Arnav Kumar

	Link Target
Internal	External
Content Author	Me	[Square]	{Curly}
Other	-	(Round)

Interesting Sites

Mathematics

(Projective Geometric Algebra) Webpage that links to (conformal) and (rigid) algebra wikis
(Art of Problem Solving) Competition problem archive, and wiki
(Proofs without words) Cool visual proofs
(Geometry Problems from IMO) Olympiad geometry problems
(Canada IMO training) Links and resources for IMO training
(Cut the Knot) A large number of mathematical puzzles

Computer Science

(Teach Yourself CS) Book and course recommendations for computer science
(pure sh bible) and (pure bash bible) Pure shell code instead of external process invokation
(Build Your Own X) Learn to build a regex engine, OS, text editor, and much more
(The Herbie Project) Restructure floating point operations to reduce inaccuracy
(Marc Ten Bosch) 4D graphics via publications and blogs
(The blog at the bottom of the sea) Graphics, gamedev, computation, audio synthesis
(Cem Yuksel) Graphics research and teaching
(Eric Lengyel) Game engines, geometric algebra, and rendering

Search Engines

(Qwant) Private search engine with independent search indexing
(wiby.me) Search engine for personalized webpages and sites for hobbyists
(searXNG) Free metasearch engine (accumulates results from multiple engines)

Games

(Puzzle Games) Galaxies, Hashi, Star Battle, and much more
(Gungi.io) Gungi, if you have a friend to play with

File Sharing

(The Null Pointer) Temporary file hosting
(Litterbox) Temporary file storage (≤ 1GB)
(Catbox) Permanent file storage (≤ 200MB)

Miscellanous

(Luke Smith's Webpage) Philosophy, unix, and linguistics
(Lospec) Colour palettes and pixel art
(Anime Girls Holding Programming Books) A Github repository of such images
(Owls in Towels) A site dedicated to owls in towels
(sadgirl.online) Guides on how to bypass paywalls and surf the web

Publications

The Dimension of Sparse Random Graph Orders

(presentation) {arXiv preprint} May 2024 - Aug 2024

Coauthored paper during undergraduate research assistantship under professor Jane Gao

Projects

WIP - 4D Raytracing Pathtracer

| C++ [devlog] July 2025

Final project for the CS 488 graphics course at the University of Waterloo

Rigid-body Particle Simulation

| C++ [gif] [gif] July 2025

Created for the CS 488 graphics course at the University of Waterloo
Simulated gravity, spherical constraints, and collision physics for rigid body particles

Software Rasterizer

| C++ [png] [png] June 2025

Created for the CS 488 graphics course at the University of Waterloo
Recreated the whole rasterization process on the CPU, including perspective transformation, triangle rasterization, depth buffering, and perspective correct interpolation

Software Raytracer

| C++ [png] [png] [png] [png] May 2025 - June 2025

Created for the CS 488 graphics course at the University of Waterloo
Implemented the Möller–Trumbore algorithm for fast ray-triangle intersection
Programmed Lambertian diffuse, specular refraction, and specular reflection behaviour, and support for spherical environment mapping

Software Raycaster

| JavaScript [web] {Github} Sep 2024 - Oct 2024

Implemented a software based raycasting algorithm with vanilla JavaScript where parameters and the scene can be manipulated

Renovating the Labyrinth

| JavaScript [web] {itch.io} {Github} Oct 2024

Solo submission made in 72 hours with vanilla JavaScript on an HTML canvas for the UW Game Dev Club's fall 2024 game jam; voted winner of the technical achievement award
Built a real time optimized ray caster with ordered Bayer matrix dithering
Programmed 2D rigid body collision behaviour and a randomized Prim's algorithm for map generation

Bloom

| Godot {itch.io} {Github} May 2024 - Jun 2024

Team submission made in 72 hours with Godot for the UW Game Dev Club's spring 2024 game jam
Implemented colour mixing, screen wrapping, movement, and flower spawning mechanics

