Minimum Eligibility

To qualify, applicants must be

• an American University (AU) undergraduate with a declared major in Science, Technology, Engineering, or Mathematics (STEM), or,  
• a rising Senior or Junior in high school who has successfully completed Algebra and Geometry, with a grade of B or better, and who has an interest in the mathematical sciences associated with careers in STEM.

All AU students and local DC, Maryland, and Virginia area high school students with an interest in STEM are encouraged to apply. Preference will be given to applicants who identify with groups historically underrepresented in STEM fields, from high school students who have not participated in a prior research project, and/or, applicants who are Pell Grant Eligible or eligible for a Free or Reduced Lunch Program at their high school.

Dates and Place

The program will run for approximately eight to ten weeks during the Summer of 2025. Exact dates will be chosen by individual mentors. Meetings may be virtual via Zoom or in person as determined by the mentor.

Administrative Requirements

• Access to Computers and Internet: Applicant must have routine access to a tablet or laptop computer that allows them to execute mathematical analysis. They must also have sufficient access to the internet to support their research and potential Zoom teleconferences with their mentor.
• Support Payments: All participants will receive a $2000 student support payment. Note the payment is taxable so participants must submit tax-related paperwork. All participants will receive payment upon completion of the required tax forms.
• Release Forms: Participants must sign a release form so American University has non-exclusive unlimited rights to any materials produced during the experience to include any video recordings of participant presentations. Participants under the age of 18 must have a parent or legal guardian sign the release form.

Applicants will pursue a project from the list below. Participants will investigate real-world phenomena or theoretical challenges using methods and tools from the mathematical sciences and create a poster and/or presentation about their results and experience. Project posters and presentations may be shared with the public.

Projects

1. Exploring linguistics with large language models: While the generative capabilities of large language models have received attention recently, they are really better used for analyzing language. The transformer-with-attention model that underlies modern large language models can be thought of a statistical relaxation of a formal grammar. This project could go in many directions —no familiarity in linguistics or large language models will be assumed --- but will aim toward attempting to understand how common grammar rules are reflected in large language models. 
   Mentor: Dr. Michael Robinson
2. Exploration of programming strategies for puzzle solving: Using online platforms such as Project Euler and Rosalind, students will explore an assortment of various mathematical concepts and programming techniques to expand what they already learned from their introductory programming classes. The ideal candidate for this project is one who loves computer programming as well as pure and applied mathematics. 
   Mentor: Dr. Donna Dietz
3. Portfolio Optimization Using R and {quadprog}: This research explores portfolio optimization using Mean-Variance Optimization, a method derived from Modern Portfolio Theory (MPT) by Harry Markowitz. Utilizing R and the {quadprog} package, we will employ quadratic programming to determine optimal asset allocations that balance risk and return. By computing expected returns, covariance matrices, and solving for efficient portfolios using the solve.QP function, this study aims to provide students with practical insights into financial modeling and quantitative analysis.
   Mentor: Dr. Hamid Semiyari