In addition to the many off-campus possibilities for summer research, students often work with our faculty on projects for credit or projects funded by grants. Projects done for credit can also lead to graduating with honors in mathematics. See the department faculty for details.
Past projects have run the gamut from studying the connection between statistics and the theory of voting (see the article from this work) to studying optimal distribution of aid in Haiti after their earthquake. Some students have also participated in summer research off-campus, both applied and pure, such as in this published article by Melissa Haire '13.
Here are some recent projects:
Voting with broad support
Suppose that there are several academic departments voting on which of two students should receive a large scholarship. (Maybe you!) Typically, one would say "majority rules"; but if one department is just a lot bigger than the other ones and votes for their student, it might not be as representative of the college as a whole. Should one also take into account how many departments felt a candidate was worthy?
Luke Cui '18 and Sunny Kim '17 are working this summer (thanks to a grant from the Provost's summer research program) on exploring this question and what to expect; it's certainly bigger than just voting on scholarships!
Optimizing Supply Chains
As you can read in Gordon's Fall 2015 STILLPOINT magazine, Ethan Kang '17 worked on continuing Professor Veatch's research in queueing theory. Essentially, if you have a lot of customers in a bunch of different lines, how does one compute their average total wait time? A recent approach using a worst-case analysis led to demonstrable progress. As quoted in the article, Ethan says, "I learned how to think creatively and formulate new ways of thinking ... I think that was the biggest achievement."
Food aid and market impacts in Darfur
The Darfur region of Sudan was one of the worst humanitarian crises in recent memory. The United Nations has experimented with given people food vouchers to buy regionally produced food in local markets instead of traditional food aid. Senior mathematics and economics major Austin Drukker developed a model to capture the tradeoffs between providing food and vouchers. Many world markets may be “flat” in an economic sense, but those in Darfur, with poor roads, rainy seasons, and civil war, are decidedly not. Using data collected in Darfur by the World Food Program and MIT’s Humanitarian Response Lab, Austin showed how costs rise as local food is exhausted and trade with other parts of Sudan must increase to meet the voucher demand. He worked with Dr. Veatch and professor of economics Dr. Stephen Smith.
Monte Carlo Optimization
Olivia Gray '14 and Juliann Booth '15 both used Monte Carlo optimization. These methods use randomness—surprisingly—to solve hard optimization problems. Working with Dr. Veatch, Olivia used simulation to investigate how to reduce idle time in manufacturing systems. (Have you ever noticed how when you work with someone, someone always seems to be waiting on someone else?). In physics and other fields, there is often a need to generate random numbers that follow some pattern. Working with Dr. Senning, Juliann learned an ingenious method, Markov chain Monte Carlo, that works even when you don’t have a complete formula for the pattern. She developed a computer tool using this method that can find the maximum of a “messy” (nonconvex) function of many variables. See this short article for more details on Olivia and Juliann's research.