Contact Info
| Phone: | 314-935-6760 |
| Website: | https://math.wustl.edu/graduate |
To earn a PhD at Washington University, a student must complete all courses required by their department; maintain satisfactory academic progress; pass certain examinations; complete all requirements for doctoral candidacy; fulfill residence and Mentored Experience Requirements; write, defend, and submit a dissertation; and apply for program completion (graduation) via Workday Student.
For the details of doctoral degree general requirements in Arts & Sciences, including an explanation of Satisfactory Academic Progress, students should review the Doctoral Degree Academic Information page of the Arts & Sciences Bulletin.
Program Requirements
- Total Units Required: 36 units (Note: Remission applies for a maximum of 72 graduate-level units.)
- Degree Length: 5 years
- Note: At least 24 units must be earned while in residence at Washington University. The student must spend at least one academic year in residence as a full-time student. The student may, with departmental permission, transfer a part of the 36 units from other universities (12 graduate credits for a PhD and only 3 credits for a master's). The typical load is 9 credit units per semester. A grade point average of B or better is required in graduate coursework and in qualifying exam courses.
- Note: Students must be enrolled in 9 graduate credits each semester to retain full-time status. As students complete their coursework, if enrolled in fewer than 9 graduate credits, they must enroll in a specific Arts & Sciences graduate course that will show 0 units but does count as full-time status. Students should connect with their department to ensure proper enrollment prior to Add/Drop.
- Funding Note: Graduate students in mathematics may ordinarily expect up to five years of support. Continuation of support each year is dependent upon normal progress toward the degree and the satisfactory performance of duties.
- For the well-prepared student, "normal progress" usually means the following:
- At the end of the second year, the student should have successfully completed the qualifying exam/course requirements.
- At the end of the third year, the student should have completed the candidacy requirement.
- By the end of the program, the student must complete the 36-unit course requirement, the eight qualifying exams/courses requirement, and the requirement of completing three additional courses.
- For the well-prepared student, "normal progress" usually means the following:
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Students must complete MATH 5090 Teaching Seminar during their second and third semesters. This course prepares them for both Assistant to the Instructor work and academic teaching duties, which are integral to all scholarly activities. Each student will have departmental duties (e.g., grading, proctoring) of no more than 15 hours per week as Assistant to the Instructor.
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Students must complete MATH 5095 Mathematical Professional Development Seminar during their third semester (fall of their second year) .
- Grade Requirement: A grade point average of B (3.0) or better is required in graduate coursework.
No one can earn a doctorate merely by completing specified courses of study. The doctoral candidate must demonstrate high scholarship and the ability to perform significant original research in mathematics.
Please note that the sequence outlined above is for "well-prepared" students. The exact point at which any student enters the sequence depends on their ability and background. When warranted, deviation from the normal sequence is permissible, and a tailored program that fits the student's ability and background will be followed.
Qualifying Requirements/Required Courses
Students must satisfy eight out of nine “qualifying requirements” associated with the following courses:
| Code | Title | Units |
|---|---|---|
| MATH 5121 | Complex Analysis I | 3 |
| MATH 5122 | Complex Analysis II | 3 |
| MATH 5151 | Measure Theory and Functional Analysis I | 3 |
| MATH 5152 | Measure Theory and Functional Analysis II | 3 |
| MATH 5221 | Geometry/Topology I: Algebraic Topology | 3 |
| MATH 5222 | Geometry/Topology II: Differential Topology | 3 |
| MATH 5223 | Geometry/Topology III: Differential Geometry | 3 |
| MATH 5331 | Algebra I | 3 |
| MATH 5332 | Algebra II | 3 |
A “qualifying requirement” consists of either of the following: 1) obtaining an A– or better in the associated course; or 2) passing an independent exam for the associated course.
We will allow two exceptions to the first item wherein a B or better is permitted. The omitted course/requirement cannot be MATH 5331 Algebra I or MATH 5332 Algebra II. The second item would be an option for new students who have proven background in a subject area or for students who took a qualifying exam course and received a grade of less than a B. (Note: A B– is less than a B.) These exams would typically be given shortly before the beginning of a new semester. What constitutes a "pass" is at the discretion of the instructor, the Director of Graduate Studies, and the graduate committee; however, the standards should be as close as possible to the standards used in Math courses.
