Read the chapter
Long-form, worked by hand, with the geometry before the algebra. The lecture video sits beside it when one is published.
15 levels · 213 chapters · free and open
Understand AI from first principles.
Not by memorising APIs, but by discovering why each idea had to exist. Every chapter answers the question the previous one left open — and you move on when you can show you understood it.
213 of 213 chapters open · new chapters as they are written and filmed
Every point is a recipe
Two arrows, and everything they can build.
Each speck is one combination of the two arrows — so much of the first, so much of the second. Drag either arrowhead: pull them apart and the cloud floods the plane, bring them onto one line and the whole thing collapses to that line. That is what a basis is, and it is chapter six.
Open this in the studio →How the course works
Do the practice
Six graded levels per chapter, from explain-it to investigate-it, plus a Python lab that runs in your browser.
Pass the test
A short multiple-choice test on the chapter you just read. Score 60% and you have it.
The path
every written chapter is open · read in any order Level 00
What does learning mean
Level 01
Linear Algebra
Level 02
Mathematics of Change
Level 03
Probability and Uncertainty
Level 04
Classical Machine Learning
Level 05
Doing Machine Learning Honestly
Level 06
Neural Networks from First Principles
Level 07
Training Deep Networks
Level 08
Computer Vision
Level 09
Sequences Language and Transformers
Level 10
Generative AI and Foundation Models
Level 11
Retrieval Tools and Agents
Level 12
Reinforcement Learning
Level 13
Research Literacy
Level 14
Production AI and MLOps
Chapters you can read today
Level 00 — What does learning mean
Level 01 — Linear Algebra
- 005 Numbers Become Vectors
- 006 Directions, Span and Basis
- 007 Dot Product: Measuring Alignment
- 008 Matrices: The Spreadsheet of Mathematics
- 009 Matrix-Vector Multiplication as Transformation
- 010 Matrix-Matrix Multiplication as Composition
- 011 A Matrix Can Transform Space
- 012 What a Matrix Does, and What a Neuron Is
- 014 Eigenvectors: What a Transformation Leaves Alone
- 015 Singular Value Decomposition
- 016 PCA: Compressing Data by Finding Important Directions
Level 02 — Mathematics of Change
- 017 Functions and Slopes
- 018 Derivatives: The Compass for Learning
- 019 Partial Derivatives: One Dial at a Time
- 020 Gradients: The Direction of Steepest Change
- 021 Partial Derivatives, Gradients and the Chain Rule
- 022 Computational Graphs: Turning Formulas Into Data Flow
- 023 Gradient Descent: Teaching a Model to Improve
- 024 Learning Rate and the Shape of the Loss Surface
- 025 Matrix Calculus for Neural Networks
Level 03 — Probability and Uncertainty
- 026 Describing Data: Mean, Variance, Distributions
- 027 Probability: Reasoning Under Uncertainty
- 028 Conditional Probability
- 029 Bayes' Rule: What Evidence Does to Belief
- 030 Random Variables and Expectation
- 031 Covariance and Correlation
- 032 Gaussian Distribution
- 033 Maximum Likelihood: Where Loss Functions Come From
- 034 Maximum A Posteriori Estimation
- 035 Entropy and Information
- 036 KL Divergence
- 037 Cross-Entropy
Level 04 — Classical Machine Learning
- 038 Linear Regression, Properly
- 039 Logistic Regression: The One-Neuron Network
- 040 Softmax and Cross-Entropy
- 041 Nearest Neighbours and the Curse of Dimensionality
- 042 Curse of Dimensionality
- 043 Decision Trees
- 044 Ensembles: Forests and Boosting
- 045 Gradient Boosting
- 046 Support Vector Machines and Kernels
- 047 Kernels
- 048 K-Means Clustering
- 049 Gaussian Mixture Models
- 050 Expectation Maximization
- 051 PCA from Eigenvectors
- 052 PCA from SVD
- 053 Dimensionality Reduction: t-SNE and UMAP Intuition
Level 05 — Doing Machine Learning Honestly
