By Sara Costa

During my sophomore year in college, my linear algebra professor told me about a research experience for undergraduates (REU). At the time, I did not know what an REU was and had no idea what to expect. That semester, I met Rachel Bailey, who was giving a talk at my university -- she served as a graduate student mentor at UConn’s REU for a couple of years. First, Dr. Bailey explained to me what an REU was. Then, she mentioned the REU at Uconn which specialized in mathematics research. We discussed the program and I realized it could be a significant opportunity to explore research and develop my academic skills. Encouraged by my professor and Dr. Bailey, I applied to the REU at UConn and was thrilled when I was accepted. As someone who had never engaged in research before, I was eager to see what the experience would bring and how it would shape my understanding of mathematics.

The first week of the REU primarily consisted of lectures covering various topics. I found this initial phase challenging because the mentors discussed complicated subjects that were often beyond my current understanding. Despite the difficulty, I appreciated that the mentors were always willing to answer the numerous questions I had, which helped me understand each research question more clearly. This support was crucial in helping me navigate the steep learning curve.

By the end of the first week, the students were divided into smaller groups to work on specific research projects. I joined a group with two other students, and together, we decided to focus on one of the Quantum Information questions. Quantum Information deals with the transfer of data and how quickly this can be done. Our group was fortunate to work with two mentors from the Quantum Information group, who were incredibly helpful in guiding us through the difficulties of our research like not getting results throughout the week or being stuck on a proof.

As the REU progressed, I quickly realized that the students involved were at various stages in their academic journey. It was clear that some had taken more advanced math courses than others, but this diversity in experience did not affect our collaboration. Instead, it enriched the research environment, as everyone contributed in different ways. Some students excelled at reading and synthesizing complex papers, while others were skilled at writing proofs or creating presentation materials. Although I was a rising junior and many of my peers were rising seniors with more advanced coursework, I found that everyone was willing to share their knowledge and help each other succeed. This collaborative spirit made the REU a truly supportive and inclusive experience.

One of the aspects of the REU that I particularly enjoyed were the weekly presentations. Every Monday, all the research groups would gather to present their progress from the previous week. These presentations were an opportunity not only to showcase our work, but also to receive constructive feedback from both mentors and peers. This feedback was invaluable in helping me improve my communication and presentation skills, and as a result I learned how to effectively convey complex mathematical ideas to others. Additionally, listening to the presentations of other groups exposed me to a wide range of mathematical topics and perspectives such as fractal integrations and Laplacian Eigenmaps. Even when I did not fully understand the content of a presentation, I found value in learning about the different approaches to problems. These sessions highlighted the variety of mathematical research and showed that there are many ways to approach and solve problems.

Participating in these weekly presentations also deepened my understanding of the research process itself. There were weeks when my group struggled to make progress or achieve any concrete results. Initially, this was frustrating, as I had assumed that research would yield steady, consistent outcomes. However, as I listened to the experiences of other groups, I realized that this was a common challenge. Research is unpredictable and setbacks are a natural part of the process. Hearing about the struggles and eventual breakthroughs of other groups helped me appreciate the nature of research and taught me the importance of perseverance and adaptability.

In addition to the presentations and collaborative work, the REU offered weekly math seminars that featured guest speakers from outside the program. These seminars were a highlight of my experience, as they introduced me to new and intriguing areas of mathematics that I had not previously encountered. The speakers, who were experts in their respective fields, presented on topics such as Number Theory, Spectral Dimensions, and Fractals. These talks sparked new interests that I might pursue in the future.

At the end of the REU, students presented their research findings at a closing event. This event allowed us to practice presenting our work to a broader audience and to engage with students from other REUs on UConn’s campus. I found this experience rewarding, as it allowed me to learn about the diverse range of research projects being conducted by students in other disciplines. I enjoyed meeting new people, discussing their work, and gaining insights into research areas outside of mathematics.

Overall, my REU experience was transformative, and I am grateful for the opportunity to participate in it. The program allowed me to explore a variety of mathematical topics, develop my research skills, and gain a clearer understanding of what graduate school might entail. Additionally, the REU provided a platform for networking with faculty members and other students. The guidance I received from my mentors as well as my peers made me feel like I was part of something special. The REU not only enhanced my academic abilities, but also helped me grow personally, as I learned to embrace challenges and persist through difficulties. The experience has solidified my interest in pursuing further research and has given me the confidence to continue exploring complex mathematical problems.

Sara Costa is an undergraduate student in her junior year majoring in computer engineering with a minor in math. She is also an athlete playing lacrosse at the University of Hartford.