The maths behind AI

Just enough maths to see inside a model: vectors, matrices, derivatives, the chain rule and probability — every idea shown with live, exact calculations.

Your learning path: The maths behind AI

3 modules, each building on the last. Create a free account to save your progress and earn XP.

Vectors and matrices

How models represent things as lists of numbers, and how a layer transforms them.

0/2 done

Vectors and dot products

Arrows, lists of numbers, and the one calculation AI uses to compare them.

10 minStart here

Matrices as transformations

Four numbers that can stretch, turn, shear or flatten the whole plane — and power every layer of a network.

11 minFree

Change and optimisation

Derivatives measure how a change in one number moves another — the engine behind learning.

0/2 done

3 Pro

Derivatives

Shrink a gap to zero and find the slope at a point — then point uphill in many dimensions.

12 min Pro lesson

4 Pro

The chain rule

Follow a nudge through a chain of calculations, and see how networks find every gradient at once.

10 min Pro lesson

Probability

Reasoning with uncertainty: conditional probability, Bayes, softmax and the loss models minimise.

0/2 done

5 Pro

Probability and Bayes

Why a positive test can still mean you probably don’t have it, and what that means for AI classifiers.

11 min Pro lesson

6 Pro

Softmax and cross-entropy

How a model turns raw scores into probabilities, and the loss that tells it how wrong it was.

11 min Pro lesson