Work In Progress (WIP) notes ↓

Below are things I'm still cooking up (view them on a computer, and give them a couple seconds to load), i.e. things that are unfinished, not super well documented, and unpolished. Nevertheless, I figured that because there's so much of it, people might find it useful?? Treat the "slides" below more as dense essays/text rather than true, bite-sized presentation aids one might use when giving talks. The goal is to turn them into neat write-ups at some point. Reach out if you want to discuss anything at all!

CGGT Master's Thesis — Interactive Multi-Observer Visualization of Special & General Relativity

CGGT_Master_s_Thesis_2024.pdf

SPRING 2024 — My next topic of study is relativity and differential geometry, for the purposes of creating interesting looking visualizations. For special relativity, I'd like to create visualizations depicting Lorentz transformations in 2D space + 1D time, as well as a separate interactive visualization of the full 3D space + 1D time, with Terrel rotation, Abberation, Doppler Effect, etc. Would it be possible to do path-tracing in such a scenario? And finally, I'd like to understand 3 key line-elements / metrics in GR that are the solutions to Einstein's Field Equations (EFE): (1) The Schwarzchild solution, (2) The Ellis Wormhole (and its modification the DNeg Wormhole), and (3) The Alcubiere Drive. It would be intersting to do interactive simulations of these with temporal effects, where you can quickly use arrowkeys to switch between reference frames to look at the same events through different POVs.

SPRING 2024 — Ever since about highschool, I was sort of "in the dark" when it came to ML. I spent roughly 2 months trying to make sense of the rapidly evolving field the best as I could, and implemented some stuff from scratch too. These slides are wildly unfinished, but as of March 26, 2024, I'm taking a little break from working on them and ML in general. I'll probably make a Khan Academy styled video on how to backprop through various layers in a Transformer at some point, as I learned some important insights there which I couldn't find anywhere else.

Key ML Resources Used:

— Probabilistic Machine Learning books by Kevin P. Murphy

— Deep learning book by Ian Goodfellow et al

— The "Little Book of Deep Learning" (google it)

— Andrej Karpathy's CS231n course + other misc lectures from Stanford, YouTube them!

— This professor's channel: https://www.youtube.com/@deepfoundations5697/featured

— DS1003 and DS1008 courses from NYU. Former's Spring '21 version has free slides + latter's lectures by Yann Lecun are up on YouTube.

— Lots of random internet browsing

FALL 2023 — inspired by the movie Interstellar, I chose my Master's thesis to be on Blackhole rendering. These are some brief slides I made on the history of General Relativity (GR) during the Fall 2023 semester, to kick off my study.

SUMMER 2023 — These are LOTS of notes on a variety of topics relevant to physics based simulation, from the very basics of linear algebra, to lots of numerical techniques for solving linear systems, lots of techniques for solving ODEs, and a basic approach to simulating rigid body collision in 2D.

SUMMER 2023 — Lots of (hard to read 😂) notes on optimization (non-ML) and a little bit of physics.

SUMMER 2023 — Lots of (hard to read 😂) notes on Vector Calculus & Fluid simulation. I was NOT able to code up a working fluid simulator, probably because I was being dumb and storing the velocities at the edges of each gridcell, which might've been overcomplicating things for a first implementation.

SUMMER 2023 — INTRO TO THE FINITE ELEMENT METHOD (my own, unfinished, unpolished notes). I wrote this up during my time as an MIT SGI Research Fellow, and it proved helpful to my project members.

FEM_Self_notes.pdf