Graphs can be seen as a way to represent pairwise relationships between objects. With graphs, we have one object type and one relationship type. In one of the most common canonical applications or graph theory, social networking, we are trying to understand and represent social groups using graphs. In that case, our object is people, our pairwise relationship is friendship, and two people have a relationship between them if they are friends.

If you are like me, you did not particularly enjoy math in high school, so the idea of learning an entirely new type of math in university might be terrifying to you. I know this can be scary and overwhelming (it was for me!), so here are some things I learned when taking my first proof-based mathematics course. Hopefully you find this helpful.

Reading through mathematical proofs sometimes feels like trying to understand gibberish while simultaneously trying to unravel where the spontaneous leaps of intuition came from.

Mathematicians definitely spend just as much time throwing around the word “creativity” as people in more conventionally artistic fields.

I was reading a bunch of articles written by math people and noticed this, and then I remembered that the math contests I wrote in high school all had some spiel about expressing creativity on them.

I also found contest math to actually be interesting, despite being pretty disastrous at it (which… most people are too but still). Like I remember once banging my head against some practice problem until someone pointed out a super elegant solution to me and I was like, how does your brain even do that???? I hate the way math is taught in school.