Applied Math Peer Mentorship Program, or A(MP)²
Launched in Autumn 2025, the Applied Math Peer Mentorship Program, or A(MP)², is focused on connecting undergraduate students with graduate student mentors to provide support, guidance, and community.
Graduate mentors can share their experiences and advice on applying to graduate school, exploring career options, navigating applied math coursework, succeeding in college, and more.
Undergraduate mentees will have the chance to connect with someone further along in their academic journey, ask questions, and gain insight into both academic and personal aspects of student life in the Department of Applied Mathematics.
Applied Math Peer Mentorship Program Math Project, or A(MP)³
The program has a project-based edition, Applied Math Peer Mentorship Program Math Project, or A(MP)³, which gives undergraduate students the opportunity to work on mathematical research projects designed and facilitated by graduate students.
Graduate mentors will be guided through the project development process by a faculty mentor and get experience guiding their mentee through the project.
Undergraduates will gain research experience and end the quarter by giving a presentation on their experience at the end of the quarter at the A(MP)³ Showcase!
Graduate students Kaitlynn Lilly, Payton Howell, and Laura Thomas started the A(MP)² program with the intention of extending their experience of community in the Department of Applied Mathematics to the undergraduate majors.
Typically, the A(MP)² program is held in the Winter quarter and the project-based A(MP)³ is held during the Spring quarter of a given academic year. Applications are solicited and planning occurs in the preceding quarter (Autumn and Winter, respectively) to ensure participants are able to jump in when the program starts!
Spring 2026 A(MP)³ Projects
Optimization methods for protein-folding.
Description: The goal of this project is to show students how various optimization methods are used to solve large problems. The students used and implemented various deterministic and stochastic gradient descent algorithms, including modern ones (BFGS, Adam) that are used in research and the industry today. We covered a paper on simulated annealing and a paper on the Adam optimizer. Both of those papers are relatively recent, and covering them provided the students with a glimpse into recent research in the field.The students used these optimization methods in the context of protein-folding. We also covered various simplified protein models. The goal here was to show how different algorithms are suited to different tasks and give them some experience wrestling with a less well-defined goal and not straightforward implementations. They generated various simulations (as animations) and other plots, and gave a presentation.
Discovering Dynamical Systems from Data with SINDy.
Description: Whether it is forecasting the next week’s weather, predicting the growth and decline of populations in a complex ecosystem, or describing how traffic flows, elaborating models of the various systems and processes in the real world is a central task of science, and mathematics provides the precise language in which models of the real world can be expressed. While many simple models can be derived from first principles, many real world processes are far more complex, and no models are readily available. What is available to scientists is observational data, which they use to make models–models that allow them to explain how something works, to predict what will happen, to control the outcome of a process. SINDy (Sparse Identification of Nonlinear Dynamics) is an algorithm that takes data of complex systems and creates parsimonious, interpretable models with few assumptions. In our work, we investigate how robust SINDy is to simple noisy perturbations to the observed data, as well as how much time series information is needed relative to the size of the feature library for SINDy to learn canonical dynamical systems.
Exploring methods for single-cell RNA sequencing (scRNA-seq) data to analyze gene expression in mice.
Description: Students will learn to analyze genomic data, specifically single cell RNA sequencing data. They will work with publicly available scRNA-seq data such as the Tabula Muris database, which contains gene expression data from 20 mouse organs, enabling students to explore a variety of biological questions. They will learn about some of the biology of genomics and differential gene expression, and exploratory analysis of genomic data through dimensionality reduction, clustering, as well as how to communicate their findings. Given the explosion in large scale -omics data in biology right now, knowing how to work with such data will be an essential skill for students wishing to pursue careers or research related to biology.
Diffusion-Driven Instability in the Discrete Setting.
Description: In this project, Catherine shows that adding diffusion and advection cannot make a linearly stable steady state of a single ODE linearly unstable, but linear instability can still occur in the discrete setting.