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Understand AI, one clear picture at a time.

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Data science and AI, from school maths to research level. Learn it the way you would on paper: a picture first, then every step of the working, then the code.

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Drag the tip. The numbers are the arrow, and the arrow is the numbers. From M01.2 Coordinates and a first look at vectors.

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Three questions point you to the right first lesson. No sign-up, and nothing to download: each lesson is a light web page that works on a phone.

Answer three questions

• New to maths, or rusty? Begin with M01.1 Numbers, algebra and notation.
• New to code? Begin with P01.1 How computers run programs.
• Ready for machine learning? Begin with ML01.1 What learning from data means.
• Heading for reinforcement learning? Try an available lesson, RL01.6 Bellman equations; the earlier RL modules are on their way.

Know exactly what to learn next, and why

Ten tracks in three stages, with two that run alongside. Pick a stage to see its courses, or pick a course to see what it needs first, where it leads, and why.

The map needs JavaScript. Every course, with what it builds on, is listed below and in the curriculum.

Explore courses by track

139 of 671 planned modules are live, each four lessons of about 25 minutes and one interactive. Open a track, then a course, to see its modules and lessons. The roadmap says what ships when.

Include planned courses

Mathematics12 courses: 6 available, 6 planned

The maths under every later track. Track page

• M01Math Foundations● all 9 modules available

  Read the notation of machine learning, and work with functions, logarithms, sets, sums and proofs.

  Start the course Course page

  1. M01.1 Numbers, algebra and notation
     1. Kinds of numbers and the number line
     2. Expressions and the rules of algebra
     3. Equations and inequalities
     4. Reading notation: subscripts, Greek letters and formulas
  2. M01.2 Coordinates and a first look at vectors
     1. The coordinate plane
     2. Right triangles and Pythagoras' theorem
     3. Distance, from the plane to many dimensions
     4. Arrows: a first look at vectors
  3. M01.3 Functions and graphs
     1. A function is a machine
     2. Straight lines: slope and intercept
     3. Parabolas and the quadratic formula
     4. Chaining and undoing: composition and inverse
  4. M01.4 Exponentials and logarithms
     1. Powers and their rules
     2. Exponential growth and decay
     3. Logarithms: the exponent as the answer
     4. Log scales and why machine learning takes logs
  5. M01.5 Trigonometry and the unit circle
     1. Sine, cosine and tangent as ratios
     2. The unit circle and polar coordinates
     3. Radians and sine waves
     4. The law of cosines and the angle-addition formulas
  6. M01.6 Sets, logic and proof techniques
     1. Sets and Venn diagrams
     2. Statements and logic: and, or, not, if-then
     3. Direct proof and counterexample
     4. Contradiction and induction
  7. M01.7 Sums, products and sequences
     1. Sequences: lists with a rule
     2. Sigma notation
     3. Arithmetic and geometric sums
     4. Products and double sums
  8. M01.8 Counting and combinatorics
     1. Counting by multiplying and adding
     2. Permutations: arrangements in order
     3. Combinations: choosing without order
     4. Pascal's triangle and the binomial theorem
  9. M01.9 Complex numbers
     1. The number i and the complex plane
     2. Adding and multiplying: moving, turning and scaling
     3. The polar form and Euler's formula
     4. Quadratics with a negative discriminant
• M02Linear Algebra I: Vectors and Matrices● all 10 modules available

  See vectors and matrices as pictures, and use them to move, solve and project data.

  Start the course Course page

  1. M02.1 Vectors as arrows and as data
     1. Vectors as arrows
     2. Vectors as lists of numbers
     3. Adding and scaling vectors
     4. Data as vectors
  2. M02.2 Linear combinations, span and basis
     1. Linear combinations
     2. Span: everything you can reach
     3. Linear independence
     4. Basis and dimension
  3. M02.3 Dot product, norms, angles and projections
     1. The dot product, two ways
     2. Length, distance and norms
     3. Angles, orthogonality and cosine similarity
     4. Projection onto a line
  4. M02.4 Matrices as linear maps
     1. What a linear map is
     2. Columns are where the basis vectors land
     3. Rotation and shear as matrices
     4. Maps between dimensions
  5. M02.5 Matrix multiplication as composition
     1. One map after another
     2. The multiplication rule, derived
     3. Order matters
     4. Shapes, identity and powers
  6. M02.6 Linear systems and elimination
     1. A system is a question about a map
     2. Elimination, step by step
     3. None, one, or infinitely many
     4. Elimination as matrices
  7. M02.7 Inverses, rank and the four subspaces
     1. The inverse: undoing a map
     2. Column space: what a map can reach
     3. Null space: what a map destroys
     4. Four subspaces and the counting rule
  8. M02.8 Determinants as volume scaling
     1. The area factor
     2. Sign, orientation and three dimensions
     3. Zero means collapse
     4. Determinants in practice
  9. M02.9 Change of basis
     1. Coordinates depend on the basis
     2. The change-of-basis matrix
     3. The same map in a new basis
     4. Choosing a good basis
  10. M02.10 Orthogonality, Gram-Schmidt and QR
      1. Orthonormal bases
      2. Orthogonal matrices
      3. Gram-Schmidt
      4. QR and least squares
• M03Linear Algebra II: Decompositions● all 10 modules available

