Mathematics / core
Structure and uncertainty
Understand linear structure, optimization, uncertain evidence, and information.
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Module 01 core
Structure and uncertainty
Understand linear structure, optimization, uncertain evidence, and information.
- 01
Vector spaces and bases
Separate a vector from its coordinates, and discover what a basis actually guarantees.
18 min - 02
Linear transformations
Read a matrix as the images of basis vectors, then use rank and nullspace to explain lost information.
19 min - 03
Eigenvalues and dynamics
Decompose repeated linear evolution into modes while recognizing the limits of diagonalization.
20 min - 04
Singular value decomposition
Factor any finite real matrix into orthogonal directions and nonnegative stretches, then quantify approximation error.
21 min - 05
Multivariable calculus
Use gradients and Jacobians as local linear models, then check the approximation numerically.
20 min - 06
Constrained optimization
Find extrema along feasible directions and use Lagrange multipliers without confusing candidates with guarantees.
21 min - 07
Probability and conditioning
Update uncertainty with evidence while keeping event direction, base rates, and independence straight.
20 min - 08
Random variables and distributions
Turn outcomes into quantities, distinguish mass from density, and calculate the mean and variability of a count.
20 min - 09
Statistical inference
Separate a sample from a model, quantify estimation uncertainty, and distinguish confidence from posterior probability.
23 min - 10
Information and entropy
Measure uncertainty and predictive mismatch in bits without confusing information with meaning or thermodynamic entropy.
22 min