Students must pass three additional courses with a B– or higher chosen from our advanced topics courses (which include MATH 5333 Algebraic Geometry), independent study/research courses, or a qualifying exam course beyond the eight required above.
The courses are typically offered in the following time frame:
- Fall: Algebra I, Real Analysis, Complex Analysis I, Algebraic Topology, Differential Geometry
- Spring: Algebra II, Functional Analysis, Complex Analysis II, Differential Topology
In exceptional circumstances, departmental permission may be requested to replace required courses with suitable alternatives. Also in exceptional circumstances, such as for students who have already completed a master's degree, the student may also petition the department to waive one or more of the qualifying requirements because of work completed previously.
It is in each student's best interest to take the courses that contain the material covered in the qualifying exams as soon as their individual program allows. Sequels to these courses, at the 5000 level, are frequently offered. The qualifying exam courses are generally prerequisites to these 5000-level courses.
Additional Requirements
Course Requirements
Students must also complete MATH 5090 Teaching Seminar. This course prepares students for both Assistant to the Instructor work and academic teaching duties, which are integral to all scholarly activities. For a typical PhD student, the course is taken twice: once in the spring of the first year and again in the fall of the second year. Each student will have departmental duties (e.g., grading, proctoring) of no more than 15 hours per week as Assistant to the Instructor.
Students must also complete MATH 5095 Mathematical Professional Development.
| Code | Title | Units |
|---|---|---|
| MATH 5090 | Teaching Seminar | 2 |
| MATH 5095 | Mathematical Professional Development | 1 |
Language Requirements
All students must demonstrate proficiency in English.
If English is not the student's native language, they must pass an oral English proficiency exam with a grade of 3 or better. If the student does not score a 3 the first time they take the exam, the director of English Language Programs for Arts & Sciences will recommend that the student take one or more courses to improve reading, writing, pronunciation, listening, or speaking skills. Note that courses "recommended by ELP" are required by the Department of Mathematics. After the recommended courses have been completed, the student is required to retake the English proficiency exam. Once the student has demonstrated the ability to handle teaching a class (by scoring a 3 or better on the exam), they will qualify for Assistant to the Instructor or Course Instructor duties.
Qualifying Examinations
Progress toward the PhD is contingent upon the student passing examinations that are variously called preliminary, qualifying, general, comprehensive, or major field exams. The qualifying process varies according to the program. In some programs, it consists of a series of incremental, sequential, and cumulative exams over a considerable time. In others, the exams are held during a relatively short period of time. Exams may be replaced by one or more papers. The program, which determines the structure and schedule of the required examinations, is responsible for notifying the Office of Graduate Studies, Arts & Sciences, of the student’s outcome, whether successful or unsuccessful.
The qualifying exam/course requirement consists of the completion of eight qualifying requirements as outlined above.
Doctoral Candidacy
Candidacy marks the transition from coursework and initial study to independent research and dissertation writing. At this stage, the student is considered prepared to contribute to their field through independent scholarship.
The status of candidacy for WashU Arts & Sciences doctoral students indicates a student has, at minimum, completed and passed their qualifying exam/paper and pre-candidacy requirements. Pre-candidacy requirements are determined by each PhD program. Those requirements may include, for example, completion of required coursework; completion of required foreign language exams; completion of the Mentored Experience Requirement; successful submission of the Title, Scope and Procedure form; and completion of the oral presentation to propose the dissertation to their Research Advisory Committee.
The pre-candidacy requirements consist of completing the qualifying exam/course requirements and additional course requirements as well as any necessary language requirements. In addition, the student must form a preliminary thesis committee called a Research Advisory Committee that includes their advisor and at least two other faculty members. The pre-candidacy requirements should be completed by the end of the second year of study.
The candidacy requirement is an oral presentation and thesis proposal to be completed by the end of the third year of study. In discussion with the advisor and the preliminary thesis committee, the student will select a topic and a body of literature related to this topic. The student will prepare a one-hour oral presentation related to the topic and a two-page thesis proposal that demonstrates mastery of the selected topic. The oral presentation is designed to expedite specialized study and to provide guidance toward the thesis. The preparatory work for the thesis proposal often becomes the foundation on which the thesis is constructed.
After the student completes the candidacy requirement, work on the thesis begins.