- 054 How Do We Know If Our Model Really Learned
- 055 Why Training Accuracy Can Lie
- 056 Overfitting and Underfitting
- 057 Bias-Variance Tradeoff
- 058 Regularization
- 059 Data Leakage
- 060 Class Imbalance
- 061 Evaluation Metrics
- 062 Calibration and Uncertainty
- 063 Baselines
- 064 Error Analysis
- 065 Hyperparameter Search
- 066 Cross Validation
- 067 Generalization
- 068 Sample Complexity Intuition
- 069 VC Dimension Intuition
- 070 Random Seeds and Reproducibility
- 071 Why One Training Run Is Not Evidence
- 072 Confidence Intervals
- 073 Ablation Studies
- 074 Statistical Significance for ML Experiments
- 075 How to Avoid Cherry-Picking
Level 06 — Neural Networks from First Principles
- 076 Meet the Smallest Neural Network
- 077 Weights and Biases
- 078 Why Does a Neuron Need an Activation Function
- 079 ReLU and Geometry
- 080 XOR: Why Linear Models Fail
- 081 Hidden Layers
- 082 Neural Networks as Function Approximators
- 083 Backpropagation: Sending the Error Backward
- 084 dW, db and dX by Hand
- 085 Matrix Backpropagation: dW, db, dX by Hand
- 086 Tensors: Numbers in Many Dimensions
- 087 Batch Computation
- 088 Build a Tiny Neural Network From Scratch
- 089 Automatic Differentiation
- 090 Build a Tiny Autograd Engine
Level 07 — Training Deep Networks
- 091 Stochastic Gradient Descent
- 092 Mini-Batches
- 093 Momentum
- 094 RMSProp
- 095 Adam
- 096 Learning-Rate Schedules
- 097 Weight Initialization
- 098 Vanishing and Exploding Gradients
- 099 Batch Normalization
- 100 Layer Normalization
- 101 Dropout
- 102 Residual Connections
- 103 Gradient Clipping
- 104 Mixed Precision
- 105 Scaling Rules for Training
Level 08 — Computer Vision
- 106 Images as Tensors
- 107 How a Neural Network Learns to See: Convolution
- 108 Kernels and Feature Maps
- 109 Padding and Stride
- 110 Pooling
- 111 Receptive Fields
- 112 LeNet
- 113 AlexNet
- 114 VGG
- 115 ResNet
- 116 Transfer Learning and Fine-Tuning
- 117 Data Augmentation
- 118 Object Detection
- 119 YOLO Intuition
- 120 Semantic Segmentation
- 121 U-Net
- 122 Vision Transformers
- 123 Self-Supervised Vision
- 124 CLIP and Vision-Language Models
Level 09 — Sequences Language and Transformers
- 125 When Order Matters: Learning From Sequences
- 126 Recurrent Neural Networks
- 127 Backpropagation Through Time
- 128 Vanishing Gradients in RNNs
- 129 LSTM
- 130 GRU
- 131 Tokens and Vocabulary
- 132 How Can a Computer Represent the Meaning of a Word
- 133 Word2Vec
- 134 Positional Information
- 135 Attention: What Should I Look At
- 136 Queries, Keys and Values
- 137 Scaled Dot-Product Attention
- 138 Multi-Head Attention
- 139 Residual Connections in Transformers
- 140 LayerNorm in Transformers
- 141 Transformers: Building With Attention
- 142 Causal Masking
- 143 How Does a Language Model Learn to Predict Text
- 144 Tokenization: BPE and Modern Tokenizers
- 145 Build a Tiny GPT From Scratch
Level 10 — Generative AI and Foundation Models
- 146 Representation Learning
- 147 Autoencoders
- 148 Variational Autoencoders
- 149 GANs
- 150 Autoregressive Generation
- 151 Diffusion Models
- 152 Contrastive Learning
- 153 Foundation Models
- 154 Pretraining
- 155 Scaling Laws
- 156 Instruction Tuning
- 157 Supervised Fine-Tuning
- 158 Preference Learning and Policy Optimization
- 159 RLHF
- 160 Direct Preference Optimization
- 161 Quantization
- 162 LoRA and Parameter-Efficient Fine-Tuning
- 163 LLM Evaluation
- 164 Hallucination and Reliability
Level 11 — Retrieval Tools and Agents
- 165 Why an LLM Needs External Knowledge
- 166 Embeddings for Retrieval
- 167 Vector Search
- 168 Approximate Nearest Neighbour Search
- 169 Chunking
- 170 Retrieval-Augmented Generation
- 171 Reranking
- 172 Tool Calling
- 173 Structured Outputs
- 174 Agent Loops
- 175 Planning
- 176 Memory
- 177 Multi-Agent Systems
- 178 Evaluating Agents