Interplanetary File Explorer

| Go, Python, JavaScript {web} {Github} {Devpost} Jan 2023

Visual file explorer of an IPFS written in Golang, Python, and JavaScript for the 2023 UofTHacks X hackathon; winner of the Estuary sponsor prize
Created vector embeddings for files in the Estuary IPFS using Co:here’s NLP embeddings on file headers
Performed principal component analysis of the vector embeddings to reduce dimensionality and be displayed interactively in 3D space with Three.js

Prognosing IPF

| Python [CWSF paper] Dec 2020 - Jun 2021

Several machine learning models written to predict the deterioration of the condition of the lungs over time for patients of Idiopathic Pulmonary Fibrosis (IPF) and give a level of confidence in the prediction
Implemented an auto-encoder, linear regression, dense neural network, and bayesian model in order to accurately predict future lung capacity and give a confidence value using initial lung capacity data, age, sex, smoking status, and more
Obtained a Laplace Log Likelihood score of −6.9 (much better than the baseline −8.1) with σ ≈ 200mL

Presentations

Dimension of Posets and Random Graph Orders

@ University of Waterloo 1^st Aug 2024

Presentation of work completed during research term under Jane Gao

Streams and Lazy Evaluation

@ Webber Academy Programming Club [notes] 13^th Oct 2023

An introduction to simulating infinite lists with streams and their manipulation

On the Catalan Numbers

@ Webber Academy Math Society [notes] 11^th Oct 2023

A derivation of the closed formula for the Catalan Numbers and examples of well known problems where the Catalan Numbers appear

Introductory Combinatory Logic

@ Webber Academy Math Society 11^th Oct 2022

Introduction to combinatory logic; showing numbers and operations on numbers can be expressed as combinators

Lectures & Lessons

High School Math Competition Lessons

Summer 2023

[divisibilty tricks] Divisibility, modular arithmetic, and deriving divisibility tricks
[writing solutions] Tips for writing readable proofs
[pigeonhole principle] The pigeonhole and generalized pigeonhole principles
[series and products] Telescoping series, common series, and term grouping strategies
[intro geometry] Basic triangle facts, and effects of transformations on geometric objects
[number bases & induction] Number bases, (strong) induction, and an example from the KJMO
[points in a triangle] Involving (circum|in|ex|ortho)centers and centroids
[cyclic quadrilaterals] Power of a point, Ptolemy's theorem, and Brahmagupta's formula

Formal Education

Waterloo Undergraduate Degree

: Bachelors of Computer Science

Term	Courses
F ’22	MATH 145	MATH 147	CS 145	ENGL 109	PHYS 121
W ’23	MATH 146	MATH 148	CS 146	CS 136L	ENGL 108B	PHYS 122	PD 1
S ’23	COOP 1	PD 11
F ’23	MATH 245	MATH 247	STAT 240	CS 245E	CS 246E
W ’24	MATH 249	STAT 241	CO 255	CS 240	CS 241
S ’24	COOP 2	PD 10	CS 251
F ’24	CS 350	CS 341	CS 370	PHYS 256	FINE 100
W ’25	COOP 3	PD 6
S ’25	CS 475	CS 480	CS 488

Academic Self-Learning

I am still going through entries ending with &.

Operating Systems

Operating Systems: Three Easy Pieces by Remzi H. and Andrea C. Arpaci-Dusseau (book)

Formal Logic & Programming Theory

The Symmetric Interaction Calculus by Victor Maia (article)
Concurrency in Go by Katherine Cox-Buday [notes]
To Mock a Mockingbird by Raymond Smullyan
Learn You a Haskell for Great Good! by Miran Lipovača (book)

Machine Learning, Probability, & Statistics

Essential Statistics for Data Science by Mu Zhu

Geometry & Graphics

Projective Geometric Algebra Illuminated by Eric Lengyel &
Ray Tracing in One Weekend by Peter Shirley, Trevor David Black, Steve Hollasch (book)
Computer Graphics from Scratch by Gabriel Gambetta (book)
University of Utah CS 4600 (lectures) (assignments)
Raycasting Series by Lode Vandevenne (lesson)