Mentored Experience Requirement
Doctoral students, MFA in Writing students, and MFA in Dance students at Washington University must complete a department-defined Mentored Experience Requirement. The Mentored Experience Requirement is a degree requirement that is notated on the student's transcript when complete. Each department has an established Mentored Experience Implementation Plan in which the number of units that a student must earn through Mentored Teaching Experience(s) and/or Mentored Professional Experience(s) is defined. Each Mentored Experience Implementation Plan outlines how doctoral students within the discipline will be mentored to achieve competencies in teaching at basic and advanced levels. Some departments may elect to include Mentored Professional Experiences as an avenue for completing some units of the Mentored Experience Requirement. Doctoral students will enroll in ASGS 8005 MTE - Assistant in Instruction Experience, ASGS 8010 MTE - Assistant in Instruction Experience, or ASGS 8015 MTE - Assistant in Instruction Experience; ASGS 8020 MTE - Mentored Independent Teaching Experience; or ASGS 8120 MTE - Mentored Professional Experience to signify their progression toward completing the overall Mentored Experience Requirement for the degree.
The Doctoral Dissertation
A Research Advisory Committee (RAC) must be created no later than the end of the student's second year; departments may set shorter timelines (e.g., by the end of the student's third semester) for this requirement. As evidence of the mastery of a specific field of knowledge and of the capacity for original scholarly work, each candidate must complete a dissertation that is approved by their RAC.
A Title, Scope, and Procedure form for the dissertation must be signed by the committee members and by the program chair. It must be submitted to the Office of Graduate Studies, Arts & Sciences, at least one year before the degree is expected to be conferred or before beginning the eighth semester of full-time enrollment, whichever is earlier.
A Doctoral Dissertation Guide and a Dissertation Template that give instructions regarding the format of the dissertation are available on the website of the Office of Graduate Studies, Arts & Sciences. Both should be read carefully at every stage of dissertation preparation.
The Office of Graduate Studies, Arts & Sciences, requires each student to make the full text of the dissertation available to the committee members for their review at least one week before the defense. Most degree programs require two or more weeks for the review period; students should check with their faculty.
The Dissertation and the Thesis Defense
The student's dissertation is the single most important requirement for the PhD degree. It must be an original contribution to mathematical knowledge, and it is the student's opportunity to conduct significant independent research.
It is the student's responsibility to find a thesis advisor who is willing to guide their research. Since the advisor should be part of the candidacy requirement, the student should have engaged an advisor by the beginning of the third year of study.
Once the department has accepted the dissertation (on the recommendation of the thesis advisor), the student is required to defend their thesis through a presentation accompanied by a question-and-answer period.
For information about preparing the thesis and its abstract as well as the deadlines involved, including the creation of the Research Advisory Committee and the Dissertation Defense Committee, please consult the Office of Graduate Studies, Arts & Sciences. Please use these additional relevant resources: the Doctoral Dissertation Guide, the Forms page, and the Policies and Procedures page.
The Dissertation Defense
Approval of the written dissertation by the Research Advisory Committee (RAC) is strongly recommended before the student can orally defend the dissertation. The Doctoral Dissertation Committee that examines the student during the defense consists of at least five members. Normally, the members of the RAC also serve on the Doctoral Dissertation Committee. The dissertation committee is then additionally augmented to ensure that the following criteria are met:
- Three of the five members (or a similar proportion of a larger committee) must be full-time Washington University in St. Louis faculty members or, for programs involving Washington University in St. Louis-affiliated partners, full-time members of a Washington University in St. Louis-affiliated partner institution. All members must be authorized to supervise PhD students and have appropriate expertise in the proposed field of study. One of these three members must be the PhD student's primary thesis advisor, and one may be a member of the emeritus faculty.
- All other committee members must be active in research/scholarship and have appropriate expertise in the proposed field of study whether at Washington University in St. Louis, at another university, in government, or in industry.
- At least one of the five members must bring expertise outside of the student's field of study to the committee, as judged by the relevant department/program and approved by the Office of Graduate Studies, Arts & Sciences.
The approval processes outlined in the RAC section of the Doctoral Council bylaws also apply to the Doctoral Dissertation Committee, including approval of each dissertation committee by the Office of Graduate Studies, Arts & Sciences.
The student is responsible for making the full text of the dissertation accessible to their committee members for their review in advance of the defense according to program rules. Washington University in St. Louis community members and guests of the student who are interested in the subject of the dissertation are normally welcome to attend all or part of the defense but may ask questions only at the discretion of the committee chair. Although there is some variation among degree programs, the defense ordinarily focuses on the dissertation itself and its relation to the student's field of expertise.
