Subject
36 entries
Mathematics
Bookmarks
Dynamic Programming: QuantEcon textbook
QuantEcon's open-source Dynamic Programming textbook teaches the mathematical foundations of sequential decision-making with Python and Julia implementations. Covers Bellman equations, value function iteration, and stochastic control — the tools behind modern RL and macro models alike.
Strange Attractors: dynamical systems visualization
A Three.js particle system visualization of Strange Attractors with a clear explainer on dynamical systems, chaos theory, the butterfly effect, and the geometry of attractors in phase space. Combines technical education with beautiful visual output.
High-Dimensional Data Analysis: Wright & Ma Textbook
John Wright and Yi Ma's graduate textbook on high-dimensional data analysis — sparse models, low-rank models, and deep networks unified under a single mathematical framework. Adopted at Berkeley, Columbia, UIUC, Tsinghua. Published Cambridge University Press 2022.
Greg Egan's Foundations: Physics for SF Readers
Greg Egan's Foundations is a four-part series explaining Special Relativity, General Relativity, Black Holes, and Quantum Mechanics for science fiction readers — accessible with high school math, focused on deriving concrete predictions rather than history or philosophy.
The MoonMath Manual: A Practitioner's Guide to Zero-Knowledge Proof Systems
The MoonMath Manual is a comprehensive, example-driven introduction to zero-knowledge proof systems, covering the mathematics from finite fields through elliptic curves to Groth16 and PLONK. Written to be accessible to practitioners without a cryptography PhD, it became a widely-used self-study resource for the ZK ecosystem.
Linear Algebra — Math for Machine Learning
A YouTube course on linear algebra specifically framed for machine learning — covering vectors, matrices, eigenvalues, and the operations that underlie neural networks. Useful complement to theoretical ML reading when the math intuition is missing.
Why and How zk-SNARK Works
Maksym Petkus provides a pedagogical ground-up explanation of zk-SNARKs, answering not just how they work but why each component exists. Structured to build from first principles with no cryptography prerequisites, making it the standard accessible reference for developers wanting to understand the math behind zkEVM and privacy-preserving protocols.
Pen & Paper Exercises in Machine Learning
Michael Gutmann's (Edinburgh) collection of pen-and-paper exercises covering the mathematical foundations of machine learning — linear algebra, optimization, graphical models, density estimation, and classification. Designed to build mathematical fluency that coding-first courses skip, using derivation rather than implementation as the primary learning mode.
Linear Algebra Done Wrong
Sergei Treil's free textbook on linear algebra, written for mathematically advanced undergrads and deliberately structured around abstract reasoning rather than computational cookbook recipes. The title is a joke — it's done 'wrong' in the sense of prioritizing theory and proof over drill.
An Intuitive Guide to Linear Algebra
BetterExplained's intuitive guide to linear algebra — builds geometric intuition for vectors, matrices, and transformations rather than drilling algebraic procedures. The right starting point before the formal treatment.
Introduction to Probability for Data Science
Introduction to Probability for Data Science by Stanley Chan is a free undergraduate textbook covering probability theory through regression and hypothesis testing, with code examples in Python, R, MATLAB, and Julia. Designed specifically for the data science curriculum rather than pure math.
Relativity: A Modern Primer
A modern introductory treatment of relativity — likely covering both special and general relativity with contemporary notation and pedagogical framing. Useful as a mathematically careful primer that bridges high school physics and graduate-level treatments like Misner, Thorne & Wheeler.
How UMAP Works
The official UMAP documentation explaining the mathematical intuition behind the algorithm — Riemannian geometry and fuzzy simplicial sets as the conceptual foundation. More rigorous than most t-SNE/UMAP comparisons and explains why UMAP preserves global structure better.
Noise in Creative Coding
Varun Vachhar's deep dive into noise functions for creative coding — covering Perlin noise, simplex noise, domain warping, and fractal Brownian motion with beautiful visual examples. The go-to reference for understanding how noise generates organic, natural-looking patterns.
Machine Learning from Scratch
Machine Learning from Scratch is a free online book deriving seven core ML algorithms from first principles — linear regression, logistic regression, naive Bayes, decision trees, ensembles, and neural networks. Mathematically rigorous, aimed at practitioners who want to understand how algorithms work mechanistically.
Mathematics for Machine Learning: Multivariate Calculus
Imperial College London's Mathematics for Machine Learning Multivariate Calculus course on YouTube — free coverage of partial derivatives, gradients, the Jacobian, Hessian, and optimization techniques needed to understand how machine learning models are trained.
Zipf's Law Arises Naturally When There Are Underlying, Unobserved Variables
A PLOS Computational Biology paper arguing that Zipf's Law — the power law governing word frequency, city size, income distribution, and countless other phenomena — arises naturally whenever observed variables are log-linear functions of hidden unobserved variables. Explains the law's ubiquity without requiring any special generative mechanism.
