The University of Central Florida, Department of Mathematics:
Research Experience for Undergraduates in Applied and Computational Mathematics for Summer 2025
Principle Investigator (PI): Dr. Katiuscia Teixeira
Faculty Mentors: Dr. Carlos Borges, Dr. Yukun Li, Dr. Zhisheng Shuai, Prof. S. Roy Choudhury, Prof. Kuppalapalle Vajravelu
Program Dates: May 19 to July 25, 2025
Application Deadline: February 14, 2025 at 11:59 PM
Award Notification: March 7, 2025
The Research Experience for Undergraduates (REU) in Applied and Computational Mathematics (ACM) 2025 program is a 10-week intensive program that actively engages undergraduate students in research-based theory and applications of mathematical technologies supporting new solutions to interdisciplinary problems.
The program will be held in person from May 19 through July 25, 2025 at the University of Central Florida, located in Orlando, Florida.
Students will work full-time on their individual or in group research projects during the summer semester. The research projects aim to address important questions in applied partial differential equations, computational mathematics, financial engineering, and mathematics biology.
The REU participants’ activities will include short courses on math contents and software, weekly research group meetings, seminars on ethics, discrimination and harassment, career opportunities, and preparation for graduate school, and social events.
Application Requirements
The student application packet consists of the completion of an online form and the submission of
- CV/Resume
- Unofficial Transcripts
- Letter of interest
- Contact information for two people who can provide a Letter of Recommendation for you (email is sufficient)
Eligibility
The program is open to
- U.S. Citizens or permanent residents of the United States;
- Sophomores, juniors, and seniors majoring in
- Pure or applied mathematics,
- Physics
- Computer sciences
- Engineering
- GPA of 2.7 or above;
- Successfully completed Calculus II;
Applications from women and underrepresented minority students are strongly encouraged.
Stipend and Commitment
Each student will receive:
- $6,000 for the summer
- Small food allowance
- On-campus housing
- Students must be willing to live in group housing. For more information, please visit the UCF Housing website.
Faculty Mentors and Research Areas
Project 1: Computational Mathematics
Faculty Mentor:
Dr. Carlos Borges
His research focuses on computational methods for inverse problems. In the Summer of 2025, REU students will be working on projects related to the modeling and development of fast and accurate solvers for the solution of forward and inverse scattering problems.
Project 2: Financial Mathematics
Faculty Mentor:
Dr. Yukun Li
His research revolves around computational finance. In the summer of 2025, REU students will be working on projects related to derivative pricing models based on the PDE approach and the data approach. This project will equip the students with machine learning skills including how to design supervised and unsupervised learning algorithms, how to pre-process and post-process the datasets, how to clean and prepare training sets, how to improve the accuracy of the algorithms, and so on.
Project 3: Mathematical Biology
Faculty Mentor:
Dr. Zhisheng Shuai
His research focuses on mathematical ecology and epidemiology. In the summer of 2025, REU students will be working on projects related to mathematical modeling and control of infectious diseases. Students will learn mathematical approaches and techniques to analyze the disease models, including the derivation of the basic reproduction number, final size relation or stability analysis of disease- free and endemic equilibria, and assessment of disease control strategies.
Project 4: Nonlinear Systems
Faculty Mentor:
Prof. S. Roy Choudhury
His research focuses on nonlinear systems. In the summer of 2025, REU students will be working on projects related to bifurcations and chaos control in systems with fractional response functions, and incorporating prey vigilance.
Project 5: Applied Ordinary and Partial Differential Equations
Faculty Mentor:
Prof. Kuppalapalle Vajravelu
Prof. Vajravelu has been actively engaged in research in the areas of Applied Mathematics, Ordinary and Partial Differential Equations, Fluid Mechanics, and Numerical Heat Transfer. Several students did Undergraduate Research with him and got NSF fellowships to do Ph. D. In the summer of 2025, REU students will be working on projects related to convective heat transfer in nanofluids and biofluids with activation energy and gyrotactic microorganisms.
2024 Participants & Projects
Title: Optimal design problems with cost function: regularity, uniqueness, and free boundary analysis
REU Students: Saja Gherri – University of Michigan, Ann Arbor
Andrew Hale – University of Minnesota, Twin Cities
Faculty Mentor: Prof. Eduardo Teixeira
Title: Accelerating the Iterative Solution of the Forward Medium Scattering Problem
REU Students: Celine Gordon – Spelman College
James Young – Florida Polytechnic University
Faculty Mentor: Dr. Carlos Borges
Title: Forward Scattering for Thin Coated Domains: Numerical Solution Using Generalized Impedance Boundary Condition
REU Students: Josh Briley– Florida State University
Abigail Lin – University of Florida
Faculty Mentor: Dr. Carlos Borges
Title: Financial Mathematics: Derivative Pricing for Financial Derivatives
REU Students: Adam Serota – Skidmore College .
Faculty Mentor: Dr. Yukun Li
Title: Investigating the Dimensional Effects on Thomas Cyclic Systems
REU Students: Mai Ellington – University of Alabama at Birmingham
Taylore Keesler – University of Central Florida
Faculty Mentor: Dr. Zhisheng Shuai
Summer 2024 Schedule
Download the Summer 2024 Schedule2023 Participants & Projects
Project 1: Distance Problems in IRn
Faculty Mentor: Prof. Eduardo Teixeira
REU Students: Jacob Shaw – Clemson University
Ngoc Tram Nguyen – University of California, Los Angeles
Maximo Fernandez – University of Central Florida
Project 2: Curriculum Learning for Inverse Scattering
Faculty Mentor: Dr. Carlos Borges
REU Students: Mikayla Fischer – University of Central Florida
Nickolas Arustamyan – University of Florida
Megan Carlson – University of Central Florida
Project 3: Theory and Applications of Pricing Financial Derivatives
Faculty Mentor: Dr. Yukun Li
REU Students: Anupama Hazarika – University of Arizona,
Alsion Tafa – University of Central Florida
Yiyuan Zhang – University of Florida
Project 4: Global Dynamics of an SIR Model with Post-Infection Mortality and Partial Immunity
Faculty Mentor: Dr. Zhisheng Shuai
REU Students: Brendan Shrader – University of Central Florida
Malcolm Griffith – University of Central Florida
Summer 2023 Schedule
Download the Summer 2023 ScheduleFor more information or any questions please contact the Principle Investigator, Dr. Katiuscia Teixeira at Katiuscia.Teixeira@ucf.edu.
