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.

You’ve started a new job, you’ve stumbled into a conversation that’s been happening for several decades, and you’re feeling way too lost to even begin to follow what anyone is talking about, let alone participate. You’re confused, so you go see John, who seems to be semi-acquainted with the people having the conversation. You briefly sketch out what (you think) you heard, and tell him that you didn’t really understand anything anyone said.

When you call yourself a “talentless hack” (which you probably don’t, but you might if we share a similar sense of humour), it’s likely for one of two reasons: either you’re caught in a situation where you suddenly have to perform or get results or do something, with zero experience or knowledge of what’s going on (at which point feeling like “a hack” is somewhat legitimate), or you’re doing it out of self-deprecation because you have imposter syndrome.

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.

One of the things I’ve been thinking a lot about lately is the fact that there are two main types of textbooks. There are reference textbooks, which are for people who are already versed in the subject area, typically academic researchers, professors, and the like. They tend to be large, contain massive amounts of information, and be unintelligible to everyone but their target audience. Then, there are expository textbooks, which are for people who actually want to learn things (aka me, a confused undergraduate student).