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College Mathematicians Dive into Variety of Hot Topics in Summer Research Program

July 20, 2011

Gesturing to a display board with diagrams and other information, Jordan Fitch explains, "This is based off of background work which looked at the overall outside shape of a slice of French bread."  He continues, "I was looking at how interior bubbles affect the outside shape of the bread."  The display summarizes his research project on "Examining Bread Foams and Periodic Structures" through Rose-Hulman Institute of Technology's Research Experience for Undergraduates (REU) in Mathematics program.

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Looking Ahead To Graduate School: Participating in Rose-Hulman Institute of Technology's Research Experiences for Undergraduates program in mathematics will help JingJing Chen of California's Pomona College realize her dreams of attending graduate school.

Now in its 22ndyear, the REU draws some of the best and brightest students from colleges across the country each summer.  The program, which is funded by the National Science Foundation, allows students to do original research in mathematics, provide a taste of graduate-level work.  It also affords students the opportunity to produce results which can then be submitted for publication in either undergraduate or professional journals.

Fitch, a mathematics student at Kentucky's Centre College, explains that after generalizing the bubble size, hexagons were used to model the interior of the bread's structure.  He adds that Plateau's Laws, which are used to describe the structure of soap film, apply in this instance because bread behaves as a capillary surface.

An opportunity to conduct undergraduate-level research is a reason why Fitch is spending his summer at Rose-Hulman, one of the nation's top-ranked colleges for undergraduate engineering, science and mathematics education.   Student-researchers from such distinguished colleges as Carnegie-Mellon University, University of Chicago, Massachusetts Institute of Technology, Harvard University, Baylor University, and Princeton University spend their summers at Rose-Hulman because of the Department of Mathematics' REU program's reputation for excellence.

Joshua Holden, associate professor of mathematics and director of Rose-Hulman's math REU, observes that one emphasis for the program has been to provide students from smaller colleges a research opportunity they might not otherwise have.  The program also provides a chance for students to earn valuable letters of recommendation for applying to graduate school.

"I'm looking into applying to graduate school and I wanted a more competitive edge for my resume," Fitch stated.

Holden adds that participation in the REU program allows students to make a better informed choice with regard to the future of their education.  "We really try to give them an understanding of what it means to be a mathematical researcher," he notes.

Assisting Holden with this year's program have been Rose-Hulman math faculty colleagues Kurt Bryan and David Finn.  These professors choose topics for each year's REU, which are then advertised to college students interested in mathematics research.  This year's topics over mathematics related to codes and cyphers, geometry that's related to baking and the mathematics that you need to find holes in things without opening them up - such as cast metals.

Holden says that topics are chosen in which "there are still new things for students to discover." Upon arrival, he says, "We give the students, depending on the professor, two to four days of lectures as background before turning them loose."  The students then work independently or in teams, with faculty mentorship, over a six-week period that Holden says is designed to "give them a taste of a graduate school research experience."

JingJing Chen, a student at Pomona College in Claremont, Calif., joined Mark Lotts of Virginia's Randolph-Macon College on research examining "The Discrete Lambert Map."  The quest is to enhance security by making cryptographic codes which are more difficult to decipher.

"We think that the security of a cryptographic system lies in finding a solution to this problem," Chen states.  "It's really nice to be able to jump into the topic and focus our energy on that."

Lotts added, "This is the first time that I've really proved things that haven't been proven before and found things that haven't been found before."

Chen chose to Rose-Hulman's REU program because of her interest in the topics being researched.

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Collaborative Effort: Rose-Hulman Institute of Technology Mathematics Professor Joshua Holden helps a student understand a problem during this summer's Research Experiences for Undergraduates program in mathematics.  Holden is director of the National Science Foundation-sponsored program.

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Working Things Out: Students in Rose-Hulman Institute of Technology's Mathematics Research Experiences for Undergraduates program get some helpful advice from professor David Finn during a recent classroom session.

"I looked at a bunch of REUs and decided on the project most appealing to me," she says.  "I think the REU experience, in general, is a really important one if you're looking to attend graduate school in math, as I am."

In addition to her research, Chen also appreciated the program's emphasis on presentations.

"It's nice to learn how to produce something, present it, and develop those skills," she notes.

Lotts chose Rose-Hulman's REU program not only because he was interested in the topics being researched, but also because it gave him the opportunity to study in a top-notch environment. '

"I wanted the experience of working on original research with other students that are interested in mathematics," he states, adding, "and obviously, Rose-Hulman has an outstanding reputation in math and science."

Learn more about Rose-Hulman's REU program.