Regulations for Doctoral Students in Mathematics

A supplement to the regulations in the Graduate School Bulletin of Information. These rules apply to all students who enter the program after the 2020-2021 academic year.

New Students

Each new student must perform Roll Call by the end of the sixth class day. It is advisable to arrive in time to consult with faculty on courses and to attend graduate school orientation.

Course Requirements

(1) Each student must register for at least 9 credits each semester in order to maintain full-time status. Students taking less than 9 credits of courses are required to register for Directed Readings (prior to passing the oral qualifying exam) or Research and Dissertation (after passing the qualifying exam) in order to earn at least 9 credits.
(2) First year students are required to complete at least 6 basic courses during the first year (see Written Candidacy Examination for more details)
(3) There is no transfer of credits.
(4) A requirement for receiving the PhD degree is completing 9 courses, or equivalently 27 GPA credits. These 9 courses are ordinarily basic courses or topics courses, but can also include up to two 400xx or 500xx level undergraduate courses, with approval by the Director of Graduate Studies. It may also include directed readings courses taken during the first year, with approval by the Director of Graduate Studies, or directed readings courses taken after the first year with a faculty member other than the student’s adviser, with approval by the Director of Graduate Studies. However, students are encouraged to register for appropriate topics courses after they have completed the basic course requirement.
(5) All students must maintain at least a 3.0 grade point average after the first semester. This is a condition for being in good academic standing, and students who fail to meet this standard risk being placed on academic probation.
(6) All students must complete roll call by the 6 th class day of each fall and spring semester.

Written Candidacy Examination

In the Department of Mathematics, the written work in the basic first year courses is counted as the written candidacy examinations. Students must complete at least 6 basic three-credit one semester courses in the first year. There are three ways to complete a basic course.

1. Take the course and receive a grade of B or better (B- is not sufficient).
2. Take a written exam from the course without taking the course and achieve a score that the instructor deems satisfactory to test out of the course. This exam should be at the level of a final exam for the course.
3. If a student places out of a first semester basic course by an oral or written exam with the instructor, then the student may count the first semester basic course as a completed basic course if the student successfully completes a sequential basic course by either method (1) or (2) above. In this case, the student may count the first semester basic course and the sequential basic course as two of their 6 required basic courses. This oral or written exam may be shorter than a typical final exam for the course. The length and format of the exam is up to the discretion of the instructor, but often consists of a discussion of the student’s previous courses in the subject and several questions about material from the course. A list of basic courses including sequential courses is found here.

The written candidacy requirement must be completed by the end of the first year. Exceptions can be granted by the graduate committee on a case-by-case basis.

The instructor teaching a course is ordinarily the one who determines whether a student places out of a course, and the one who will give a final exam for students attempting to test out of a course. The instructor may defer this responsibility to another faculty member. The standard for earning a satisfactory score on the final exam is at the discretion of the instructor, and the instructor has discretion to choose not to allow a student to attempt to test out of a course. Students wishing to place or test out of a basic course are strongly encouraged to do so early in the semester.

Advisers

The Director of Graduate Studies assigns to each new student a first-year adviser. By the end of the first year, the student must pick an adviser for the oral candidacy examination. There is no requirement that the first-year adviser be the adviser for the oral candidacy examination. The student may choose several advisers at the end of the first year. After successfully passing the oral candidacy exam, the student may switch to a different adviser with the consent of the new adviser. In such circumstances, the student does not need to retake the oral candidacy examination.

Oral Candidacy Examination

The oral candidacy examination cannot be taken until the written candidacy examination is completed. Students are required to pass the oral candidacy exam by the end of second semester of their second year. Students who wish to take the oral candidacy exam after March 1 of the second semester of their second year must get approval by the Director of Graduate Studies. Extensions of time to pass the oral candidacy exam beyond the end of the second semester of the second year may be granted by the graduate committee on a case-by-case basis.

In the oral candidacy exam, the student gives a talk on an “advanced topic.” The adviser for the oral candidacy exam and the Director of Graduate Studies must both approve the topic.

The board of examiners for the oral candidacy examination by convention consists of four examiners, although a committee with five examiners is allowed. The members of the board of examiners are selected by the Director of Graduate Studies based on suggestions of the student and adviser.

The student should prepare a syllabus for the oral candidacy examination, and this must be approved by the adviser and the Director of Graduate Studies, and must be made available to the board of examiners at least one week before the oral candidacy examination.

