By Stacie Baumann, 2017 graduate of West Virginia Wesleyan College, currently a doctoral student at Auburn University, and Matthew Jones, Virginia Tech, class of 2018
Editor’s note: The editors thank Stacie and Matthew for taking the time to share their thoughts and insights with us about their REU experiences. For students who are interested in applying for an REU, lists of programs can be found here and here. To read more about student and faculty experiences with REUs, see our other articles on this topic.
I did not know what a Research Experience for Undergraduates (REU) was until one of my professors suggested I apply to REUs at a few different institutions. I went to a small liberal arts college with few research opportunities. I applied to a handful of different REUs and was excited when I received my acceptance from Marshall University. I was excited to spend eight weeks of my summer at a different institution and to learn what mathematical research really looked like. I was also nervous that I would be behind the other students academically. When I arrived, my nerves were calmed and the excitement continued.
If I learned anything from participating in the REU at Marshall University, it was how to be frustrated. Before the REU, I had certainly encountered a few difficult proofs in my courses, some of which I spent a couple of days thinking about. However, I had never spent an entire summer obsessed on one seemingly tiny mathematical problem. Throughout the months of June and July, I thought about mathematics at breakfast while drinking my coffee. I thought about mathematics while sitting in a classroom at Marshall. I thought about mathematics while playing cards in the evening. I went as far as to buy a 3-foot-wide whiteboard to keep beside my bed that I could grab in the middle of the night and test out propositions.
When I describe that experience to my friends outside of the mathematics community, they usually say, “That sounds awful”. But in actuality, it was the most exciting experience of my brief mathematical career. In a short span of time, I learned a great deal of exciting new mathematics that I would not have been exposed to in a normal course at my home institution. I learned a great deal more about the mathematical community in general, how research works and where I might fit in. Most importantly, I learned how exhilarating the process of figuring things out mathematically can be.
I have had a few small research-based projects in different classes. However, none of them compare to my experience at the Marshall University REU. I got to spend eight weeks with nothing to worry about except math. Unlike the other projects, I did not have any other schoolwork or activities to complete. All I had to worry about was the research. I found myself thinking about it at all times of the day. I would lay down to go to sleep and have to get up to write down an idea that came to me. I would be at the gym working out and I would think of an idea. I found it funny how I could spend all day working on something and then whenever I started to do something else the solution would pop into my head. I enjoyed working on something no one had ever worked on before. Unlike homework, there was no obvious correct solution and my adviser did not always have all the answers. My adviser was able to lead us in the correct direction most of the time, but because he did not have the answers sometimes he was as stuck on a problem as we were. I felt a great sense of accomplishment when I was able to prove something new. At the end of the summer we proved the result we set out to prove and I was extremely proud of the rest of my group and myself.
In the middle of the summer, the work I was doing with my group had nearly slowed to a halt. We had a good deal of success in June, but by July, we really did not know how to proceed. I was spending almost every free moment that I had in the Marshall Graduate Student’s office trying to parse through sheets and sheets of output from Mathematica programs, looking for patterns. It seemed like every morning that our research group met, I would have a new proposition to test, only to find a counterexample before going to lunch. It was immensely frustrating, especially because some of the other research groups within the REU seemed to be making so much more progress than us.
However, all of the frustration was worth it when I finally made a minor breakthrough and found a combinatorial pattern that I thought might be the basis of a future result. When I found what I had been looking for, it seemed like it had been blatantly obvious, yet it had taken me weeks of work to find it. The moment was exhilarating. Whole new avenues of inquiry were suddenly opened up, and for a week, the project looked extremely promising.
Then I got stuck again. But that’s the beauty of it. Because of the experience I had in the REU, I knew that with enough hard work and creative thinking, I would eventually make another small step in the right direction. It was like hiking in unfamiliar territory. Most of the time, I was walking in an almost random direction, completely unsure of whether I was on the right path or not. But then, I would see a sign and know which way to turn.
The most important thing the REU provided was the opportunity to take risks. Because there are no grades, I had the freedom to focus very intently on a single topic. For once, it was okay to fail, okay to suggest a proposition that I would find a counterexample for a few hours later. In most of the mathematics courses I have taken, the focus has been on getting the correct answer in the most efficient manner possible. But the most efficient manner excludes all of the wrong turns and stumbles that someone had to make to get to that point. Through my experience at the REU, I was able to explore the un-polished bits of mathematics that don’t make their way into our textbooks.
My experience through the REU has strengthened my ties to the mathematical community. Throughout the summer I met many professors from different universities and I got to meet fellow students who have similar career goals as me. The REU gave me the opportunity to travel to the Joint Mathematics Meetings in Atlanta, Georgia. It was amazing to see so many mathematicians in one place. I got to listen to experts talk about fields of study I am interested in and I got to meet many different undergraduates, graduates, and professors at universities with graduate programs. Without the REU, I would not have had the funding to be able to go to the Joint Mathematics Meetings or have anything to present at the Meetings.
I feel as though I am at a great advantage compared to the students at my institution who did not have an REU experience. During our senior thesis class, I had the advantage of already having completed research. I had experience with the process of picking a research question, learning the background, and completing meaningful research. During the REU we spent many hours learning how to present our progress. This made my presentations during my senior thesis much easier to prepare for and made me much more confidant presenting in front of my classmates. I felt ahead of my classmates who were unable to participate in an REU.
Also, the REU was an amazing experience outside of mathematics. The other students and I spent almost every night together playing card games, watching movies, or going to a local restaurant for trivia night. We even went to Cincinnati, Ohio one weekend. We got to visit the Newport Aquarium and explore the city. The nine of us became a close-knit group by the end of our eight weeks. It is nice to have students at other institutions to compare experiences. We all still keep in contact and visit each other.
Working in a team with other undergraduate researchers and in a program with other research teams provided new avenues for growth as well. I learned about doing mathematics in teams, something that I had little experience in, and how to efficiently divide labor while keeping everyone on the same page. By working with other students, I also gained appreciation for different student’s mathematical backgrounds and strengths. Talking with the other research teams also helped; their research exposed me to areas of combinatorics outside of what I was working in. Also, friendly competition between the groups helped motivate my team to keep going when we were stuck on a problem.
Through the REU, I gained more exposure to the larger mathematical community. Our program had regular speakers from other areas of the department and other schools come and talk, further exposing us to topics of current research. I learned about how the work I was doing fit in with research being done by other mathematicians (many with much more experience than me). The REU also allowed me to participate in the 2017 Joint Mathematics Meetings in Atlanta, Georgia in January where I was able to see the full breadth of current mathematics research beyond combinatorics. The other participants and I were able to learn more about graduate school by talking to our mentors and other mathematicians and attending the Graduate School Fair at the meetings in Atlanta.
When I declared my mathematics major my original goal was to eventually become an actuary. The summer after my freshmen year I did an internship at an actuary firm and realized that is not what I wanted to do for the rest of my life. Then, I decided I wanted to go to graduate school for pure mathematics, but I was unsure. After my REU experience I am confident that I have chosen the correct path. Overall, the Marshall University REU was unforgettable. I suggest that undergraduates apply to as many REUs as possible, because I think every student should have the opportunity to have this experience at some point before they graduate.
After participating in the REU, I feel as though I know so much more about mathematics. But even more, I feel as though I know more about how much there is out there that I don’t know. The program has motivated me to pursue a PhD in mathematics and do more mathematics research in the future, whether in combinatorics or another field. I suspect the frustration coming my way will be worth it.