Student Research

National Research Experience for Undergraduates Program at �鶹��Ƶ (NREUP 2022)

NREUP 2022 was sponsored by the Mathematical Association of America (MAA) to provide students with research experience in Applied Mathematics. Students worked collaboratively together in groups under the supervision of their mentors on an active mathematics research problem.

In Summer 2022, students developed and explored specialized techniques called nonstandard finite differences to produce numerical solutions to ordinary differential equations. Since there are very few instances in which closed-form analytical solutions for ODEs and PDEs can be found, we used these numerical analytical techniques to produce accurate approximations to solutions of problems derived from real-world mathematical models.

List of participants:

• Alexis Guevara (Oxy)
• Alex Gutierrez-Diaz (California State University, Los Angeles)
• Amelia Threatt (Oxy)
• Johnny Sierra (California State University, Los Angeles)

Research Products

REU 2022 Oral Presentation:

• “Numerical Investigations of Nonlinear First-Order Ordinary Differential Equations” (August 3, 2022, Summer Research Program Conference)

Research Experiences for Undergraduates 2021 (REU 2021)

In Summer 2021, a NSF-sponsored REU was hosted by �鶹��Ƶ virtually by Zoom. The faculty involved in the program were Jim Brown and Treena Basu. Research topics were coding theory and numerical analysis. Please see more information about REU 2021 here.

List of participants:

• Livia Betti (University of Rochester)
• Zaheer Coovadia (Boston College)
• Mayra Diaz (Heritage University)
• Fernando Gaitan (Wesleyan University)
• David Iniguez (California State Polytechnic University, Pomona)
• Alexandra Scott (Tufts University)
• Aiyana Spear (Wellesley College)
• Japheth Varlack (Lee University)

Research Products:

REU 2021 Oral Presentations:

• Coding Theory group: From Codes to Lattices over Real Quadratic Fields: The Comparison of Associated Theta Functions
• Numerical Analysis group: Unity Approximations in the Construction of NSFD Schemes for 1st Order and Systems of ODEs

REU 2021 Written Presentations:

• Coding Theory Group: Lattices in real quadratic fields and associated theta series arising from codes over ${\bf F}_{r}$ and ${\bf F}_2 \times {\bf F}_2$.
• Numerical Analysis group: Unity Approximations in the Construction of NSFD Schemes for 1st Order ODEs and Systems of ODEs

REU 2021 Publications:

• J. Brown, L. Betti, F. Gaitan, A. Spear, J. Varlack, Lattices in real quadratic fields and associated theta series arising from codes over F₄ and F₂ × F₂, Designs, Codes and Cryptography, 2023, https://doi.org/10.1007/s10623-023-01258-w.

Research Experiences for Undergraduates 2020 (REU 2020)

In Summer 2020, a NSF-sponsored REU was hosted by �鶹��Ƶ virtually by Zoom. The faculty involved in the program were Jim Brown, Treena Basu and Eric Sundberg. Research topics were data science, number theory, and positional game theory. Please see more information about REU 2020 here.

List of participants:

• Jessica Rae Booher (Westminster College)
• Victor Cho (Cypress College)
• Justine Dell (Haverford College)
• Merrick Hua (Arcadia High School)
• Hanna Noelle Griesbach (Elon University)
• Amanda Hernandez (Rice University)
• Matthew Mena (El Camino College)
• Hannah Sheats (St. Andrews College)
• Ann Thompson (University of Texas - Austin)
• Sireesh Vinnakota (Pomona College)

Research Products:

REU 2020 Oral Presentations:

• Data Science group: Utilizing Machine Learning to Predict Student College Decisions
• Number Theory group: Eigenform product identities of genus two Siegel modular forms of general congruence level
• Positional Game Theory group: Extremal Hypergraphs for the Erdos-Selfridge Theorem

REU 2020 Written Presentations:

• Data Science group: Utilizing Machine Learning to Predict Student College Decisions
• Number Theory group: Eigenform product identities of genus two Siegel modular forms of general congruence level
• Positional Game Theory group: Extremal Hypergraphs for the Erdos-Selfridge Theorem

REU 2020 Publications:

• J. Brown, J. Dell, H. Griesbach, and A. Hernandez, Eigenform Product Identities of Genus Two Siegel Modular Forms of General Congruence Level, International Journal of Number Theory, (to appear.)