The oral candidacy examination begins with a presentation by the student lasting between 30 and 50 minutes. This is followed by questions on material from the presentation and the syllabus from the board of examiners. With the consent of the student and the adviser, people besides the board of examiners may attend the presentation, but they must leave before the questions. The examination cannot last longer than two hours and must last for at least one and a half hours, unless the committee unanimously agrees to end the examination.

After the completion of the oral candidacy examination, the four examiners vote “pass” or “fail”. The student passes the oral candidacy examination if at least three of the four examiners vote “pass”, and otherwise, the student has not passed the exam. If the committee has five examiners, the student passes the oral candidacy examination if at least four of the five examiners vote “pass”, and otherwise, the student has not passed the exam. If the student has not passed the examination, the committee may recommend that the student do some additional work such as submitting written work, giving a talk, or retaking the examination, and then the committee will vote again. A retake of the examination must have approval of the Director of Graduate Studies and the Graduate School. At most one retake of the examination is allowed. The student and Graduate School are informed immediately whether the student passed, requires further work, should retake the examination, or fails. The student is not informed of how each committee member voted. If a student fails, the examiners must hold a second vote to determine whether to recommend the student for a master’s degree, and this result is reported to the Director of Graduate Studies.

In the Department of Mathematics, there is no requirement for a doctoral dissertation proposal.

Admission to Candidacy

The Graduate School requires that all PhD students must be admitted to candidacy by the end of their eighth semester. To qualify for admission to doctoral candidacy, a student must complete the program coursework requirement of at least 9 courses with a cumulative GPA of 3.0 or better, pass the written and oral parts of the doctoral candidacy examination. In rare circumstances, the Director of Graduate Studies may waive part of the 9 course requirement.

Thesis

Thesis research under the supervision of the thesis director begins after the successful completion of the candidacy examinations. The thesis must contain original research, and should be at a level such that a publication based on the results is deemed suitable for publication in a good peer-reviewed mathematics journal.

After the thesis director has approved the thesis, the student submits the thesis to three official readers. The readers must be approved by the Director of Graduate Studies, and although they are usually faculty at Notre Dame, they may include experts from other institutions. The official readers certify that the thesis is worthy of defense, although they may request further changes after approving of the thesis. The thesis defense occurs after the readers have approved the thesis.

Thesis Defense

The thesis defense is an oral examination on the contents of the thesis and its relation to other work in the same area. The board of examiners for the thesis defense consists of four examiners who are usually the thesis director and the three official readers. Any change from this convention must be approved by the Director of Graduate Studies. It is permissible for a student to have two advisors, in which case one of them is designated as the official thesis director and the other may be an official reader.

The examination begins with a 30-50 minute presentation by the Ph.D. candidate, prepared in consultation with the thesis director (who also sets the length). A round of questions by the examiners follows this presentation. There may be questions about specific points in the thesis, and also about the importance of the research and what further work it suggests. A thesis defense is public, in the sense that people other than the candidate and the members of the board of examiners may be present for the lecture. Such people must leave the room prior to the questions by the examiners and the vote. Voting is as for the oral candidacy examination. The thesis defense may not last for more than two hours. The student and Graduate School are informed immediately whether the student passed, requires further work, should retake the examination, or fails. The student is not informed of how each committee member voted.
 
After a successful defense, the candidate may still need to make minor changes in the thesis. Then the final version of the thesis, signed by the thesis director, is submitted to the Graduate School.
 
Getting the thesis read and approved, scheduling the thesis defense, making corrections, and having the thesis accepted by the Graduate School is a time-consuming process that requires strict adherence to the timetables set by the Department of Mathematics and the Graduate School. The thesis must be submitted to the readers well before the Graduate School deadline for submission of theses. The latter is roughly two months before the graduation date. August graduation entails special difficulties, since there are fewer faculty members available during the summer to serve as official readers.

There are strict rules about formatting, margins, etc., which must be observed if the thesis is to be accepted by the Graduate School. The Ph.D. candidate should be sure to consult the Graduate School’s Guide for Formatting and Submitting Doctoral Dissertations and Master’s Theses (available on the Graduate School’s website at http://graduateschool.nd.edu/resources-for-current- students/dt/). This document changes from year to year, so it is important to consult the current version and other students who have recently written theses.

Summer Registration Requirement

Graduate students receiving a summer stipend must register for their program’s zero-credit “Independent Summer Research” section. Registering for this course will ensure proper classification for tax purposes.

