Overview
We emphasize project-based learning at the intersection of applied mathematics, data science, and mathematical modeling. Students learn by working on real research questions that connect theory, data, and decision-making in public health and healthcare systems. Our approach integrates classroom instruction with research practice, allowing students to develop technical skills while contributing to ongoing lab projects.
Project-Based Learning
Students in the courses and research groups learn by building models, analyzing data, and evaluating interventions. Emphasis is placed on:
- Problem formulation: translating real-world questions into mathematical or data-driven models
- Data analysis: working with real datasets, uncertainty, and incomplete information
- Model implementation: simulation, estimation, and validation
- Interpretation: understanding model assumptions, limitations, and policy relevance
- Communication: writing, visualization, and presentation of results
Student Mentorship & Research Training
The lab provides mentorship opportunities for undergraduate and graduate students with interests in applied mathematics, data science, and modeling. Students work closely with the PI (Dr. Majid Bani-Yaghoub) and lab members in a collaborative environment and are encouraged to take increasing ownership of their projects.
We welcome students at different stages of training. Prior research experience is helpful but not required. Curiosity, commitment, and willingness to learn are essential.
Students may participate through (1) course-based research projects offered in a variety of courses, such as Data-Driven Modeling (Math 401) and Mathematical Methods Data Science (Math 5545), (2) Undergraduate research experiences, (3) Graduate thesis or dissertation research or (4) Independent study (Math 5590)
How to Get Involved
Students interested in joining a project are encouraged to reach out to Dr. Bani via email. Please include:
- A brief description of your academic background and interests
- The types of problems or methods you would like to work on
- Your current program and year
Basic Computational Resources
Below are a few sets of codes written in MATLAB.
A) Codes for Simple Disease Models
B) Codes for Simple Population Models
Sample Simulation: Dynamics of the Lorenz System
The Lorenz system is a set of three ordinary differential equations, first developed by the meteorologist Edward Lorenz while studying atmospheric convection:
See section 4.5 of the book "Differential Equations and Dynamical Systems" by Lawrence Perko , 3rd edition
For µ > 1 there are two critical points which bifurcate from the origin. The homoclinic loop occurs in the Lorenz system at the bifurcation value μ near 13.926
A symmetric pair of unstable periodic orbits results from the homoclinic loop bifurcation at μ =13.926. Some periodic orbits in the one-parameter family of periodic orbits are generated by the subcritical Hopf bifurcation at one of the nontrivial steady states. The bifurcation value is μ = 24.74.
Near the bifurcation point μ = 24.74, the Lorenz system has a strange attractor. More precisely, this strange attractor appears at μ= 24.06.
A stable, nonsymmetric, periodic orbit born in a period-doubling bifurcation at μ = 148. The period-doubling cascade that occur in the Lorenz system for 145 <μ <167.
Additional Simulations
Delayed PDE Modeling and Simulations (Part 1)