Curriculum
32 topics across 8 tracks — from limits to functional analysis.
Every topic connects forward to formalML topics it enables.
Prerequisite Graph
The full dependency graph — arrows show prerequisites. Filled nodes are published topics.
Limits & Continuity
The rigorous foundation — epsilon-delta definitions, convergence, completeness.
Epsilon-Delta & Continuity
Completeness & Compactness
Uniform Convergence
Single-Variable Calculus
Differentiation, integration, and the theorems connecting them.
The Derivative & Chain Rule
Mean Value Theorem & Taylor Expansion
The Riemann Integral & FTC
Improper Integrals & Special Functions
Multivariable Differential Calculus
Gradients, Jacobians, Hessians — the engine of optimization.
Partial Derivatives & the Gradient
The Jacobian & Multivariate Chain Rule
The Hessian & Second-Order Analysis
Inverse & Implicit Function Theorems
Multivariable Integral Calculus
Multiple integrals, change of variables, and the big theorems of vector calculus.
Multiple Integrals & Fubini's Theorem
Change of Variables
Line Integrals & Conservative Fields
Surface Integrals & the Divergence Theorem
Sequences, Series & Approximation
Convergence tests, power series, Fourier analysis, and approximation theory.
Series Convergence & Tests
Power Series & Taylor Series
Fourier Series & Orthogonal Expansions
Approximation Theory
Ordinary Differential Equations
Existence theorems, linear systems, stability, and numerical methods.
First-Order ODEs & Existence Theorems
Linear Systems & Matrix Exponential
Stability & Dynamical Systems
Numerical Methods for ODEs
Measure & Integration
Sigma-algebras, Lebesgue integral, Lp spaces — the rigorous foundation of probability.
Sigma-Algebras & Measures
The Lebesgue Integral
Lp Spaces
Radon-Nikodym & Probability Densities
Functional Analysis Essentials
Metric spaces, Banach and Hilbert spaces, calculus of variations.