Learning paths

How to study here #

Every lesson is built for active learning: you learn more by retrieving and doing than by re-reading. A good routine for one lesson:

1. Predict. Answer the "Predict first" questions before you read. Being wrong is useful: it makes the right answer stick.
2. Read with the figures. Move every slider and drag every point. Ask yourself what will happen before you move it.
3. Answer the quick checks in the text without scrolling back.
4. Code. Open the Colab notebook and solve the exercises. Look at a solution only after you tried.
5. Add the recall cards to your review deck, and mark the lesson as done.
6. Review daily. Open Review for 10 minutes a day. Each card comes back just before you would forget it (spaced repetition). This is what makes the knowledge last.
7. Before an exam or interview, read the track's Quick recap page.

Path 1: Mathematics for machine learning #

For students and engineers who want a solid base before ML. About 8–12 weeks at 5–7 hours a week.

1. Start here: notation and Python — the language and the tools.
2. Linear Algebra, parts 1–3 (matrices, eigenvalues, SVD and PCA).
3. Calculus for ML — gradients, the chain rule and backpropagation.
4. Probability and Statistics — distributions, the Gaussian, estimation.
5. Optimization — gradient descent and its relatives.
6. Information Theory — entropy, cross-entropy and KL divergence.

Path 2: From zero to deep learning #

For people who want to understand and build neural networks. About 12–16 weeks.

1. Start here, then Linear Algebra lessons 0–4 and 8–9.
2. Calculus for ML up to backpropagation.
3. Probability and Statistics, the first half.
4. ML Fundamentals (coming soon) — regression, classification, generalization.
5. Optimization — SGD, momentum, Adam, schedules.
6. Deep Learning — from MLPs to transformers.
7. Then choose: Generative Models, Large Language Models (coming soon) or Reinforcement Learning.

Path 3: Large language models #

For engineers who want to understand and work with LLMs.

1. Linear Algebra lessons 0–1, 8 and 15 (attention and LoRA), and Information Theory lessons on cross-entropy.
2. Deep Learning: backpropagation, normalization, attention and the transformer.
3. Large Language Models (coming soon) — the full track.
4. Reinforcement Learning: policy gradients and PPO, for RLHF and RL with verifiable rewards.
5. ML Systems: memory, mixed precision, parallelism and serving.

Path 4: Machine learning for science #

For physicists, engineers and climate or Earth scientists.

1. Linear Algebra (the full track; lessons 13–19 are the numerical and scientific part).
2. Calculus for ML and Probability and Statistics.
3. Deep Learning and Generative Models (diffusion and flow matching).
4. ML for Science — differentiable simulation, data assimilation, neural operators, uncertainty.
5. ML Systems for training large models on clusters.

Path 5: Preparing for ML interviews #

1. The Quick recap pages of Linear Algebra, Probability and Statistics, ML Fundamentals and Deep Learning.
2. ML Interview Prep — coding, ML breadth, system design and behavioral rounds.
3. Daily Review: add the cards of these tracks with "Add a whole track".