Search for tag: "illinois geometry lab"

TBA

The goal of this project is to create interactive Mathematica-based visualizations of interesting mathematical topics for use in instruction and outreach activities. This semester we focused on…

An edge-induced vertex coloring is a vertex coloring of a graph that is obtained from an edge coloring via some specific rule. In this project we assign non-empty subsets of {1, 2,..., k} to the…

In this project, we proved that we can write any permutation in the form of product of (n-1,1)*(n-2,1)*(n-3,1)*...* (1,1)$ shuffles , and we are currently exploring how one can define an analogue…

In this project, we studied the Firefighters on Graphs problem. Given a graph G, a fire breaks out at time t = 0. At every subsequent turn, certain vertices are protected, and the fire spreads to…

TBA

Given n strands, a braid is a sequence of crossings in which adjacent strands are passed over or under each other. The braid group, Bn, is the group of all braids on n strands. Given any group G, and…

We study the ratio, in a finite graph, of the sizes of the largest matching in any pair of disjoint matchings with the maximum total number of edges and the largest possible matching.A trivial…

On a Maker-Breaker game there are two players, Maker and Breaker, where Maker wins if they create a specified structure and Breaker wins if they prevent Maker from winning indefinitely. A 3-AP is…

An automated theorem prover is a program that takes as input a statement and proves (or disproves) it. Theorem provers can be very useful: computers are reliable and fast, allowing us to explore…