papers during the dissertation writing period.