There was a time when many people believed that research in mathematics was beyond the reach of undergraduates. That viewpoint is long since debunked, thanks in part to the Research Experience for Undergraduates program at the National Science Foundation (NSF). With support from several NSF grants or UNL's Undergraduate Creative Activities and Research Experiences, providing undergraduate research opportunities has been a priority for the UNL mathematics department for several years. Three NSF grants have had a special impact on undergraduate research by UNL mathematics majors.
In 2005, a grant from the National Science Foundation that fosters interdisciplinary undergraduate programs brought the math department and the School of Biological Sciences together.
Research for Undergraduate in Theoretical Ecology (RUTE), is a $900,000 grant funded in 2005 by NSF's Undergraduates in Biology and Mathematics (UBM) program. UNL's grant brings together faculty from mathematics and the School of Biological Sciences to engage in interdisciplinary research in theoretical ecology.
"Life science is projected to be the major research thrust in the 21st century, as physics was in the 20th century, and quantitative issues in the life sciences play a crucial role," said Professor David Logan, a RUTE math mentor.
UNL is one of 20 universities recognized nationally for its joint programs and awarded a grant under this NSF initiative. Over the past four years, 36 students have been awarded RUTE scholarships. During the spring semester, students take MATH 316 to prepare students for their summer research project, which often takes place at Cedar Point Biological Station near Ogallala.
This year's projects were parasitology, understanding the fitness and life history characteristics of certain parasites that are present in insect larva and adults in aquatic systems (mentored by Logan and biology Professor John Janovy), and plant diversity, examining the effects of nutrient additions and herbivory on the composition and spatial structure of prairie plant communities (mentored by Jean Knops, Ben Nolting and Natalie West).
Undergraduate Brittany Bunker, a junior mathematics major, spent 12 weeks in Summer 2010 at the Ogallala station, studying gregarine parasites in damselflies.
"We spent most of our time in the lab dissecting the damselflies, then measuring and identifying the parasites found in their guts," Bunker said. "Cedar Point is a really beautiful place and the atmosphere there is very relaxed. Our team is now working on modeling the data we collected with math and statistics, and we hope to write a publishable paper soon."
In the summer of 2008, a team had the opportunity to do its research in Borneo, in Southeast Asia, led by UNL Assistant Professor of Biological Sciences Sabrina Russo. Four undergraduates, including mathematics and premedicine major Autumn Shapland who graduated in Spring 2010, spent six weeks on the third-largest island in the world, at the southern end of the South China Sea, collecting data at Lambir Hills National Park in Sarawek, Malaysia. The park has one of the largest and last remaining tracts of lowland mixed dipterocarp forest, which is a forest type that has become scarce due to the demand for tropical timber.
The students' project examined the growth strategies of trees in relation to their light and soil environments to understand the development of the vertical structure of the forest. The students first worked with Russo to analyze their data and then with UNL mathematics Professor Richard Rebarber to develop a mathematical model describing the process of tree growth using their data set.
(photo 1)- In 2008, undergraduates Brett Bogenrief, Ethan Jensen (back row), Autumn Shapland and Katherine Heineman (front row) spent six weeks in Borneo collecting data at Lambir Hills National Park in Sarawak, Malaysia, as part of UNL's RUTE program, a grant that brings mathematics and biological sciences together to engage in interdisciplinary research in theoretical ecology.
In 2009, another team of four undergrads also went to Borneo, including senior math and biology major Eric Price (far left in photo), senior math and physics major Brian Hemen (third from left in photo) and biology majors Aimee Koenig and Jenna Jo Comes.
Students are assisted by mentors in the formal write-up of the summer research, which is published in a professional journal or presented at a professional meeting.
The RUTE grant's principal investigator is Associate Professor Glenn Ledder with co-PIs mathematics Professors Logan and Bo Deng, and Professor Emerita Svata Louda in biology.
The Nebraska Research Experiences for Undergraduates in Applied Mathematics grant, under the direction of Professors Rebarber (PI) and Gordon Woodward (a former co-PI), has been funded by NSF since 2002 and attracts students from across the country. Since 2002, students who have participated in the program have published seven papers in research journals (two more will be published soon) and four papers in undergraduate research journals, and have made several research presentations at professional meetings.