Attendance by a minimum of four members of the Doctoral Dissertation Committee, including the committee chair and an outside member, is required for the defense to take place. This provision is designed to permit the student's defense to proceed in case of a situation that unexpectedly prevents one of the five members from attending. Students should not plan in advance to only have four members in attendance. If four members cannot attend, the defense must be rescheduled. The absence of all outside members or of the committee chair also requires rescheduling the defense.
Students, with the support of their Doctoral Dissertation Committee chair, may opt to hold their dissertation defense in person or by utilizing a virtual or hybrid format.
Submission of the Dissertation
After the defense, the student must submit an electronic copy of the dissertation online to the Office of Graduate Studies, Arts & Sciences, by the established deadline for their graduation term. Dissertations must be submitted no later than three months after the oral defense of the dissertation. Petitions for an extension to the three-month limit may be submitted to the director of graduate studies for consideration and approval.
The submission website requires students to choose among publishing and copyrighting services offered by ProQuest's ETD Administrator. Students are asked to submit the Survey of Earned Doctorates separately. The degree program is responsible for delivering the final approval form, signed by the committee members at the defense and then by the program chair or director, to the Office of Graduate Studies, Arts & Sciences. Students who defend their dissertations successfully have not yet completed their PhD requirements; they finish earning their degree only when their dissertation submission has been accepted by the Office of Graduate Studies, Arts & Sciences.
As part of their degree requirements, PhD students must complete a program-defined Mentored Experience Requirement (MER) as per these guidelines. The Mentored Experience Implementation Plan (MEIP) is the written articulation of a program-defined degree requirement for PhD students to engage in mentored teaching activities and/or mentored professional activities, collectively referred to as the MER.
Mentored Experience Requirement (MER)
Philosophy of Teaching
At most major universities, mathematics departments teach numerous courses that are fundamental to a variety of disciplines. Effective instruction in mathematics courses is therefore fundamental to the discipline.
Upon completion of their degree many of our graduates go on to academic positions. Our graduate program wants them to receive adequate preparation in teaching and instructional methodology so that they will be effective in the classroom at Washington University in St. Louis as well as be able to start their new positions with success.
Preparatory Engagement
Preparatory Engagement activities are those that represent an introduction to the foundational skills associated with teaching or communication. Pedagogical preparation engagement activities are normally completed before students are permitted to engage in assisting or teaching in a classroom.
Mathematics pedagogical preparation consists of two one-credit semester courses taken over the period of two semesters (spring of the students' first year and fall of the students' second year). These courses are taught by faculty in the department from a detailed syllabus of topics. Topics covered during the course include pedagogical issues of teaching, both general and those specific to mathematics, and administrative issues associated with teaching.
Campus resources such as the Center for Teaching and Learning (CTL) are utilized for additional information about effective teaching methodology. A key component of the course is that students must prepare a “mock” calculus lecture that is presented during the course and constructive feedback is provided. Student presentations are recorded so they can be critiqued, and further comments can be provided. Direct mentoring is provided to the students when serving in the role of Assistant to the Instructor.
Mentored Teaching Experiences (MTEs)
Assistant in Instruction (AI)
An Assistant in Instruction (AI) is a PhD student who is directly engaged in the organization, instruction, and/or support of a semester-long course primarily taught by a faculty member. An AI receives mentorship from a faculty member related to best practices in classroom engagement, instruction in the field, interpersonal engagement, and other relevant skills. Students and mentors complete a mentorship plan prior to the start of each AI experience. To complete each AI assignment and to ensure that it applies toward their degree requirements, students must register for the appropriate course number for each semester of engagement. Refer to the "Required Pathways for Completion" section below for course numbers and details.
Mathematics provides a planned sequence of teaching opportunities. During the students' second year of studies, they begin service in the Calculus help sessions and take on a more active teaching opportunity by serving as an Assistant to the Instructor for the calculus classes. Graduate students are assigned two to four sections of introductory calculus or statistics courses to assist with when serving as an Assistant to the Instructor.
