William & Mary

Undergraduate Research

If you are a mathematics major, or are thinking about becoming one, you already know that learning mathematics is exciting. Your professors can assure you that discovering mathematics is an even more exciting activity, and William and Mary undergraduates can participate in that process through undergraduate research programs.

What is research in mathematics? Mathematical research goes beyond reading someone else's discoveries in a textbook or journal, and beyond solving problems that you have not solved before. Mathematical research involves first determining what are the right questions to ask, and then attempting to answer them. To varying degrees, this involves solving problems that nobody has solved before, often with little idea of what approaches and which techniques might work, and sometimes without a clear initial idea of what the question really is. It involves intuition as much as knowledge, and its unstructured nature is often frightening to beginners, whether they are undergraduates, mathematics doctoral students, or professional mathematicians presented with a challenge they have never seen before. Students are usually introduced to research through a carefully supervised apprenticeship process in which they are treated as junior colleagues whose research skills and insight develop through close interaction with a faculty supervisor.

There are many opportunities for undergraduate mathematics majors at William and Mary to participate in mathematical research. These include independent study courses, the Honors Program, summer internships and participation in summer Research Experiences for Undergraduates (REU) programs around the country. Undergraduate mathematical research at the College often results in professional publications. Many research articles have been published by mathematics undergraduates who worked with faculty members at the College, and more are being considered by professional journals. 

Internships that draw upon one's mathematical skills can show students what industrial mathematics is really about, and can give students an early start in their post-college job searches. They can also give students valuable experience in working on teams, something that is often missing from a traditional undergraduate mathematics program. Information about internship opportunities is available through the college's Career Services Office.  Furthermore, the department circulates such information by e-mail to its majors. Finally, nearby federal laboratories-NASA's Langley Research Center and the Department of Energy's Jefferson Laboratory-also provide some internship opportunities.

Writing an Honors Thesis, or participating in summer REU programs, can give students a preview of what would be involved in mathematics doctoral study. Students with strong academic records, whose overall performance in mathematics courses (including at least one of Math 307 and Math 311) through the junior year is very strong, should consider the possibility of writing an Honors Thesis. They should also investigate REU programs for the summer between their junior and senior years (and possibly a year earlier), particularly if they are considering graduate school in mathematics.

The National Science Foundation and other federal granting agencies support about two dozen REU programs around the U.S., including two at William and Mary. Most of these programs are small, involving about ten students each. REU participants typically receive modest stipends and free on-campus housing for eight to ten weeks in a summer, and work closely with a faculty member on a research problem in mathematical sciences. Different REU sites typically focus on different research areas, and a list of REU sites and their research foci is published in Notices of the American Mathematical Society and SIAM News. On the Web, the list of REU sites is available from the National Science Foundation. In addition, students may explore REU opportunities via the Web site of the Mathematical Association of America or by sending an e-mail inquiry to REU.dms@nsf.gov. Admission to REU programs is competitive and requires letters of recommendation from faculty members.