Community Outreach

Uni High Project (June 2019)

I worked with three Uni High students on a month-long research adventure in chip-firing games on graphs. (Poster)



A graph (in the language of combinatorics) is a set of vertices connected by edges. Suppose we have a pile of "chips" on each vertex, and we can transfer chips between vertices given certain rules. This is known as chip-firing. In this project, we will investigate various chip-firing games by asking and answering questions about their behavior. By experimenting with and playing these games, we will make conjectures and hopefully prove our conjectures while learning about mathematical writing and rigor.

Uni High Project (June 2018)

I worked with three Uni High students on a month-long research adventure in graph theory and minimum-distance walks. (Poster)

Suppose a city is made up of islands connected by bridges. The founding problem of graph theory was: Is it possible to walk around the city so that you cross each bridge exactly once, and end up where you started? We could view this city as a graph - a set of vertices (islands) connected by edges (bridges) - and from this point of view, ask when it is possible to walk around the graph, traversing each edge once and only once. This project will explore a generalization of this problem. More particularly, if each edge of a graph is traversed at least once, what is the minimum number of edges that must be repeated? What if we add weights (distances) to the edges, and wish to find the minimum distance route that traverses all edges? We will explore these questions using examples, and prove some of our results. Moreover, we will code some of the algorithms we develop to find these minimum distance routes.

From 2019 to 2020 I was a Writing and Math Partner (WAMP) with the EJP, helping students who are inmates at Danville Correctional Center with their math classes and writing skills. I have also helped run an Algebra Fundamentals workshop during the summer.

From 2018 to 2020, I was the Outreach Committee Chair for the UIUC graduate student chapter of the AWM. Below are some activities I planned or helped plan.

Sonia Math Day

Sonia Math Day is a day-long program for high school girls that introduces them to higher-level math concepts in fun, accessible ways.

"Sonia Math Day allows graduate students to use their passion for mathematics to fuel the same excitement for high school girls, who get to see that mathematics encompasses much more than only what is taught in school."


Adventures in Algebra (Spring 2019)

What if we did arithmetical operations, but without numbers? What do we mean by an "algebraic structure?" Students learn about groups and various hands-on activities with groups.

How can we view hair braiding as a mathematical group? Which braids "undo" each other, and can we find a finite generating set for an infinite group?

What does wallpaper have to do with groups? There are 17 different wallpaper groups, and they can be identified by which transformations of the plane they contain. Which wallpapers belong to which group?

Walks Through Mathematics (Fall 2018)

What is a mathematical walk? What is an Eulerian Circuit, and how can we find them? Explore Hamiltonian paths and the Traveling Salesman Problem.

What is a random walk, and what kinds of probabilities can we study? Where do you end up when walking randomly?

How can we solve mazes on surfaces such as Klein bottles and toruses? Can we solve the utilities problem on a mug?

Knot Theory (Spring 2018)

What is a (mathematical) knot? What are knot diagrams? What makes different knots different?

Math and Magic (Fall 2017)

A two-person mind-reading magic trick: Given any five cards in a standard deck, one person hides a single card and arranges the remaining four to "code" the hidden card. Then the second person, who hasn't been watching, can automatically deduce which card is hidden. The reason this works involves a lot of math, including the pigeonhole principle, modular arithmetic, and permutations.

Girls Engaged in Math and Science (GEMS)

GEMS is a series of weekend workshops for middle school girls that introduce them to higher-level math concepts in fun, accessible ways.

Math and Culture (Spring 2020)

Math and Nature (Spring 2019)

Snow and Symmetry: Why is snow shaped the way it is? Why is symmetry common in nature, and how can we view it from a mathematical perspective? We will make snowflakes in all sorts of different ways and observe their structure.

Crystals and Polyhedra: What is a crystalline structure, and how can we model it? Crystals often come in the form of 3D solids, called polyhedra. How can we understand polyhedra mathematically? We will explore these ideas by making various forms of crystals and learning to argue why mathematical formulas must be true.

Amphibian Population Dynamics:

Frogs are important to ecosystems, but at the same time some of their species are in great risk of extinction. We will play games with dice and coins to simulate frog extinctions from their habitats, and we will use ideas from probability to investigate various extinction factors.

Math Nature Walk: Math is the building blocks of nature. By going out in nature and looking for math in the forest, we will notice and discuss the many ways that numbers, symmetry, and probability appear in the places we least expect it.

Math and Art: Tessellations (Spring 2018)

What is a tiling? What is a tessellation? Which shapes can be tiled evenly? Can we come up with rules to make new, unique tessellating shapes?