Research Experiences for Undergraduates (REU)

This REU program, running from May 18th to July 11th, 2025, will provide undergraduate students with an engaging collaborative research experience in broad areas of Applied Mathematics, including Financial Mathematics, Biomathematics, Mathematical Fluid Dynamics, and Geophysics. 

Students will be prepared for their research through an intensive workshop on computing with MATLAB. Students will also participate in a workshop on mathematical writing using LaTeX. They will receive instruction on delivering effective presentations, preparing posters, and writing research papers. Students will have the opportunity to disseminate their research findings through presentations at mathematics and interdisciplinary conferences, as well as publication in open-access journals. The REU program will also provide guidance on the graduate school application process.

Mentors list and projects’ descriptions :

Project #1. Arash Fahim "Applications of power series and differential equation in stochastic modeling"

Differential equations are now the backbone of stochastic modeling in economics and in financial risk management. In some applications, we shall solve them numerically, while in others we require to solve them in closed-from. In this project, students apply their knowledge of ordinary differential equations to find closed form solutions for the ordinary differential equations. Then, they use the solution to infer conclusions about a problem that is modeled by the differential equation.  No knowledge of economics or finance is required for this project. The main requirement is the understanding of power series from univariate calculus, ordinary differential equations, and other basic knowledge of univariate and multivariate calculus.

Project #2. Bhargav Karamched "Lattice Models for Describing Competing Ant"

This project focuses on developing a stochastic lattice model to describe the dynamics of ant species competing for food. The model will simulate how far ants are willing to travel for food, considering the potential risk of encountering an enemy species that could compromise their nest location. Students will simulate ant movement by implementing finite difference numerical methods to solve the mean field model. The model will incorporate factors such as pheromone production, ant diffusion, and inter-species battles to understand the complex foraging behavior of ants. Students will learn to formulate, analyze, and interpret the model in the context of ants, gaining insights into how groups of individuals can interact to efficiently perform a group task. No prior knowledge of PDEs or stochastics is required for this project.

Project #3. Malbor Asllani "Pattern Formation in Complex Networks"

This project delves into the fascinating phenomenon of pattern formation in complex networks, which are used to represent various systems, from neural networks and gene regulation to social media interactions. Pattern formation in such networks is mathematically modeled using reaction-diffusion systems, which describe how entities interact and diffuse over the network. These systems utilize discrete structures like the graph Laplacian, transforming the equations into coupled ordinary differential equations (ODEs). Students will investigate these ODEs by employing linear stability analysis to identify equilibrium points and understand how small perturbations evolve. This analysis reveals whether patterns form and connects the dynamics of the system with the network structure through a mathematical tool called the Master Stability Function. Students will utilize numerical methods, such as the Euler scheme, to simulate the system on networks and compare the results to theoretical predictions.

Project #4. Aseel Farhat, Sanghyun Lee "Data Assimilation and Parameter Prediction Algorithms for Subsurface Flows and simplified models in Fluid Dynamics"

This project focuses on developing data assimilation and parameter prediction algorithms for subsurface flows and simplified models in fluid dynamics. The project will involve exploring various aspects of modeling for subsurface flow, conducting stability and existence analyses for these systems, and developing numerical approximation and solution algorithms. Students will also be introduced to finite difference methods for numerical simulations and programming in Matlab or Python. The project will also involve testing the developed numerical algorithms on toy models in fluid mechanics, such as the viscous 1D viscous Burgers equation, the Lorenz system, and shell models of turbulence.

Eligibility:

• NSF-funded applicants must be US citizens or permanent residents. 

• REU applicants must be without a bachelor's degree, preferably in their second or third year in the major, and the bachelor degree will not be awarded before the end of the REU program. 

• REU applicants must have completed the Calculus series, Linear Algebra, and Ordinary Differential Equations (ODEs) with a grade of B or higher in these courses at their institution.

• Applications from women and underrepresented groups are strongly encouraged.

Stipend: 

Each participant will receive $675 per week during the 8-weeks summer program, that is $5,400 for the period of the program. 

Lodging, meals, and travel expenses: 

Participants will receive free accommodations in on-campus furnished shared apartments within walking distance to the Mathematics Department, dining halls, and restaurants and shopping centers in Tallahassee.

Each participant will be provided with $500 towards their on-campus meal plan during the summer program.

     Each participant will receive reimbursement for up to $500 for travel expenses to and from the summer program.

When should you apply the REU?

The application deadline is March 31, 2025 (extended to April 4, 2025). 

How to apply to REU? 

Each applicant must upload the following documents:

• • • • Curriculum Vitae

      • An unofficial transcript

      • A cover letter including a personal statement expressing your interest in the program and listing at least two projects of interest, numbered by preference

      • At least one reference letter

Apply online at https://www.mathprograms.org/db/programs/1769. Application review begins March 31, 2025, with decisions sent by mid-April. The program starts May 18, 2025.

[Please note that the site mathprograms.org is currently unavailable and being restored. Please monitor our website for possible deadline changes based on the site's status. Update: mathprograms.org is active as of 03/28/2025. The deadline has been extended to 04/04/2025.]

About Florida State University:

Florida State University is one of two flagship research universities in the State University System of Florida, with its main campus in Tallahassee serving over 40,000 students. Tallahassee, located in North Florida, has a population of approximately 190,000. It is adjacent to the Apalachicola National Forest and about twenty-five miles from the Gulf of Mexico, providing easy access to pristine beaches and natural habitats. The city enjoys a warm climate, with an average annual high temperature of 80 degrees Fahrenheit and an average annual low of 56 degrees Fahrenheit. 

The Department of Mathematics at Florida State University is a vibrant hub for mathematical research and education, offering a supportive environment for students and faculty to excel in both theoretical and applied mathematics.The department's commitment to research is evident in its diverse range of research areas, including algebra, analysis, topology, combinatorics, differential equations, computational mathematics, data science, and mathematical biology. The department provides a comprehensive curriculum with various undergraduate and graduate programs, preparing students for successful careers in academia, industry, and government.

Recommendation of how to get to Tallahassee: 

Tallahassee, Florida is accessible by various modes of travel.  Tallahassee International Airport (TLH) offers direct flights to and from several major cities, including Miami, FL, Atlanta, GA, Charlotte, NC, and Dallas, TX. If a direct flight is not available, travelers can also fly to nearby airports in Jacksonville (2.5 hours drive) or Orlando (4 hours drive) and rent a car or take ground transportation to Tallahassee. 

For those who prefer driving, the city is located on major highways like I-10 and I-75. Once you've arrived, getting around Tallahassee is easy with options like taxis, ride-sharing services, and public transportation.

Contact information:

If you have any questions or need more information, please contact afarhat@fsu.edu.