"Current Developments in Mathematics" Seminar:

An Exemplary Element Snapshot

Department of Mathematics, University of Southern California

"Current Developments in Mathematics" is a year-long, for-credit course required for all first-year graduate students. The course is designed to expose students early on to current research being conducted within the department as well as mathematical research in general.

Description of the exemplary element

This seminar, "Current Developments in Mathematics," is intended especially for the beginning graduate students in mathematics.

A working mathematician spends a good amount of time at various special talks. Such talks are often less than polished, and at this seminar the students learn how to get the most from them. Accordingly, all participants of the seminar are expected to attend the weekly sessions of the department's Mathematics Colloquium.

There is an additional meeting every week where the students discuss material from the colloquium and listen to a series of informal talks on various topics of pure and applied mathematics. Many points in those talks are left to the participants as exercises, and further readings on the topic of the talk are suggested. Four lecture series are planned for each semester.

Details of the seminar

The seminar is mandatory for the first-year graduate students in the doctoral program.

The course instructor is responsible for finding the speakers for the lecture series and for grading the students' work.

The lecture series is presented by USC faculty from within and outside of the department.

The seminar was first offered during the Spring 2002 semester with two goals in mind:

Accordingly, the students are expected to do the following:

Seminar Syllabus for Fall 2003

Educational purpose of this element

The main objectives of the "Current Developments in Mathematics" seminar are:

1. To introduce the participants to the current research areas in mathematics and to the research activities of the members of our department.

2. To develop and to practice the basic skills in formal mathematical writing.

3. To develop and to practice the skills of active listening to mathematical presentations.

Evidence of the seminar's impact

Some of the positive developments we have observed since instituting the "Current Developments in Mathematics" Seminar are:

Reflection from a faculty member

by Sergey Lototsky, Associate Professor

While the original idea for the seminar belongs to Feodor Malikov, I was the organizer or co-organizer of the seminar for three semesters (Fall 2002, Fall and Spring 2003), and oversaw significant changes in the format. Although the students occasionally complained about the increasing work load, most actually enjoyed the challenges of understanding often incomprehensible lectures and working on non-standard problems. Not all the participants were the first-year math Ph.D. students. More senior math Ph.D. students would often sign up for the seminar, and once there was an engineering student among the participants.

One of the most dramatic changes the seminar has produced is an increased interest of our students in the department colloquium. Having been a colloquium chair before the seminar was introduced, I remember the shame I felt when the seminar room was less than a third full, with hardly a single student in the audience. The colloquium attendance is no longer a problem now, and it is pleasing to see that the students continue to attend even after it is no longer a requirement.

Even though I am no longer in charge, the format of the seminar continues to evolve. Now the participating students get a chance to practice their oral skills as well. I believe that this is exactly the way this seminar should continue--expanding the math horizons of the students while presenting them with new challenges and opportunities.

Reflections from a seminar student

by Nathan Glatt-Holtz

The "current developments in mathematics" seminar is, in my opinion, a useful addition to the graduate curriculum at USC.

I have attended two different iterations of this class. As part of both classes we were required to attend weekly seminars offered by the department. In the fall of 2003 the course consisted of a sequence of four extended talks given by members of the faculty at USC. Each presentation represented a major area of active research in the department. In particular we heard presentations on Probability, Algebraic Geometry, Computational Biology and Dynamical Systems. After each talk we were required to write a short description of what we had gleaned. We also submitted a final paper exploring a research area associated with one of the talks in more detail. I found one talk on dynamical systems theory especially compelling. My final paper outlined current developments and methodologies in information theory and dynamical systems.

This year's seminar differed significantly in format. Each student had to pick a research article and give a presentation in front of the class. This was the first research article in Mathematics that I have read and understood in detail, an existence proof for a nonlinear ordinary differential equation. The instructor did a good job of picking out challenging but accessible articles on a variety of fields represented in the department. We were encouraged to participate in the talks and to ask questions.

I think these seminars have been valuable for several reasons. Most importantly, they have encouraged many students to make a regular habit of attending weekly seminars and colloquia. I have learned a lot about how to make something out of a talk in an unfamiliar research area. In general, first year graduate courses involve building a toolbox of technical skills necessary for research. These seminars, by contrast, have fostered a broad appreciation of current areas of active research and the questions that they try to address. I have found this bigger picture to be helpful in navigating a daunting new world. In particular I think I have made a more informed choice of a research topic and an advisor as a consequence. Finally putting together the required papers and presentations has been a friendly introduction to the more unguided world of research (again in contrast to the more technical nature of your average graduate level homework assignment or take-home exam.)

I found the greater emphasis on student participation in the more recent seminar to be a significant improvement. I think I have been able to glean more from the presentations by being pushed to ask questions and interact. However, I found the summary papers to be helpful in digesting the talks I attended (despite general frustration at the time with these write-ups) , and it might be useful to reincorporate these summaries in future seminars.