In the first part of this talk, I made the case that theory is useful because it allows us to find (or at the very least, have the correct toolkit and language to explore) solutions to real-world problems. In this part, we are going to look at some examples of such problems and develop mathematical language to be able to discuss them more abstractly. I’ve put the term “real-world” in quotes in the title, because I’m going to be talking about these problems in a lot of generality. However, I want to stress that specific instances of these problems are actually relevant in industry, and I think it’ll be easy to see why once I start talking about them.

Here’s another roundup of some interesting things I’ve come across lately and would like to talk about! As always, I’m sure there’s some great stuff I read but cannot for the life of me remember.

This one is extremely late, since I’ve been incredibly busy and finding time to write has been hard. I think I looked at some of this stuff back in… November? October? Oops. I’ve decided I want to keep these to only 4–5 items per post, so more posts should be coming shortly! There are definitely other things I’ve looked at that I want to talk about.

I just finished a blog post where I discuss things I’ve recently learned about how to read research papers. I almost included this as a point in that post, but I think it’s important enough to warrant its own article.

Here’s the idea: you absolutely should not be reading the sections of a research paper in order.

It took me a while to learn this one – I can’t remember if I first read this advice somewhere, if someone told it to me, or if I reverse-engineered it from advice I got about how to write papers. It doesn’t matter which one came first, really – my point is that I only found this out in a roundabout way through googling and trial and error and harassing people with questions.

Last summer, I spent a good chunk of my time doing an undergraduate research project during which I worked on a project largely by myself, under the supervision of a math professor. I then took a graduate level course in a related area this fall, where I investigated the theoretical underpinning behind my summer project. I had no idea what I was doing or what I had gotten myself into. As a result, I learned a lot, and tried to keep note of the various things I had learned. This is the first installment, on what I learned from trying to read math and theoretical CS papers.

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.