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Summer Is for Research:Students and REU Programs
January 22, 1999

Pictured here on a field trip to the USS Augusta, in Groton,
Connecticut, participants in the 1998 REU program at Worcester
Polytechnic Institute completed research projects in a wide range of
mathematical topics. (Photograph courtesy of Arthur C. Heinricher, WPI)
While many undergraduates spend their summers parking cars,lending a
hand in family businesses, or trekking across Europe, others are heading
back to college campuses to tackle mathematical problems, working
alongside academic mathematicians who believe that, contrary to
conventional wisdom, undergraduates are more than capable of making
high-quality contributions to mathematical research.
Thanks to specialized programs known as Research Experiences for
Undergraduates (funded primarily by the National Science Foundation with
support from educational organizations and institutions), these
students can learn to focus their talents on various fields in the
mathematical sciences-in some cases coming away from the experience with
published papers or completed projects that they can add to their
college resumes.
Since 1977, Joseph A. Gallian has run such a program at the
University of Minnesota, Duluth. Gallian spends the year searching for
problems that will interest students, takes special care to match
students with problems that suit their talents and interests, and then
encourages them to get right down to work.
“REU programs offer multiple benefits to students,” says Gallian.
“First and research experience in which they develop their ability to
plan and carry out research in mathematics. This entails finding
problems, solving problems, posing problems, learning existing
techniques, adapting methods and, in some cases, developing new
approaches.
“In a successful research experience,” Gallian continues, “students
learn how to work independently, how to cope with frustration, and how
to overcome failure. They learn how to present their research to others
and how to write a mathematics research paper in a form suitable for
publication. Some students even have their work published in leading
professional journals.”
REU students can expect to live and work with other students who love
mathematics and excel at it, Gallian points out; the program gives them
the chance to network with people who are likely to be significant
contributors to the mathematics profession in the future. And, because
REU programs are widely recognized by the mathematics community for
identifying talented students and for helping students to develop their
talent, Gallian believes that participants in these programs enhance
their chances of getting into the graduate schools of their choice and
of receiving graduate fellowships.
Finally, since most REU programs offer organized recreational and
social activities, Gallian says, “students who participate in an REU can
expect to have fun!”
Gallian offers students applying to REU programs the following helpful hints:
- Request detailed information from program directors before you begin
the application process. Many programs have Web sites that provide
information on content, faculty, dates, and logistics, in addition to
reports on the experiences of former participants.
- Apply to more than one program.
- Application deadlines often vary, so mark the deadlines of the programs that interest you and apply well before those dates.
- About a week before each deadline, e-mail the program director to verify that your application is complete.
- Describe your qualifications for participation.
- Personalize your application by listing both your mathematical and nonmathematical talents.
- Discuss your long-term career plans and how the program fits into this plan.
- Explain your reasons for applying to each program and let the
program director know if his or her program is your first choice.
- If you are accepted at one program on your list but would
prefer another, contact the director of your preferred program and ask
for a definite answer before the enrollment date for the program that
has accepted you.
Learning to Communicate
Approaches to student research
opportunities can differ from program to program. At Worcester
Polytechnic Institute, for example, REU participants benefit from
lessons learned in the institute’s project-based approach to its
undergraduate program—an approach that WPI has used for 25 years to
provide a capstone experience for students in their major fields of
study. Local business and industry sponsor many of the projects.
According to Arthur C. Heinricher, organizer of the projects program,
interest in these projects from business and industry has exceeded
WPI’s expectations. “We have many more companies interested in
sponsoring student projects than we have students to undertake
projects,” he explains. “The REU program provides us with an opportunity
to work on projects in the summer, brings in very talented
undergraduates, and helps us promote our project program with local
companies.
“We have learned a lot about how to communicate with companies, to
identify a project that has significant mathematical content which will
be accessible to undergraduates, and to guide students in attacking an
open-ended problem,” he adds. “The students get access to decision
makers at the companies; it is very clear that the company is going to
use a student’s work to help make a decision (maybe even a very
expensive one), and this has an impact on students that no amount of red
ink on a test or homework can ever have.”
One WPI student described four aspects of the project experience this
way: (1) Problem formation is the hardest part of the project; (2)
problem solving is the most exciting part; (3) computation is the most
frustrating part; and (4) presentation is the most valuable part.
“Participants can learn a lot about how difficult it can be to
communicate outside the discipline,” Heinricher says. “They learn about
how the focus for a project can evolve and change in a very short time
and how important it is to communicate their mathematical results in a
way a company can understand and use.”
Opportunities in the Classroom
Not all summer opportunities
for undergraduates involve research. For example, in an effort to
encourage and inspire young women who are interested in careers in
mathematics, Carleton and St. Olaf Colleges, in Northfield, Minnesota,
offer a Summer Mathematics Program consisting of coursework, colloquia,
and panel discussions geared to women students.
Reactions to the program, which began in the mid-1990s and is open to
women who are finishing their first or second years in college, have
been extremely positive. Participants have called the experience
“awesome,” “informative,” “rigorous,” “challenging,” and “inspiring.”
Some participants have gone on to consider graduate programs in
mathematics; others have used the experience to build their confidence
and enhance their ability to succeed in other fields. Program organizers
do have one regret: Each year, say Deanna Haunsperger and Stephen
Kennedy, two of the organizers at Carleton, the program turns away more
than a hundred talented young women. If more women could participate in
this and other programs of its kind, Haunsperger and Kennedy believe,
the chances that more women would complete advanced degrees in
mathematics could only improve.

Participants in the Summer Mathematics Program at Carleton and St. Olaf
Colleges
take advantage of coursework, colloquia, and activities designed to
encourage their interest in mathematics. (Photograph courtesy of Deanna
Haunsperger, Carleton College).