Calculus

Reverse-Process Synthetic Data Generation for Math Reasoning

Training LLMs on mathematical reasoning by inverting easy-to-solve problems: generate derivatives, reverse them into integration exercises with full step-by-step solutions.

Watch: Calculus, The Big Ideas

Calculus as one idea examined from every side: a seven-episode animated playlist running from limits through the derivative, the integral, the fundamental theorem, gradients, and optimization.

Calculus Made Easy

Notes

Still the gentlest and most irreverent intro to calculus ever written.

Mathematics for Machine Learning

Notes

Unified LA + multivariate calc + probability for ML-minded people.

Differentiation: Three Ways

Three approaches to computing derivatives, forward-mode AD, reverse-mode AD, and finite differences, each with different trade-offs for numerical computing and machine learning.

How to Teach a Computer Calculus with Pattern Matching

Define patterns, define replacements, repeat until done. Watch a 90-line rewrite engine learn to differentiate.

Numerical Differentiation

Choosing step size h for finite differences: small enough for a good approximation, not so small that floating-point errors eat your lunch.

Forward-Mode Automatic Differentiation

Dual numbers extend our number system with an infinitesimal epsilon where epsilon^2 = 0. Evaluating f(x + epsilon) yields f(x) + epsilon * f'(x)—the derivative emerges automatically from the algebra.