formalCalculus
The calculus and analysis foundations behind modern machine learning.
Deep-dive explainers combining rigorous mathematics, interactive visualizations, and working code. The prequel to formalStatistics and formalML.
10 Tracks · 35 Topics
Limits & Continuity
The rigorous foundation — epsilon-delta definitions, convergence, completeness.
4 published · 0 planned Explore →
Single-Variable Calculus
Differentiation, integration, and the theorems connecting them.
4 published · 0 planned Explore →
Multivariable Differential Calculus
Gradients, Jacobians, Hessians — the engine of optimization.
4 published · 0 planned Explore →
Multivariable Integral Calculus
Multiple integrals, change of variables, and the big theorems of vector calculus.
4 published · 0 planned Explore →
Sequences, Series & Approximation
Convergence tests, power series, Fourier analysis, and approximation theory.
4 published · 0 planned Explore →
Ordinary Differential Equations
Existence theorems, linear systems, stability, and numerical methods.
4 published · 0 planned Explore →
Linear Algebra
Vector spaces, linear maps, matrix algebra, and spectral theory — the algebraic backbone of optimization, statistics, and ML.
2 published · 0 planned Explore →
Probability Foundations
Kolmogorov axioms, conditional probability, the union bound — a concrete-probability ramp to the measure-theoretic foundations.
1 published · 0 planned Explore →
Measure & Integration
Sigma-algebras, Lebesgue integral, Lp spaces, and the Radon-Nikodym theorem — the rigorous foundation of probability.
4 published · 0 planned Explore →
Functional Analysis Essentials
Metric spaces, Banach and Hilbert spaces, calculus of variations.
4 published · 1 planned Explore →
How the topics connect
The full prerequisite graph — every arrow is a concept you'll want before the next. Hover a node for details, or view the full curriculum.
Where this leads →
Probability and statistics built on this calculus — distributions, estimation, hypothesis testing, Bayesian inference.
Visit formalStatistics →Machine learning theory built on this calculus — optimization, learning theory, generative modeling.
Visit formalML →