Advice for Second Year Graduate Students in Mathematics

This document contains advice for second year students in mathematics.    For rules and regulations, see the web page

Beginning of Fall Semester

It is advisable to arrive on campus by the Wednesday before classes start, so that you can attend organizational meetings for your tutorial sections. There is also TA training the day before classes start. Remember to do Roll Call before the end of the 6th day of classes. We cannot pay your stipend if you do not complete Roll Call.


As it says in the rules and regulations, all students must be registered for at least 9 credits each semester to maintain full-time status. These 9 credits typically come from a combination of basic courses, second year courses, Topics courses, and Directed Readings courses. Each student should decide how many courses to attend in consultation with their adviser. Some students take zero courses, but instead take nine credits of directed readings in order to better focus on preparation for their oral examination. The DGS recommends that at least 50% of your time on average during the semester should be spent on work that contributes to your oral examination preparation, which may include taking courses. Generally, it is a good idea for 2nd year students to enroll in topics courses in their area, and to attend conferences and seminar talks in their area of research.

It is not uncommon for 2nd year students to initially enroll for one or two courses plus directed readings, and to decide after a month or so that they want to drop their courses in order to focus more of their time on oral examination preparation. For this reason, we recommend that 2nd year students register for 9 credits of directed readings in addition to whatever courses they will take, so that if they drop courses later, they will continue to have the necessary 9 credits.

Be aware that the course requirements changed recently, and you need to complete at least 9 semester-long courses, including basic courses, to graduate from Notre Dame.   Reading courses taken with your adviser after the first year do not count toward that total, but first year reading courses and reading courses with other faculty do count.

Getting Help/Outside Activities

Most of our students have a productive relationship with their adviser and continue to work on their thesis with their adviser. However, if there are problems, we advise the student to speak to the DGS when the issues arise. Very occasionally, students switch to a different adviser before the oral qualifying exam. It is perfectly OK to switch to a different adviser after the student has passed the oral qualifying examination. The student does not then have to retake the oral qualifying examination with the new adviser even if the new adviser works in a different area of mathematics.

We encourage you to find enjoyable things to do with your time outside of math. Very few mathematicians can work productively 12-14 hours per day, so if there is a sport you enjoy, or you sing or play a musical instrument, or you are part of a faith group, then it is a good idea to continue those activities in graduate school. Some people take courses in other departments. This is most often to acquire a skill, but can be done just for general interest.  

Graduate school can be a stressful time and this can affect your health, including your mental health. We encourage you to take care of yourself physically, and if you need someone to talk to outside of the program, consider reaching out to university counseling services.

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 the 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.” Usually the “advanced topic” is a paper in the student’s area of interest, but may consist of material from an advanced textbook. Usually the adviser suggests the topic, or the student chooses the topic from a range of options suggested by the adviser, but it is fine if the student suggests the topic. The adviser and DGS must 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 syllabus typically consists of a reference for the paper or book chapters to be covered, and a list of background material that is needed to understand the advanced topic. We recommend that this list of background material includes specific book chapters or specified material from lecture notes or other materials.

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.

It is a good idea for students preparing for the oral examination to talk to other students in the same area who have already passed the oral examination, in order to get some perspective on the experience. It is common for students to get nervous during the examination and many students have passed the exam without answering every question correctly.

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

Admission to Candidacy and the MS degree

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. Many student will be eligible for admission to candidacy after their fourth semester.

Many students will have completed the requirement for a Master’s Degree in Mathematics from Notre Dame by the end of their fourth semester. The requirements are passing the written candidacy exams (i.e., completing 6 basic courses), passing the oral candidacy exam at a PhD or Master’s level, and completing 30 hours of coursework. While the Master’s Degree is not a requirement to receive the PhD Degree, many students choose to receive the Master’s Degree along the way to their PhD. There is a form to fill out in order to receive the degree, and students have to request to receive the Master’s Degree. Students who leave the program at the end of their second year are frequently eligible for a Master’s Degree, and in this situation, the Master’s Degree is a helpful credential to acquire.


Essentially all our students receive a summer stipend, so we require that  students at the end of their second year register for their program’s zero-credit “Independent Summer Research” section. Registering for this course will ensure proper classification for tax purposes.   

Students should also speak to their adviser about whether there are summer schools or conferences in their research area and attend these when they are useful for the student’s development. The department has a membership in MSRI that allows us to send a small number of students to MSRI summer schools. The DGS also has a limited travel fund to fund student travel to conferences.