Counting With Groups

Group theory is a key component of abstract algebra, and it turns out that abstract algebra is useful in solving many real life problems such as detecting errors in codes, figuring out puzzles, and performing card tricks. Our study focuses on how group theory can help solve counting problems. We will present Burnside's Counting Theorem and the unweighted version of Polya's Enumeration Theorem and show how they can be used to streamline the process of solving coloring problems, and problems that involve multi-sets.