Summary of Official Requirements for the Ph.D. Degree

1. Courses and credits–six completed basic courses, at least nine basic and topics courses subject to the exceptions listed above, plus further credits to make a total of 60 credits.
2. Residency– 4 consecutive semesters of full-time study (as required by the Graduate School). The term “full-time’’ means that the student is registered for at least 9 credits, and that the schedule is approved by the adviser.
3. All students must teach or serve as a teaching assistant for at least four semesters, unless this requirement is waived by the Director of Graduate Studies.
4. Written and oral candidacy examinations
5. Admission to Degree Candidacy by the end of the eighth semester, which requires completion of Step 1 above.
6. Thesis carried through the following steps:
   a. Approved by the adviser and all three readers
   b. prepared for electronic submission
   c. signed by adviser
   d. accepted by the Graduate School
7. Thesis Defense (this cannot occur until steps 1-5 and 6a are completed), and the student must pass the Thesis Defense in order to be eligible to graduate.

Student Status

The Mathematics Department does not admit students to the graduate program who plan to study on a part-time basis.
 
A student is considered to be full-time if he or she is registered for at least 9 credits and the adviser certifies that the student is working full-time. At first, the work is almost entirely tied to courses. Later, the thesis is the main focus.  In some cases, the student may simply register for 9 credits of research and dissertation.
 
To be in good academic standing, a student must maintain a G.P.A. of at least 3.0 and be on schedule in terms of course work and examinations. In addition, once the student is no longer registered for basic courses, the adviser must indicate that the student is making satisfactory progress. The adviser indicates the student is making satisfactory progress by giving the student a grade of B or better in Directed Readings or a grade of S in Research and Dissertation. Thus, it is essential for the student to keep the adviser informed about the student’s progress
 
A student who does not succeed in passing the first year courses is not permitted to continue in the second year. A student who does not pass the candidacy examinations by the end of the second year is not permitted to continue in the third year unless given an extension of the deadline by the Director of Graduate Studies. A student who, for two consecutive semesters, fails to maintain good academic standing (as described above) is not permitted to continue further.
 
A student must fulfill all doctoral requirements, including the dissertation and its defense, within eight years from the time of matriculation.  Failure to complete any of the Graduate School or departmental requirements within the prescribed period results in forfeiture of degree eligibility. A student is normally expected to finish within five years.

The M.S. Degree

The graduate program in the Mathematics Department is almost entirely a Ph.D. program. Students are not normally admitted directly to a Master's program. There is a Master of Science in Interdisciplinary Mathematics degree, for students who do not need funding and wish to pursue an interdisciplinary project, or to carry out serious mathematical work while pursuing a Ph.D. in another department. (The requirements for the MSIM are available through the Director of Graduate Studies.)
 
A student who is working toward a Ph.D. in Mathematics may qualify for a Master of Science degree along the way, if he or she has accumulated 30 credit hours, has passed the written candidacy examination, and has either passed the oral candidacy examination or (without passing) exhibited sufficient knowledge to obtain a positive recommendation from the examiners. Having met the requirements, a student must also ask to have his or her name put on the graduation list.  The Master of Science degree is not given automatically.
 
The Director of Graduate Studies, with the approval of the Graduate Committee, has the ability to approve a plan of study resulting in a Master of Science for those students within the PhD program who decide they want to leave without taking an oral exam.  Most likely, but not always, this plan involves the writing of a Master thesis.

Financial Support

The goal of our financial support is to provide enough income so that our graduate students can focus on mathematics, hopefully earn a Ph.D., and help the department with our teaching needs. Continued financial support requires the student to maintain good academic standing, and to carry out in a conscientious way any teaching (or other) duties associated with the support. A sixth year of funding is only available in some cases and will be decided by the graduate committee. Supported students may do mathematical relevant work, like tutoring or helping with online homework, up to two hours per week, with the permission of their adviser. Teaching assistants and fellowship holders are not allowed to take any employment for more than two hours per week without special approval from their adviser and the Director of Graduate Studies, including during the summer semester. Students supported by non-departmental funds might be expected to help with conferences, maintain web sites, online classes, etc. In this case what is required must be made clear prior to the start of the support and approved by the funder, adviser and Director of Graduate Studies. Decisions about financial support are made at the end of the spring semester for the next academic year. Students are informed about support at that time.

Teaching Opportunities

For an academic job, teaching experience is vital. First year students have no teaching duties. Most second year students are expected to attend TA orientation, which is held before classes in the fall semester. For exceptions see the Director of Graduate Studies. Second year students and many third year students are assigned to be a Teaching Assistant (TA) in a multi-section course. The opportunity to teach does exist, usually as the instructor of one section of a multi-section introductory course, under the supervision of a senior faculty member, or a summer class.
 
