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 firstyear 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: To broaden the math horizons of graduate students beyond the regular classesTo give the students a better idea about the research done at the departmentAccordingly, the students are expected to do the following: Write four 200word reports on each talk given in the lecture series.Write two 200word reports on the Colloquium talks of the student's choice.Solve a total of ten problems (chosen by the student) from those offered in the lecture series.Write a 10page paper on the subject of one of the lecture series.
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: An
increased attendance at the department colloquium and other seminars.
Second and thirdyear students continue attending the colloquium even
though they are not required to do so. Students
started to appreciate the importance of good mathematical writing.
After the seminar, several students enrolled in a special class on
formal science writing.An
enhanced feeling of a real mathematical community within our
department. The seminar helps bring together the firstyear graduate
students, who are otherwise spread over different classes and do not
get a chance to meet regularly. Similarly, the faculty in charge of the
seminar (and, to a lesser degree, the faculty members presenting
lecture series) get a chance to know the strengths and weaknesses of
the new students.



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 coorganizer 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
nonstandard problems. Not all the participants were the firstyear
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 continueexpanding the math horizons of the students
while presenting them with new challenges and opportunities.


Reflections from a seminar student by Nathan GlattHoltz 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 takehome 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 writeups) , and it might be useful to reincorporate these
summaries in future seminars.


