An interactive field guide / Math for ML
Build intuition.
Then do the math.
See a vector stretch. Watch a surface change. Connect the mathematics to the ideas behind machine learning.
Start with the foundations ↗For first-year college students. Start with curiosity.
A positive scale preserves the direction.
The course map
One idea builds on another.
Begin with ten complete foundation lessons in modules 0 and 1. Each connects an explanation to an experiment and a prediction. The remaining course is in development.
Supplement
Math starter kit
Algebra, functions, coordinates, and the language of mathematics.
Numbers that tell a story →Functions are machines →Give a point an address →Read symbols as sentences →Change, one small step at a time →How do you know it is true? →§1–2
Getting started & notation
Read mathematical symbols and check the shape of an expression.
The math behind a prediction →A field guide to the symbols →Know what kind of thing you have →Let dimensions catch mistakes →§3.1–3.5
Vectors & spaces
Build intuition for vectors, distance, inner products, and projection.
What can you build from two directions? →Vectors as coordinates and displacements →Which sets keep every linear combination? →What must a linear map preserve? →Why do matrix columns describe a map? →What disappears, and what can you reach? →How can distance define a limit? →Does changing length change convergence? →How does a product measure alignment? →How large can an inner product be? →Why is the perpendicular foot the closest point? →§3.6–3.11
Understanding matrices
Explore eigenvectors, symmetry, and the geometry of quadratic forms.
Which directions stay on the same line? →Which changes leave the diagonal sum alone? →When does a transformation flatten area? →Which matrices preserve length and angle? →Can a symmetric map be split into three simple steps? →Which direction gives the largest quadratic value? →When is every nonzero direction uphill? →Why does a larger eigenvalue make a shorter ellipse axis? →§3.12–3.17
SVD & matrix tools
Connect subspaces, matrix norms, low-rank approximation, and pseudoinverses.
What does a matrix stretch? →Which part of an input survives? →How much can a matrix amplify a vector? →How much can you discard? →Can you undo a map that loses information? →How do columns and outer products build a matrix? →§4.1–4.7
Calculus & optimization
Understand gradients, curvature, the chain rule, and local minima.
Where are you allowed to look for a minimum? →Which direction changes the value fastest? →What linear map describes a nonlinear change nearby? →How does curvature change a step? →Why does a quadratic gradient contain a transpose? →How does a change travel through a composition? →How accurate is the local picture? →When does a stationary point really minimize? →