In order to teach their own class, students must first successfully serve as a Teaching Assistant and have satisfactorily lectured in the Mathematics Teaching Seminar (Math 83990). The Mathematics Teaching Seminar runs every spring semester.  All students are expected to teach/TA for at least two years as part of their mathematical education. The Deans, Kinesis-Fernández Richards Family, and CSC fellowships allow the holder to take up to 2 years off from TA or teaching duties, when it makes mathematical sense, with the approval of their adviser and the Director of Graduate Studies. TA or teaching duty exemption possibilities to be attached to other similar outside fellowships will be considered as they are earned.

Travel 

All travel must be approved prior to traveling.  Travel to attend conferences and to give seminars is encouraged.  Travel approval forms are available on the department web site.  These forms must be completed prior to travel when going on a research trip, and prior to any travel where TA or teaching duties are missed, and any extended personal trip.  If a student is a TA or is teaching a multi-section course, the course coordinator or instructor and the advisor must sign the form. If you are the sole instructor for a course or not serving as an instructor or TA, then your adviser’s signature on the travel form is sufficient approval.
 
Department funds for graduate student travel are limited. All other funding sources should be exhausted before requesting department funds. Most meetings provide some sort of travel support for graduate students. Be sure to ask your adviser for support. Advisers with research funding are normally expected to cover their students’ travel expenses. If you are giving a talk, you should also apply for funds through the Graduate Student Government (https://gsg.nd.edu/funding-awards/conference-presentation-grants/). This also needs to be approved BEFORE your trip (a minimum of 1 month prior to the conference start date).  In your request for department funding, be sure to document what external funding is available and what funding you’ve received or have been awarded. If you are asking for department funding, please see the Director of Graduate Studies for an additional signature
authorizing reimbursement.

The Director of Graduate Studies 

The Director of Graduate Studies has responsibility in the following areas:

1. Overseeing and troubleshooting the Ph.D. program.
2. Coordinating the graduate admissions process including assigning initial advisors.
3. Act as resource for prospective and current graduate students.

The department’s Associate Chair makes teaching assignments with the help of the Director of Graduate Studies.

The Department Chair and the Director of Graduate Studies, in consultation with the adviser, when appropriate, make recommendations for fellowships and stipends.

Grievance Procedure

If a mathematics graduate student has a grievance, the procedure is to go first to the Director of Graduate Studies, unless the grievance involves the Director of Graduate Studies, in which case, the student should approach the Department Chair.  The Director of Graduate Studies, or the Department Chair, will try to work with the parties involved to reach a solution.  If this is not sufficient, the Department Chair will appoint an ad hoc committee of faculty members and students (not directly involved) to hear a particular case.  If the student feels that this is not enough, then he or she may appeal to the Graduate School.  The Graduate School Policies and Grievance and Appeal Procedures can be found in the Graduate School Bulletin of Information or on their website at http://graduateschool.nd.edu/resources-for-current-students/.

Departmental Appeal of Dismissal

A graduate student who fails to meet the requirements involving coursework and exams may be dismissed from the program with approval by the Director of Graduate Studies and the graduate committee. These requirements are:

1. completing 6 basic courses toward the written candidacy exams in the first year,
2. completing the oral exam by the end of the second year,
3. earning 36 credit hours within the first three year with a GPA of at least 3.0

There are further grounds for dismissal, which are more subjective including failure to make adequate progress in research, failure to work with the adviser toward the thesis document, or failure to perform TA duties properly.  Before a student is dismissed for these more subjective grounds, he/she will receive a warning letter from the Director of Graduate Studies, with specific steps that need to be carried out by a specified time.  At the end of this time, the Graduate Studies Committee will determine whether the steps have been carried out. If the decision is negative, then the student is dismissed. There are very limited grounds for appealing dismissal.  The student must show that the decision resulted not from his/her failure to meet expectations, but from personal bias or improper procedures. Since the decision to dismiss involves the Director of Graduate Studies, an appeal, if any, starts with the Chair, who will appoint an ad hoc committee, if appropriate. A further appeal to the Graduate School is possible, under very limited conditions.  See the Graduate School Bulletin of Information.

Graduate School Regulations

There are a number of graduate school regulations and policies that impact the department. For example, all graduate students are required to attend the Responsibilities and Ethics in the Conduct of Research workshop and graduate school orientation. Some of these policies and regulations can be found in The Graduate Bulletin of Information (http://graduateschool.nd.edu/resources-for-current-students/).