Ordinary programming means writing down the rules yourself: if this, do that. But how do you write the rules for recognising a cat, or a spam email, or a friend's handwriting? Nobody can. Machine learning flips the problem on its head — instead of coding the rules, you show the computer thousands of examples and let it learn the rules for itself.

That single shift powers almost everything that feels magical about modern computing: voice assistants, recommendations, translation, self-driving cars and the large language models you might be reading this with. Underneath the magic, though, it's all built from ideas you can actually understand — lines, slopes, distances and dot products.

The maths it's made of

Machine learning is where your maths comes alive. A data point is a vector; a model's prediction is a dot product; a layer of a neural network is a matrix times a vector; and "learning" itself is just rolling downhill on an error surface using the slope — the derivative. If you've worked through linear algebra, you already hold most of the keys.

The shape of the journey

This course climbs in seven stages, each building on the last.

• Stage A — Foundations. What learning from data even means: features, labels, training and the all-important idea of generalizing to new data.
• Stage B — Linear regression. The "hello world" of ML: fit a line, measure its error, and roll downhill with gradient descent to make it better.
• Stage C — Classification. From predicting numbers to predicting categories: the sigmoid, logistic regression, decision boundaries and nearest neighbours.
• Stage D — Trees & ensembles. A completely different, rule-based style of model: decision trees and the forests built from them.
• Stage E — Fitting & evaluation. The central craft of ML: overfitting, the bias–variance tradeoff, regularization, and how to score a model honestly.
• Stage F — Neural networks. Stack simple neurons into deep networks, push data forward, and train them by backpropagation.
• Stage G — Unsupervised learning. Finding structure with no labels at all: clustering and dimensionality reduction.

Stage A — Foundations

1. What Is Machine Learning?
2. Supervised vs Unsupervised
3. Features and Labels
4. The Feature Vector
5. The Training Loop
6. The Dataset: Train and Test
7. Generalization

Stage B — Linear regression

1. Fitting a Line
2. The Hypothesis Function
3. The Cost Function
4. Visualizing the Cost
5. Gradient Descent
6. The Learning Rate
7. Multiple Features
8. The Normal Equation
9. Feature Scaling

Stage C — Classification

1. Classification
2. The Sigmoid Function
3. Logistic Regression
4. The Decision Boundary
5. Cross-Entropy Loss
6. k-Nearest Neighbours
7. Multiclass Classification

Stage D — Trees & ensembles

1. Decision Trees
2. Entropy and Information Gain
3. Overfitting a Tree
4. Random Forests

Stage E — Fitting & evaluation

1. Overfitting and Underfitting
2. The Bias–Variance Tradeoff
3. Regularization
4. Train, Validation, Test
5. Accuracy, Precision, Recall

Stage F — Neural networks

1. The Neuron
2. Activation Functions
3. A Layer of Neurons
4. Stacking Layers
5. Forward Propagation
6. The Loss Landscape
7. Backpropagation
8. Training a Network
9. Why Go Deep?

Stage G — Unsupervised learning

1. Clustering
2. k-Means
3. Dimensionality Reduction
4. Principal Component Analysis

Let's get started

We begin at the very beginning — what it actually means for a machine to "learn" anything at all, and why that's such a powerful idea.

Let's get started → What Is Machine Learning?