I am committed to fostering inclusion and belonging within a diverse learning environment, where each student’s unique background and perspective is respected and valued as an integral part of our educational journey. By creating a classroom atmosphere that emphasizes mutual respect, active engagement, and the celebration of different viewpoints, I aim to empower students to see themselves as capable contributors to their academic and professional fields. I believe that learning flourishes when students feel seen and supported, and I strive to ensure every individual has the opportunity to grow, thrive, and succeed in an equitable and supportive setting.
Colorado School of Mines
Linear Algebra (Spring 2021, Fall 2024, Spring 2025)
Introduction to Scientific Computing (Fall 2020, Fall 2022)
Calculus III (Fall 2019)
Calculus II (Spring 2019, Spring 2020)
Calculus I (Fall 2021)
Red Rocks Community College
Calculus III (Fall 2023)
Calculus I (Fall 2022, Spring 2023, Summer 2023)
College Trigonometry (Fall 2022, Spring 2023)
College Algebra (Fall 2022, Spring 2023)
University of Colorado at Denver
Calculus III (online course, Spring 2020)
Calculus II (Spring 2019, Fall 2019)
College Algebra for Business (Spring 2019)
Mathematics for Liberal Arts Majors (Fall 2018)
University of Colorado at Colorado Springs
Precalculus (Fall 2016, Spring 2017, Summer 2017)
Calculus for Business (Fall 2017, Spring 2018)
Course Description
The beta cells of the pancreas produce and secrete insulin, the primary hormone in managing the body’s glucose levels, for instance after a snack or meal. This interdisciplinary course utilizes differential equations, stochastic processes, and simulation in MATLAB to explore the mathematics behind beta cells and insulin in the human body. Using the Hodgkin-Huxley neuron model as a starting point, students will learn how beta-cell and insulin models have been developed and implemented. We will employ a combination of analytic and computational tools from mathematics and statistics throughout the course. Students will be expected to critically analyze research results in published literature and place them in the context of the background developed in class. The course will culminate in a project that provides students the opportunity to study and present a topic not addressed in class, such as a new model or research question. Prerequisites: Intro to Differential Equations, Intro to Linear Algebra. Prior programming experience, especially scientific computing/numerical analysis, recommended but not required.
Course-Level Learning Outcomes
Discern the qualitative properties of differential neuroendocrine models by constructing and analyzing phase diagrams to explain how fundamental assumptions and parameter values affect modeled system behavior
Simulate oscillations in the membrane potential of beta cells by numerically solving differential beta-cell models in MATLAB (or other computing language) to relate physiologically inspired modeling choices to resultant model-based dynamics
Explore mathematical conditions wherein differential neuroendocrine-cell models exhibit behaviors such as spiking and bursting by incorporating additional assumptions into the classical Hodgkin-Huxley neuron model to demonstrate how key dynamics can emerge in neuroendocrine cells
Scrutinize research articles related to course content by employing a systematic approach to reading research to make connections between course content and modern research
Simulate oscillations in plasma insulin acting on various time scales by numerically solving differential insulin concentration models in MATLAB (or other computing language) to relate physiologically inspired modeling choices with their resultant whole-body-level dynamics and compare modeling results to clinical observations
Infer probability distributions for model-derived indices of metabolic health from whole-body-level plasma data by numerically inverting a Bayesian hierarchical model that combines dynamical and statistical assumptions to estimate and quantify uncertainty in clinically relevant quantities that cannot be observed directly
Formulate and investigate a research question related to beta cells through some combination of literature search, numerical simulation, dynamical systems analysis, and data analysis to extend knowledge and experience of neuroendocrine modeling beyond the course content