- 179 Failure Modes and Guardrails
Level 12 — Reinforcement Learning
- 180 Agent, Environment, State, Action and Reward
- 181 Markov Decision Processes
- 182 Return and Discounting
- 183 Bellman Equation
- 184 Value Iteration
- 185 Policy Iteration
- 186 Q-Learning
- 187 Deep Q Networks
- 188 Policy Gradients
- 189 REINFORCE
- 190 Actor-Critic
- 191 Exploration vs Exploitation
- 192 RL for Language Models
- 193 Preference Optimization and RLHF Revisited
Level 13 — Research Literacy
Level 14 — Production AI and MLOps
- 201 From Notebook to Application
- 202 Saving and Loading Models
- 203 Model Serving
- 204 Batch vs Online Inference
- 205 Latency and Throughput
- 206 Batching
- 207 Quantization for Inference
- 208 Experiment Tracking
- 209 Dataset Versioning
- 210 Model Versioning
- 211 Monitoring
- 212 Data Drift
- 213 Model Drift
- 214 Retraining Pipelines
- 215 Distributed Training
- 216 GPU Memory and Performance
- 217 AI System Design
Why learn machine learning this way
Stanford-level depth, without the prerequisite maze
Vectors appear when we need to describe several features at once. Derivatives appear when we need to know how a prediction changes. Nothing is taught before the problem that demands it.
Open, and free to read
The curriculum is a public repository and the videos are on YouTube. No paywall, no subscription, and the pipeline that builds the lectures is open source too.
What you need before you start
School algebra and a willingness to do arithmetic by hand. No calculus, no linear algebra and no Python are assumed — the maths is built here, in the order a problem demands it, starting from four house prices and a rule nobody has written down yet.
What you will be able to do
Derive gradient descent rather than quote it. Read a matrix as a map and say what it does to space. Explain why a single line cannot solve XOR and what a hidden layer buys. Train a small network, and know which part of the loss curve is telling you something.
Questions people ask before starting
What do I need to know before I start?
School algebra, and a willingness to do arithmetic by hand. Calculus, linear algebra and Python are not assumed — each is built here, in the order a problem demands it. The first chapter starts from four house prices and a rule nobody has written down yet.
Does it cost anything, and do I need an account?
No, to both. The chapters, the lecture videos, the exercises and the interactive studios are free to read and use with no sign-up, no paywall and no subscription. The curriculum is a public repository and the pipeline that builds the lectures is open source too.
How many chapters are there, and how much is published?
The course plans 213 chapters across 15 levels, from what learning means through linear algebra, calculus and probability to neural networks, transformers and reinforcement learning. 213 are published today; the rest are written and filmed in order, and levels open in order too.
How long does a chapter take?
Longer than a tutorial and shorter than a textbook chapter. They are long-form and worked by hand, with six graded exercises and a Python lab at the end, so an hour or two is realistic if you actually do the work. Reading one without doing the exercises takes far less and teaches far less.
Do I need to install Python?
No. The practice lab runs Python inside the browser, so there is nothing to install and nothing to configure. If you would rather work locally, every chapter's code is in the public repository.
What is the studio?
An interactive simulation built for one chapter, sitting in that chapter's Practice tab. Nothing in it moves until you move it: you drag the basis vectors and watch the matrix rewrite itself, push two columns together until the determinant hits zero, or turn a line through a point cloud until the variance peaks.