Each summer, 10 students are chosen for the eight-week summer program. For 2010, 126 undergraduates applied for the 10 positions, offering evidence of both the program's popularity and the quality of the students chosen for the program. Each group includes three or four undergraduates, a math graduate assistant and a faculty mentor. The goal is to give students as full a research experience as possible, including how to define a good problem, how to solve a problem, how to give rigorous proofs, how to write mathematics and how to give a talk or present a poster.
A few recent projects, and their mentors, have been: Graph Theory (Jamie Radcliffe), Modeling in Ecology (Ledder), Mathematical Models of Neurons (Deng), Matrix and Integral Models for Predicting Population Dynamics (Rebarber and Brigitte Tenhumberg), Differential/Difference Equations (Allan Peterson), Life History of Plants (Ledder), Calculus on Time Scales (Peterson), and New Models for Heat Conduction and Elasticity in Structures with Cracks (Petronela Radu).
"We want to interest more students in research areas," said Woodward, chief undergraduate adviser for the math department. "The program is successful because we choose focused research projects that don't require lots of background mathematical knowledge. We teach the mathematical tools that relate to that focus - and then we let the students go."
Added Logan, "Our goal is for students to write a research paper or present a paper. There is tremendous value in learning those skills as an undergraduate."
Senior mathematics major Zach Norwood participated in an REU at Indiana University-Bloomington during the summer of 2009, in which he worked on the project, "Finite Groups with Many Involutions."
"What I enjoyed most about the REU was the chance to connect with math students from other universities and to spend eight weeks on a single interesting research problem. It was also nice to get to learn some new mathematics over the summer," Norwood said.
(photo 2)- Undergraduates Dustin Walker, Dennis Rogers and Daniel Wiechert, students in Math in the City, presented their research at a workshop on Dec. 3, 2010.
Math in the City, created by Assistant Professor Petronela Radu and first offered in Spring 2006, is a course that offers undergraduates a research-like experience in mathematical modeling. Radu teamed with Assistant Professor Stephen Hartke last year and received an NSF CCLI grant (Course, Curriculum, and Laboratory Improvement) to further develop the course as a model for export to other universities.
Students who take the Math in the City course work in groups with experts from local businesses and research and administrative centers to model and analyze various aspects of a real-world problem of current interest. This trains students to overcome the challenges of working with real data and the assumptions present in mathematical models.
Past projects have included: Water resource analysis of Lake McConaughy (Nebraska Department of Natural Resources); Medical Trial Analysis (with UNMC); Lincoln Housing Market (with the Office of the Lincoln County Assessor); Green Construction (with the firm The Architectural Partnership); and Recycling in Lincoln (with the City of Lincoln and Von Busch and Sons).
RUTE Participants from UNL
- 2010: Austin Barnes, Brittany Bunker, Matt Shuman
- 2009: Kevin Ahrendt, Brian Hemen, Eric Price
- 2008: Autumn Shapland
- 2007: Emily Matthews, Ed Rubin, Ken Shum, Beth Ann Tidemann, Noah Weiss
REUs (and Locations) Attended by UNL Undergrad Math Majors
- 2010: Adam Azzam (Claremont College), Amy Been (Carleton College), Jay Cummings (NSA), Kate DeJong (George Washington Un.), Nicole Gaswick (UNL, Peterson), Laila Gharzai (Un. of Strasbourg, France, Organic Chem)
- 2009: Jessica Alley (Cal State San Bernardino, Knot Theory), Jay Cummings (Un. of West Georgia), Nicole Gaswick (Texas A&M, "pre-REU"), Laila Gharzai (Johns Hopkins), Laura Janssen (Jacobsen) (Canisius College), Tyler Lemburg (Clemson Un.), Zach Norwood (Indiana University-Bloomington), Billy Sanders (Hope College)
- 2008: Steve Davis (NC State Un., Applied Math), Travis Johnston (NSA), Wen Lou (Un. of Maine), Charles Sherer (MI State Un.), Noah Weiss (UNL)
- 2007: Scott Hottovy (NSA), Tyler Lemburg (Trinity Un.), Wen Lou (Tenn. Tech Un.), Ashley Patefield (George Washington U)
