Applied Mathematics Research Program for Undergraduates: A Journey of Discovery at Florida International University

Authored on July 11, 2023 by Justin Wisby.
group photo of Gregory, Katherine, Aliah, Rene, Kennedy, Jacob, Jason, Oleg, and Diego

Group photo of Gregory, Katherine, Aliah, Rene, Kennedy, Jacob, Jason, Oleg, and Diego.

At Florida International University (FIU), we are proud to be in the sixth week of our eight-week-long "Applied Mathematics Research Program for Undergraduates" (AMRPU). This program, now in its third year, is a unique opportunity for undergraduate students to immerse themselves in the world of mathematical research. The AMRPU covers a wide range of topics, including Graph Theory, Numerical Analysis, Partial Differential Equations, Dynamical Systems, Analysis, Differential Geometry, and Machine Learning. The program is designed to expose students to research topics with the goal of discovering new mathematics. It's a delicate balance to find problems that are accessible to students but still profound in the field, and that's exactly the challenge we embrace in this program.

Our 15 participating students are expected to put in over 300 hours of work over the course of the program. This intensive experience serves as a jumping-off point for future dissertations and a unique opportunity to further network and expand their contacts. FIU student Kennedy S.Vallenilla, who is working on a project in Graph Theory, shared her experience: "The REU improved my professional skills significantly. I am better prepared for presentations and learned how to work in a group."

Kennedy at the board

Kennedy S.Vallenilla proving some important theorem

The AMRPU is not just about research; it's also about professional development. Students attend numerous talks and workshops on communication and professional development. These sessions are designed to prepare them for the rigors of graduate school and beyond. Jacob Glidewell, a student from the University of Alabama working on an Analysis project, expressed his appreciation for these sessions: "There have been plenty of talks and workshops on communication and professional development at the REU. I feel prepared to tackle graduate school now knowing the skills presented to me here."

Group Photo with Jacob, Luiz, Oleg, and Mikhail

Jacob Glidewell with his group understanding frames and bases.

The program culminates in a final symposium on July 28th, where students will showcase their research. This event is a testament to the hard work and dedication of the students and their mentors. Graduate students play a crucial role in the AMRPU, mentoring every project and working tirelessly to ensure its success. Alex David Rodriguez, the graduate student mentor for the partial differential equation group, shared his experience: "This is my third year helping out. I'm always excited to tackle research and this year is no exception. I really enjoy learning this material as much as I enjoy the mentoring aspects."

Alex at the board

Alex David Rodriguez helping his group understand new, complicated, research.

The AMRPU has a proven track record of success. Last year's students were able to secure spots in graduate programs at prestigious universities like the University of Kansas and the University of Arizona. This year's cohort is expected to follow in their footsteps. Aliah Sow, a student from Iowa State working on Machine Learning, shared her experience: "This Mathematics REU program has given me great insight into what it would be like to pursue mathematical research as a career. The skills, experiences, and opportunities I have gained from participating in this program have further motivated me to continue studying and pursuing mathematics as a career."

Aliah at the board

Aliah Sow at the board working on her new project.

The AMRPU is funded by the National Science Foundation (NSF), a testament to the quality and impact of the program. The NSF's support enables us to provide this unique opportunity to students from across the country. Grayson Light, who is working on differential geometry, shared his enthusiasm: "Over the past two months, I have had an incredible time here. The work I do in Geometry is motivating and exciting, and the friends I’ve made push me to work hard while also allowing me to develop interpersonal relationships with people in my field."

Grayson and Diego at the board

Grayson Light and Diego Castro Estrada being enthralled by the world of Differential Geometry

The AMRPU is more than just a research program; it's a transformative experience that shapes the future of its participants. As Beckett Sanchez, an FIU student in Alex David Rodriguez's group, put it: "I am incredibly passionate about the REU program and the opportunities it has provided me. The program has not only allowed me to explore my interests but has also deepened my love for the subject and motivated me to pursue further academic and professional achievements in the field."

Beckett Sanchez becoming the next great mathematician.

Beckett Sanchez becoming one of the best mathematicians of the near future.

 As we near the culmination of this year's Applied Mathematics Research Program for Undergraduates, the excitement builds for the final symposium on July 28th. This event is not just a showcase of the students' research, but a celebration of their journey, their perseverance, and their intellectual growth. It's a gathering of minds where students, mentors, and faculty come together to engage in insightful discussions, share perspectives, and provide constructive feedback, further enriching the learning experience.

The symposium also serves as a platform for students to demonstrate their communication and presentation skills, honed over the course of the program. It's not merely the end of the program, but the beginning of a new chapter in their academic journey. The knowledge, skills, relationships, and experiences gained will serve as a strong foundation for their future pursuits. As we look forward to the symposium, we are filled with pride for our students and gratitude for the opportunity to contribute to their journey in the fascinating world of mathematics.

We also want to shout out Alejandro, Bernie, Kizzy, and Katherine for their assistance during the program!

Update: Some of our members have been presenting research done at the REU at regional and national conferences and we are very proud of their continuing work.

Grayson Light standing in front of a projected slide at a conference in Dayton Ohio.