Why I'm Not a Fan of R-Squared
John Myles White's argument that R-squared is a misleading metric for regression model quality — it conflates the variance of x with model fit and can be gamed. A clean critique that every data scientist who uses linear regression should read.
The Theorem Every Data Scientist Should Know
Jean-Nicholas Hould's explainer on the Central Limit Theorem as the foundational theorem every data scientist needs to internalize — why sample means approach normality, and why this underpins most of frequentist hypothesis testing and confidence intervals.
Inconvergent: Generative Art by Anders Hoff
Anders Hoff's (inconvergent) generative art site — algorithmic drawings that simulate natural processes like erosion, growth, and diffusion. His work is notable for making mathematical processes legible as aesthetic objects.
Math Dance
An imgur image captioned 'Oldie, but a goodie. Math dance!' — a humorous mathematics meme saved from the data science community's social feed.
The Kernel Trick
Eric Kim's explanation of the kernel trick in support vector machines — how kernels enable SVMs to classify non-linearly separable data by implicitly mapping it to a higher-dimensional space. One of the cleaner intuitive explanations of a mathematically dense concept.
Math Dance
Matt Massie tweet of a 'math dance' — a playful visual involving mathematics and dance. Saved as a personal curiosity.
Bayesian Machine Learning via Category Theory
Culbertson and Sturtz's 2013 paper applying category theory to Bayesian machine learning — using the Kleisli category of the Giry monad to formalize supervised learning, stochastic processes as priors, and the Kalman filter. Heavy theory, but part of the broader push to give probabilistic ML rigorous foundations.
Quaternion: 3D Rotation for Quantified Self Data
Tweet from SFDataScience meetup about quaternions as the right representation for 3D rotation data from phone accelerometers/gyroscopes. Quaternions avoid gimbal lock and enable smooth interpolation — more practical than rotation matrices for sensor fusion.
The Mathematical Shape of Big Science Data
Quanta Magazine on topological data analysis (TDA) and Ayasdi's commercialization of it — using persistent homology to find structure in high-dimensional data where standard clustering fails. One of the more intellectually ambitious 2013 data science articles.
Delightful Puzzles
Gurmeet Manku's curated collection of mathematical and logic puzzles, many with elegant solutions that reveal deeper structure. A classic reference for interview preparation and recreational mathematics.
Math ∩ Programming Primers
Jeremy Kun's Math ∩ Programming blog primers page — a growing collection of self-contained posts bridging undergraduate mathematics (linear algebra, group theory, topology, probability) and programming. The best resource for programmers who want mathematical depth without a full course sequence.
I'm a Bandit — Sébastien Bubeck's Optimization Blog
I'm a Bandit is Sébastien Bubeck's research blog on optimization and online learning — covering convex optimization, bandit algorithms, and randomized methods at a level between textbook and paper. One of the best technical blogs in theoretical ML/optimization.
Big Data and the Topologist
Low Dimensional Topology blog post on what topologists bring to big data — specifically topological data analysis (TDA) and the Mapper algorithm for finding shape in high-dimensional datasets. An unusual perspective on why geometric intuition matters for data analysis.
How to Fold a Julia Fractal
Steven Wittens' (acko.net) interactive explainer on Julia sets and complex number iteration — using animated WebGL visualizations to show how complex plane geometry folds into the fractal boundary. One of the best mathematical explanations written for the web.
Probability Theory — A Primer
Jeremy Kun's Math ∩ Programming blog post introducing probability theory from first principles — sample spaces, events, probability measures, conditional probability, and random variables. Part of his series making advanced mathematics accessible to programmers.
The Mathematical Hacker
Evan Miller's essay arguing that programmers who invest in mathematical fluency gain compounding advantages — because math enables them to evaluate methods rather than just apply them, and to work with uncertainty and probability naturally. The case for quantitative education in software.
Probability and Statistics Cookbook
Matthias Vallentin's probability and statistics cookbook — a dense reference PDF covering distributions, estimation, hypothesis testing, and Bayesian methods in concise formula sheets. The kind of reference you keep open in a second tab when doing statistical work.
Why Is 'x' the Unknown?
A TED talk by Terry Moore tracing why 'x' became the symbol for an unknown quantity — it comes from the Arabic 'xei' (thing/something), transliterated into Spanish via a sound that doesn't exist in Spanish phonology. A reminder that mathematical notation has contingent historical origins.
Bayes' Theorem: Conditional Probabilities
A Vassarstats reference page on Bayes' Theorem and conditional probabilities. The theorem is the backbone of Bayesian reasoning: updating prior beliefs with new evidence to get a posterior probability.