What to Expect if You're Expecting (Which You Shouldn't)
So, I lied. I'm not a grad student yet. I'm close, though! As long as I don't fail out of undergrad this semester a I am good to go. I've even started doing stuff for my future boss so it would be super awkward if I came up to him and was like "hey, buddy, uh, turns out I'm a failure, k thanx bye."
But in any case, all that means for this blog is that it is not going to be as advanced as some of the super cool math sites I've seen on Neocities. Gosh, I super admire people like holeinmyheart making top tier high-level math proof humor or beedge making super cool coding tutorials, and I hope I get there someday, but, uh, this website (at least at first), is probably going to be closer to undergraduate-level math tutorials. Because that's what I can do. And I intend to do it well.
In any case here are some of the things that will probably come up:
- Basic Fluid Simulation: I'm currently doing a project to create a super simple Incompressible Navier-Stokes equation solver, so those will probably be the first entries into the "Math Animations" page. It'll include code and everything so that someone can download it and follow along
- Bayesian Inference: This is what I'm planning on going into Grad School for. I got hooked up with a Biophysics lab that does physics-based machine learning stuff (i.e. not black box, stick in data and let it make it's own brain kind of machine learning) and a lot of it is Bayesian Analysis and computational statistics. It was rough to get through a lot of the material as an undergrad, but what really got me was how finnicky the Monte-Carlo Markov Chain software was to debug. So at some point I want to write up a document with something along the lines of "An Undergrad's Guide to Writing and Debugging a MCMC Sampler" so that I don't forget all the weird quirks-in-the-machine I've learned. This will be in the "Writing and Tutorials" section
- (Re)Learning more Coding Languages: I've learned a lot of languages, but recently I've only used MATLAB, which is obviously not very practical if I want to share my work with anyone. Eventually I want to refresh myself on Python, C++, and Fortran (for data analysis stuff), but I'll also have to learn about MATLAB parallelization and GUI making. Stuff about this stuff will probably show up in the "Blog" section, "Writing and Tutorials" section if I end up making something good, or the "Animation" section if I use making animations as a way to practice a language.
- I love theory. I would never want to do theory for a living, because that sounds really hard, but I love learning about theory and applying it. So over time, I want to go through all the stuff they don't teach you in public university undergrad and learn it thoroughly. I don't know where to start, but I know that I have pretty big gaps in
- Real Analysis: esp. integration, Lebesque Integration, measure theory, multivariable calculus
- Complex Analysis: Never taken it in my life
- Probability: The formal structure, stochastic processes, proving that sampling processes recover identical statistics to the original distribution
- Numerical Analysis: They actually teach this pretty well, but I could use more practice with 2D and up stuff, I don't think I could do it off the top of my head.
- Chaos: Chaos is cool, and it might become relevant later, since I'm looking at molecular systems.
- Polynomials: I have not learned anything deep about these
- Topology: Never taken it
- Differential Geometry: Took a very basic class. We ended up only talking about differential geometry in very specific cases, and didn't formally define things like manifolds and stuff. Should come back and relearn that stuff rigorously
- Group Theory: I only vaguely know what group theory is. It would be useful to learn some basic theorems and such