Session leader: Nicolette Meshkat
Session topic: TBA
We all know about functions, but in this Math Circle we will explore a more general notion of a function, called a relation. Relations are a useful concept because their inverse always exists and when they exhibit three special properties called reflexivity, symmetry, and transitivity, they become equivalence relations. We will explore what it means to be an equivalence relation and what are some useful applications of equivalence relations. In particular, we will look at equivalence classes and examine how these help us categorize our sets into more useful sets. Finally, we will look at one of the most famous uses of equivalence classes: numbers “modulo” a number. This idea is very important in number theory and we will play around with some modular arithmetic.
Nikki Meshkat is a Clare Boothe Luce Assistant Professor in the Department of Mathematics and Computer Science at Santa Clara University. She received her PhD from UCLA in 2011 was a postdoc at North Carolina State University before joining SCU. When not thinking about math, she enjoys running, cooking, skiing, and spending time with her baby and toddler.