If you’re a computer science student, you probably had to take an introductory discrete math course at some point. Did you enjoy it? If so, this talk probably isn’t for you, so you can feel free to skip the rest. (Or not – hopefully you feel like you can still learn something from me!) Jokes aside, it’s actually okay not to enjoy your intro to discrete math course: like, personally, I loved mine, but I also completely hated my discrete probability course and would prefer never to see it again. But I pick on discrete math because I feel like if it’s taught well, it can be a turning point for many people, and it certainly was for me.

When I’m trying to approach a highly specialized topic for the first time, one of my tactics is to find a recording of a research-geared workshop about it and watch it as my introductory crash course. The benefits of this are as follows:

• I am learning about the subject from (hopefully) a credible expert in the field.
• Workshops and talks usually try to be self-contained, which means basic background info will likely be given and I won’t have to pore through 10 different research papers, searching for an obscure definition, in vain.
• Talks typically have the benefit of including visuals and informal intuition conveyed by the speaker, which generally won’t make it into academic papers, because they’re not rigorous. However, the visuals and informal statements and intuition are invaluable for gaining a better understanding of the information.
• The speaker will generally include a bibliography and mention related works, which is a great jumping off point for further investigation and saves me from having to figure out what the seminal sources are myself.

However, there are also some drawbacks:

One of my quests during the research project I did last summer was to find a way to simulate pointers in Python, or at the very least, get some sort of named reference-like behaviour from the language. Unfortunately, I quickly learned that this is quasi-impossible, because Python is a language that aims to abstract as many implementation details away from the user as possible, and gives programmers very limited ways in which to interact with the language.

While all NP-hard optimization problems are identical in terms of exact solvability, they may differ wildly from the approximative point of view. If the goal is to obtain an answer that is “good enough”, some problems become much easier (such as KNAPSACK), while others (such as CLIQUE) remain extremely hard.

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.