About this course
163 formulas, each explained symbol by symbol. 8 modules that follow one method: learn the idea, practice it by hand, implement it in Python.
Course content
How to use this guide
7 min
0.1 Numbers, variables and the rules of algebra
7 min
0.2 Functions and graphs
6 min
0.3 Exponents, roots and logarithms
9 min
0.4 Summation and product notation
10 min
0.5 Sets, logic and the symbols of proofs
4 min
0.6 Geometry and trigonometry essentials
5 min
0.7 Sequences and series
4 min
0.8 Counting
3 min
Practice lab
3 min
Checkpoint quiz
Quiz
3 min1.1 Scalars, vectors, matrices and tensors
3 min
1.2 Vector operations
12 min
1.3 Matrix operations
10 min
1.4 Systems of linear equations
3 min
1.5 Determinant
5 min
1.6 Inverse
3 min
1.7 Span, independence, basis and rank
5 min
1.8 Linear transformations
4 min
1.9 Orthogonality and projections onto subspaces
6 min
1.10 Eigenvalues and eigenvectors
8 min
1.11 Positive definite matrices and quadratic forms
3 min
1.12 Singular value decomposition
7 min
1.13 Least squares and the normal equations
5 min
1.14 Principal component analysis
4 min
1.15 Matrix norms and tensors
3 min
Practice lab
3 min
Checkpoint quiz
Quiz
3 min2.1 Limits and continuity
5 min
2.2 The derivative
6 min
2.3 Differentiation rules
9 min
2.4 Applications of derivatives
5 min
2.5 Integrals
9 min
2.6 Series and Taylor expansion
6 min
2.7 Partial derivatives and the gradient
7 min
2.8 Jacobian and Hessian
5 min
2.9 The multivariable chain rule
3 min
2.10 Matrix calculus
3 min
2.11 Multiple integrals and change of variables
5 min
Practice lab
3 min
Checkpoint quiz
Quiz
3 min3.1 Probability basics
4 min
3.2 Conditional probability and Bayes' theorem
9 min
3.3 Random variables and distributions
3 min
3.4 Expectation, variance and covariance
9 min
3.5 Distributions you must know
12 min
3.6 Joint distributions and the i.i.d. assumption
3 min
3.7 Law of large numbers and central limit theorem
3 min
3.8 Descriptive statistics
3 min
3.9 Estimation: maximum likelihood and MAP
9 min
3.10 Confidence intervals and hypothesis tests
7 min
3.11 Correlation and simple linear regression
4 min
3.12 Bayesian inference
5 min
3.13 Information theory
7 min
3.14 Simulation: Monte Carlo, bootstrap and Markov chains
5 min
3.15 Statistics of model evaluation
5 min
Practice lab
3 min
Checkpoint quiz
Quiz
3 min4.1 Anatomy of an optimization problem
6 min
4.2 Optimality conditions
3 min
4.3 Convexity
5 min
4.4 Gradient descent
8 min
4.5 Stochastic and mini-batch gradient descent
5 min
4.6 Momentum and adaptive methods
5 min
4.7 Second-order methods
3 min
4.8 Constrained optimization
6 min
4.9 Regularization as optimization
4 min
4.10 Convergence in practice
4 min
4.11 Three gradients every practitioner should derive once
4 min
Practice lab
3 min
Checkpoint quiz
Quiz
3 min5.1 The neuron and the layer
4 min
5.2 Activation functions
5 min
5.3 Loss functions
5 min
5.4 Forward pass, backpropagation, update
6 min
5.5 Vanishing and exploding gradients
7 min
5.6 Regularization and generalization
4 min
5.7 Normalization layers
3 min
5.8 Convolutional networks
4 min
5.9 Recurrent networks: RNN, LSTM, GRU
5 min
5.10 Attention and the transformer
9 min
5.11 The arithmetic of large language models
6 min
5.12 Transfer learning and LoRA
3 min
5.13 Tuning hyperparameters
3 min
Practice lab
4 min
Checkpoint quiz
Quiz
3 min6.1 Numerical computing
3 min
6.2 Trees and gradient boosting
5 min
6.3 Time series and forecasting
3 min
6.4 Kernel methods and Gaussian processes
3 min
6.5 Latent variables and variational inference
3 min
6.6 Generative models
3 min
6.7 Reinforcement learning
3 min
6.8 Learning theory and scaling laws
3 min
6.9 More mathematics, and what it unlocks
3 min
Practice lab
3 min
Checkpoint quiz
Quiz
3 min7.1 The map: which mathematics powers which algorithm
4 min
7.2 Study plan, week by week
3 min
7.3 College courses and books
3 min
7.4 The project ladder
3 min
7.5 Notation at a glance
4 min
Checkpoint quiz
Quiz
3 min