Mentored Independent Teaching (MIT)
MIT is a semester-long experience for PhD students who engage as the primary instructor or co-instructor of a course under the mentorship of a faculty member as part of the MER. Students and mentors complete a mentorship plan prior to the start of each MIT experience. To complete each MIT assignment and to ensure that it applies toward their degree requirements, students must register for the appropriate course number (ASGS 8020 MTE - Mentored Independent Teaching Experience) for each semester of engagement. Refer to the "Required Pathways for Completion" section below for more details.
Mathematics does not require MIT though opportunities may be available to engage in MIT to obtain 20 to 60 MER units. For graduate students further along and better prepared, as judged by the Mathematics Graduate Committee and the CTL representative, they may be assigned an MIT. Feedback on teaching and instruction is provided by the instructor of the course through observations of the graduate student and through meetings for the course.
Mentored Professional Experiences (MPEs)
The MPE is an unpaid professional experience for PhD students that allows students to develop skills and experiences relevant to their intended career outcomes. Students and mentors complete a mentorship plan prior to the start of each MPE. To complete each MPE assignment and to ensure that it applies toward their degree requirements, students must submit the Mentorship Registration Request form for approval and register for the appropriate course number (ASGS 8120 MTE - Mentored Professional Experience) for each semester of engagement. Refer to the "Required Pathways for Completion" section below for more details.
Mathematics allows students to take 0 to 2 MPEs, which will be approved by the Director of Graduate Studies in consultation with the Graduate Committee and the Office of Graduate Studies.
A wide variety of MPEs are available, including (but not limited to) the following:
- Focused research and experience in grant administration as part of the student or advisor's grant which may involve time spent at another university with an outside mentor.
- An internship in industry or government.
Required Pathways for Completion
Students work with their faculty mentor and their Director of Graduate Studies to plan how and when they will complete their MER. Students register during the normal registration period for courses in accordance with one of these approved pathways.
Several different pathways are possible to complete the MER. The specific pathway that a student follows should be discussed with the Director of Graduate Studies. Since a student's circumstances or needs can change during the program, it is possible for a student, in consultation with the Director of Graduate Studies, to change pathways. In order to qualify to engage in MIT, students must complete preparatory engagement (two semesters of teaching seminar) and two MTEs (any combination of 5-, 10- or 15-unit MTEs are allowed). The possible pathways are listed below. When a student is participating as an AI, they will sign up for ASGS 8010 MTE - Assistant in Instruction Experience; when they are engaging in MIT, they will sign up for ASGS 8020 MTE - Mentored Independent Teaching Experience.
Pathway #1
| ASGS 8010 | Take six times |
Pathway #2
| ASGS 8010 | Take five times |
| ASGS 8020 | Take one time |
Pathway #3
| ASGS 8010 | Take 5 times |
| ASGS 8120 | Take one time |
Pathway #4
| ASGS 8010 | Take 4 times |
| ASGS 8020 | Take one time |
| ASGS 8120 | Take one time |
Pathway #5
| ASGS 8010 | Take 4 times |
| ASGS 8020 | Take two times |
Pathway #6
| ASGS 8010 | Take 4 times |
| ASGS 8120 | Take two times |
Pathway #7
| ASGS 8010 | Take three times |
| ASGS 8020 | Take one time |
| ASGS 8120 | Take two times |
Pathway #8
| ASGS 8010 | Take three times |
| ASGS 8020 | Take two times |
| ASGS 8120 | Take one time |
Pathway #9
| ASGS 8010 | Take two times |
| ASGS 8020 | Take two times |
| ASGS 8120 | Take two times |
Optional Activity: Teaching Intensive Pathway (TIP)
The TIP is an optional pathway for those students whose career interests lie in academia or another field that would benefit from extended teaching experiences. This immersive experience allows students to further explore the breadth and depth of teaching best practices and pedagogy related to their respective field. Students who are interested in participating in this elective experience must formally request to participate, which is subject to program approval. Due to this experience being an elective, unpaid experience, students who participate in the TIP will not receive compensation.
Optional Pathway #1
| ASGS 8010 | Take once |
Optional Pathway #2
| ASGS 8010 | Take two times |
Optional Pathway #3
| ASGS 8020 | Take once |
Optional Pathway #4
(Not available for Pathways 2, 5, 7, 8, and 9)
| ASGS 8020 | Take two times |
Optional Pathway #5
(Not available for Pathways 5 and 9)
| ASGS 8010 | Take once |
| ASGS 8020 | Take once |