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The National Science Foundation (NSF) has renewed Lafayette’s grant for the Research Experiences for Undergraduates (REU) mathematics program for five more years. The College has participated as an REU site for the last six years and for six years in the ’90s. Nearly 40 Lafayette students and 100 students from other colleges and universities have conducted research through the program.
“This is one of our flagship research programs in the math department and the College,” says Gary Gordon, professor of mathematics. “I think it has put Lafayette on the map for undergraduate research nationally. We’re known as one of the top places to send students to do research over the summer.”
REU is an intensive, eight-week summer research experience in which students investigate unsolved problems in mathematics, working in small groups directed by faculty. With up to 150 applications each year for the eight spots available to students from other institutions, Lafayette professors have a large, talented pool of students from which to choose for their individual programs.
“[We] pick students who we think may not necessarily have research opportunities elsewhere, so we want this to really have an impact on them,” says Gordon, noting that applicants come from all parts of the country. “You really want to open the door to a kid who may not have a research opportunity at his or her own school.”
For more information or to apply, visit the math department’s REU web page. Applications for this summer’s program are due Friday.
Four Lafayette mathematics majors traveled to San Antonio to present their REU research at the AMS-MAA-SIAM Joint Mathematics Meetings Jan. 12-15, and one presented at the eighth annual Nebraska Conference for Undergraduate Women in Mathematics Feb. 3-5.
Jenna Bratz ’06 (Springfield, Pa.), Jordan Tirrell ’08 (West Grove, Pa.), Stacey Altrichter ’06 (Chatham, N.J.), and Kevin Ehly ’06 (Sellersville, Pa.) participated in the undergraduate research session at the joint meetings in San Antonio.
A member of Phi Beta Kappa, America’s oldest and most respected honor society, Bratz conducted EXCEL Scholars research with Elizabeth McMahon, professor of mathematics. Throughout the summer, Bratz worked with students from Brown University, Smith College, and Mesa State University to research automorphisms [functions from the graph to itself that is one to one and onto, meaning that things can be moved while preserving the integrity of the original structure] of Cayley graphs and determine connections between group theory and graph theory. She is continuing her research this year in an honors thesis.
“Attending the conference in San Antonio was a real learning experience for me,” says Bratz, who plans to study applied mathematics in graduate school for a career in engineering or medicine. “It was wonderful to be in an environment with mathematicians who share a real love for their work. I was able to see what other research is being done, and presenting our research at one of those sessions was very beneficial to me. All in all, [it] was four days very well spent.”
Bratz plays varsity field hockey and received the Maroon Club’s 2005 female Scholar-Athlete of the Year award. She is a peer mentor, peer tutor, and member of Calculus Cavalry, Fellowship of Christian Athletes, Lafayette Christian Fellowship, and Alpha Phi sorority.
Tirrell studied the perfect cuboid problem, an open mathematical problem about 3-D boxes, as an EXCEL Scholar with Cliff Reiter, professor of mathematics. The notion behind the research is that every edge in the 3-D box – created by seven lengths and diagonals – is an integer. “Pursuing the Perfect Parallelepiped,” a paper Tirrell co-authored with Reiter, has been accepted for publication in JP Journal of Algebra, Number Theory and Applications. Tirrell is extending his research into another EXCEL project.
“Presenting my research at the conference was an excellent opportunity to explore the mathematical community and has inspired me to continue academic pursuits in mathematics,” says Tirrell, who plans to attend graduate school and teach on the college level.
He is a peer tutor, tour guide for the admissions office, and member of Tennis Club and Table Tennis Club.
Robert Root, associate professor of mathematics, advised Altrichter’s NSF-funded EXCEL project. Now completing an honors thesis on a more challenging model, Altrichter analyzed a simple mechanical model of the vertebral column of a sunfish. The goal of the NSF program is to investigate the selective pressures that gave rise to vertebrae in fish. The researchers believe that these pressures arise from the mechanical advantages vertebrae offer for swimming. Altrichter plans to attend graduate school in pursuit of a Ph.D. in applied mathematics with a focus on dynamical systems and differential equations.
“Traveling to San Antonio for the AMS conference was a great opportunity to experience what hopefully will be in store for my future,” says Altrichter. “I was able to meet both students and professors interested in the same topics that I enjoy. Their questions pertaining to my work have furthered my knowledge of the subject, and their suggestions have given me new possibilities to look into for my project. The conference provided a good atmosphere to practice for my thesis defense later this semester.”
“It is invigorating and inspiring to mingle with four or five thousand people who have made mathematics a central part of their lives,” adds Root. “Most important is the sense that mathematics is a great discipline and a worthy career, rich with important challenges and satisfying rewards.”
Altrichter is a peer tutor, lab proctor for the math department, and student representative for the admissions office. She also is a member of Calculus Cavalry, Math Club, Physics Club, and Soccer Club.
An EXCEL Scholar, Ehly collaborated with Gordon to classify symmetry using combinatorics, or various counting methods. He studied the icosahedron, a three-dimensional geometric shape comprised of 20 triangles that is one of the five famous platonic solids known to the ancient Greeks. He presented his results in a 15-minute lecture accompanied by slides and a 3-D model. Gordon and Ehly will submit results for publication later this semester.
“The conference was a nice opportunity to see what research is currently being conducted in the various fields of mathematics,” says Ehly, who plans to pursue a Ph.D. in math and teach on the college level. “Being given the chance to present at this conference as an undergraduate was a helpful experience as well. It forced me to reevaluate my work and figure out the best way to present [it] to someone who may not be familiar with the problem.”
Ehly is completing honors thesis research on geometric topology under the guidance of John Meier, professor of mathematics. A member of Delta Upsilon fraternity, he has served on its executive board and as vice president of scholarship.
Advised by McMahon, Marquis Scholar Maureen Jackson ’06 (Steubenville, Ohio) traveled to the University of Nebraska in Lincoln to present her honors thesis research on the mathematics behind the game of Set, in which players must identify a group of three cards from 12 with a variation of colors, numbers, symbols, and shading. Her research explores how different branches of math, including combinatorics, probability, linear algebra, and geometry, affect the outcome. Jackson plans to teach math on the secondary level.
“I was really excited about going to the Nebraska Conference for Undergraduate Women in Mathematics,” says Jackson, a member of Phi Beta Kappa. “I never imagined when I started my thesis that I would one day be presenting it at a conference. It is a great opportunity for me to articulate all that I have learned so far to people who are really interested in math. I am also very interested to get the big picture of the types of math research that people do. Something I think [high school] students often wonder, ‘Why is math important to know?’ Learning about different things that people study will give me numerous ways to answer this question that I will surely encounter as I begin to teach.”
Jackson is a photographer for The Lafayette and a member of Lafayette Christian Fellowship. She is a past recipient of the Eugene P. Chase Prize given to sophomores who demonstrate scholarship as first-year students. She participated in a three-week study-abroad trip to study The Land and Landscape of Ireland. She was a math teaching assistant at the Johns Hopkins Center for Talented Youth for two summers. She has participated in the International Students Association Extravaganza and has volunteered as a child care aide.
As a national leader in undergraduate research, Lafayette sends one of the largest contingents to the National Conference on Undergraduate Research each year. Forty students have been accepted to present their research at this year’s conference.