Many of us can say we’ve had the experience of staring at a math problem as if it were written in a different language, or with symbols from another planet. Nellie Brushaber wouldn’t have any problem translating for us though; she speaks fluent math.
A subject often deemed dry and confusing is described as exhilarating and complex by Nellie. Her passion for mathematics has taken off during her time at UW-Eau Claire, and she is nowhere near finished exploring the subject.
“People often believe there is not much to discover about math, and that what is out there is all there is,” Nellie said. “But there is so much left to learn, and mathematics research is always happening!”
Nellie came UW-Eau Claire from Oronoco, Minnesota, and while she was working through middle and high school, she always dreamed of becoming a teacher. When Nellie arrived on campus as a freshman, she decided to pursue a math education major. As time went on, Nellie discovered what she really wanted to do was research. The good news for Nellie is that UW-Eau Claire is one of handful of universities that offer such a wide range of research opportunities and outstanding support from faculty and staff.
Dr. Carolyn Otto was one of the first to notice Nellie’s dedication to mathematics, and Otto offered Nellie some unique research opportunities within the discipline. Otto and Nellie worked together on an exciting student-faculty research project.
“There are typically two types of students in my classes,” Otto said. “Those who ask questions only related to class materials, and those who ask questions far beyond what we are learning in class. Nellie was definitely in the latter group.”
After noticing Nellie’s dedication and interest in everything mathematics, Otto thought she would make a perfect candidate for research. When presented with the opportunity, Nellie did not hesitate.
Nellie discovered the world of math research provided her with a range of opportunities that could be combined with other interests. Eventually, Nellie switched from a math education major to a mathematics major with an emphasis in statistics.
“Although being an education major taught me a lot, I found out how much I could do with statistics and never looked back,” Nellie said. “Stats allows me to use math whenever I want, and the research opportunities are endless. I still value the education courses I took, because maybe one day I will teach in higher education, and they also taught me resilience in my own learning.”
With the guidance of Dr. Otto, Nellie and her fellow student researchers have worked on and presented their knot theory research. To put it simply, this project explores knot and link tricolorability within knot theory, which is an area of study in the discipline of topology. Topology is the study of geometric figures that remain unchanged, even when they are distorted.
“The easiest way to explain topology is to think of it as geometry that we can bend and twist,” said Dr. Otto. “It is the study of how shapes change, but the mathematical theories researchers come up with cannot cut these shapes and reattach them. Essentially, if you know how to untangle Christmas tree lights then you know everything you need to about knot theory.”
Nellie’s research group explored knot and link tricolorability with a focus on knots and twists that can be been seen in DNA. The application of the theory has been extremely exciting for the group because it combines mathematics research and biology.
“Math research is so cool to me because, as mathematicians, we are able to discover new information that can later be used by people from almost any discipline,” Nellie said.
All of Nellie’s research has led her to many other opportunities that she didn’t even realize were possible. Some of these opportunities have included helping develop UW-Eau Claire’s Math 380 course, Research in Mathematics, attending and presenting at two out-of-state conferences and receiving a personal visit from Chancellor James Schmidt and Provost Patricia Kleine at the annual Celebration of Excellence in Research and Creative Activity (CERCA).
“I had been so excited about the research my team and I put together that I tweeted the chancellor right before the math retreat at CERCA,” Nellie said. “We were going to present our work and I personally asked him to stop by and, guess what…he did!”
Nellie is proof that asking for what you want and jumping at opportunities can lead to great outcomes. However, even with all of the recognition her research is receiving, Nellie remains humble.
“I am a huge believer in a balanced life,” Nellie said. “Even with all of these awesome academic opportunities, I have found that my best semesters have been when I get enough sleep, play volleyball, and constantly say ‘yes’ to friends who ask me to hang out.”
The concept of balance is something we can all take away from Nellie’s story. Hard work and dedication are key to academic success, but learning to relax and enjoy the little things is equally important. You don’t have to be an expert in knot theory to understand that while creating balance is difficult, with a little bit of math and a lot of luck, anything is possible.