CID Summer 2005 Convening: Supporting Intellectual Community

Topic 2: Promoting Effective Advising and Mentoring

USC Department of Mathematics

This Snapshot describes how the doctoral program in the DEPARTMENT OF MATHEMATICS helps promote effective advising and mentoring by departmental faculty. The faculty-student relationship is a critical element of doctoral programs and a building block of our intellectual community.

Summary Description

In the spring and fall 2004 semesters, the USC Department of Mathematics introduced several new activities into its graduate program.

The Mentoring Triplets program triples up a faculty member, senior graduate student, and new graduate student. The three meet on an informal basis approximately once a month to discuss mathematics, degree progress issues, teaching strategies, or whatever else might come up. The idea is for the faculty member to mentor both students and for the senior graduate student to mentor the new graduate student and to help him or her integrate into the department.

The Tuesday Lunch Bunch works this way. Every Tuesday, all interested faculty, graduate students, and staff have a bring-or-buy-your-own-lunch in one of the University's cafeterias. We use it as an informal opportunity to discuss mathematics, teaching, students, departmental business and politics, national politics, sports, general gossip, etc..

In August 2004, we inaugurated our Graduate Qualifying Examination Preparation Sessions, with sessions geared toward 4 of the department's 8 exams (with plans to expand the program to include all the exams). Each of the weekly sessions is facilitated by a senior graduate student who is currently assigned to be a grader for the corresponding courses this semester. For students planning to take the exams in the current or future semester, the sessions provide an opportunity for them to work together on old exams, review relevant material, become familiar with the kinds of problems that typically appear on exams, and to receive pointers on studying and preparation skills.

As of Fall 2003, we have implemented a new weekly graduate seminar, Current Developments in Mathematics, as a year-long, for-credit course required for all first-year graduate students. The course is designed to expose them early on to current research being conducted within the department as well as mathematical research in general.

In Spring 2004, we introduced Seminar Mentoring in the department's Analysis Seminar series. Instead of the traditional invited speaker setting, participants of the seminar are asked to present a research paper that is in direction of their research but has considerable general interest (papers of great impact). The seminars are presented by senior and junior graduate students, as well as several faculty members. Participation of audience in form of questions and comments from the audience is encouraged. Additionally, students are required to ask a question at least once during every presentation. External speakers are also invited to give a standard research talk every three weeks or so.

Finally, the department devotes a portion of its Departmental Colloquium funds to sponsor two or three graduate students at our regular dinners in honor of the week's Colloquium speaker.

More Details about Fostering Intellectual Community
Mentoring Triplets, Tuesday Lunch Bunch for All Weapons of Math Instruction, and Graduate Students Departmental Guests at Colloquium Dinners

Goals for Advising

The primary purpose of all of these activities is to foster an intellectual community of faculty, senior students, and junior students. The activities provide mathematicians with opportunities for communicating and learning the necessary skills to complete a Ph.D. program successfully and reach their full research potential. The introduced activities are designed to enhance different aspects of critical thinking, promoting the sharing of knowledge and improving the research atmosphere. They are a way of making the students feel that they are a part of something larger than a student body that simply attends classes, takes exams, and does research; in particular, it is an opportunity to share in and belong to a departmental "family" and the mathematics community as a whole. These activities give faculty, students, and staff a chance to get know each other and to engage in intellectual exchange in settings other than classrooms and offices.


Mohammed Ziane, Faculty: The Department of Mathematics at USC offered a seminar class for new graduate students. The seminar goal is to introduce students to "research." The seminar speakers in the first three weeks were faculty members of the mathematics department, as well as faculty from outside departments, such as the Engineering and the Physics Department. The seminar format consists of a biography of the faculty and historical reasons for their choice of a research topic, followed by an overview of their research field, collaborators, and open problems in the field, and finally the students were strongly encouraged to ask questions. The next couple of weeks, post-doctoral fellows at the department presented their research, and it was followed by finishing graduate students, who were given a chance of a friendly audience to present their thesis. Finally, the important part of seminar consists in the active participation of students in the seminar. This was done in the beginning of the semester, when faculty members were asked to suggest easy-to-read papers. The new graduate students had six weeks to study the papers and present them in the seminar.

The seminar experience was a great success. Students were very enthusiastic and active participants of the seminar. They learned about the various interests of faculty research.

Jessie Coe, Graduate Student: Beginning graduate school can be an intimidating experience, especially without any connections to one's department. The Mentoring Triples program is one way in which the USC math department aids new students in developing these connections. Mentoring triplets consist of a faculty member, a senior graduate student, and an incoming graduate student, with the goal of providing the new student with a forum in which to ask questions about his/her program of study and receive guidance in working towards the Ph.D goal. While I was still getting my feet wet in the math department, my mentoring triplet met for lunch. It was reassuring to hear both an established professor and a senior graduate student share anecdotes about their trials and tribulations during their respective first years of study. The knowledge that they were once in the same position as me-- with the same concerns I was having, and yet made it through, and could now look back on that time and laugh--provided perspective and a much needed confidence boost, with the added benefit of a free lunch.

Asher Shamam, graduate student:The Mentoring Triplet Idea was fully implemented department-wide during the past academic year with varying degrees of success.

My personal experience has been a positive one. The mentoring triplet I was a part of consisted of a tenured faculty member, a senior PhD graduate student (myself), and an entering PhD student. We met for lunch on an irregular basis, somewhat infrequently. I believe the reason for this infrequency is that people tend to spend their lunch with peers who are at the same place along the programs, and perhaps more importantly peers who are from the same cultural, and or share the same mother tongue.

However, despite the substantial cultural differences present--I am Israeli, the entering student is German, and the faculty member is Ukrainian-- I consider my triplet to be functional one. The basic reason is that through the little time expended, our short informal meetings, and even hallway interactions, a sense of belonging was fostered for the benefit of the entering student. Tips for success in the program were offered (to the entering student), and in addition, in my case, exhaustive notebooks that I compiled for each of the four screening exams were shared with the student. The screening exams pose the first major hurtle in our program, and are probably one of the important factors related to the attrition rate in the Doctorate program in the USC mathematics department.

Some triplets were dysfunctional! That is there was no meaningful exchange of information and very little or no interaction. This may stem from various causes, not the least of which, is the availability of time, cultural differences, as well as the desire or lack there of, to make the triplet functional.

We have not formally assessed the effectiveness of the mentoring triplet, and it is not clear to me how we might do this. Perhaps one way may be in the form of a questionnaire with some specified numerical response range, much like a typical course or instructor evaluation questionnaire handed out at the end of the semester.

It is interesting to consider ways of improving the selection of the triplets so that their chance of being functional is maximized. Probably some major obstacles in this challenge are the unpredictability of human relationship dynamics and the vast cultural diversity that exists in most mathematics departments.

Evidence of Progress:

There have been indications that some combination of the ideas implemented has made a real difference in the success of graduate students in recent years and enhanced the atmosphere in our department. There has been a huge improvement in performance on screening and qualifying exams. The attendance at colloquia, seminars and other department events has increased, with more students and more faculty becoming involved. This in turn encourages faculty to bring in more distinguished speakers and enhance the overall activity and visibility of the department. The students' participation in department activities has increased as well.

Contact Information

Contact Persons:

Faculty: Francis Bonahon, Igor Kukavica, Gary Rosen, Mohammed Ziane

Email addresses:,,,

Graduate Students: Jessie Coe, John Mayberry, Asher Shamam

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