  Take matrices apart with eigenvalues and the SVD, and use them for PCA and least squares.

  Start the course Course page

  1. M03.1 Eigenvalues and eigenvectors
     1. Vectors that stay on their line
     2. The characteristic polynomial
     3. Trace, determinant and eigenspaces
     4. Complex eigenvalues: a rotation hidden inside
  2. M03.2 Diagonalization and matrix powers
     1. A = P D P inverse
     2. Powers through the eigenbasis
     3. Fibonacci and linear recurrences
     4. The power method
  3. M03.3 Symmetric matrices and the spectral theorem
     1. Real eigenvalues, perpendicular eigenvectors
     2. The spectral theorem
     3. A sum of rank-one pieces
     4. The Rayleigh quotient and the extreme directions
  4. M03.4 Positive definite matrices and quadratic forms
     1. Quadratic forms: bowls and saddles
     2. Tests for positive definiteness
     3. Cholesky: a square root by triangles
     4. Minima, curvature and ellipses
  5. M03.5 Singular value decomposition
     1. Every matrix turns a circle into an ellipse
     2. Finding the SVD through A-transpose A
     3. Rectangular matrices and the four subspaces
     4. A sum of rank-one layers
  6. M03.6 Low-rank approximation and PCA
     1. The best rank-k approximation
     2. Image compression by rank
     3. PCA from the covariance matrix
     4. PCA by SVD, in practice
  7. M03.7 Least squares and the pseudoinverse
     1. Least squares as projection
     2. Three ways to solve, and which to trust
     3. The pseudoinverse
     4. Ridge, truncation and noise
  8. M03.8 Matrix norms and conditioning
     1. Measuring the size of a matrix
     2. The condition number
     3. Ill-conditioning in data
     4. Conditioning and gradient descent
  9. M03.9 Markov matrices, graphs and PageRank
     1. Markov matrices
     2. Steady states and Perron-Frobenius
     3. Graphs as matrices
     4. PageRank
  10. M03.10 Tensors and index notation for deep learning
      1. Tensors as arrays with many axes
      2. Index notation and the summation convention
      3. einsum: any contraction from scratch
      4. Tensors inside a network layer
• M04Calculus I: Single Variable● all 10 modules available

  Understand rates of change and accumulation, and find the lowest point of a function.

  Start the course Course page

  1. M04.1 Limits and continuity
     1. What a limit is
     2. Limits by algebra
     3. One-sided limits and infinity
     4. Continuity and the intermediate value theorem
  2. M04.2 The derivative as slope and rate
     1. From average rate to instantaneous rate
     2. The tangent line and linear approximation
     3. The derivative as a function
     4. Derivatives by computer: finite differences
  3. M04.3 Differentiation rules and the chain rule
     1. Powers, sums and constant multiples
     2. Exponentials, sine and cosine
     3. Products and quotients
     4. The chain rule
  4. M04.4 Optimization in one dimension
     1. Critical points and the first-derivative test
     2. The second derivative and convexity
     3. Optimisation problems solved exactly
     4. Gradient descent and Newton's method in one dimension
  5. M04.5 Integrals as accumulated area
     1. Distance from speed: adding up thin slices
     2. Riemann sums and the definite integral
     3. Signed area, properties and the average value
     4. The trapezoid rule and integrals of sampled data
  6. M04.6 The fundamental theorem of calculus
     1. The area function
     2. Part one: the slope of the area is the height
     3. Part two: integrals from antiderivatives
     4. Net change and the round trip
  7. M04.7 Integration techniques
     1. Substitution: the chain rule in reverse
     2. Integration by parts: the product rule in reverse
     3. Improper integrals: areas that run to infinity
     4. When no antiderivative exists: Simpson's rule and quad
  8. M04.8 Sequences, series and Taylor approximation
     1. Sequences and the geometric series
     2. Does the sum settle? Convergence tests
     3. Taylor polynomials
     4. Taylor series and the size of the error
  9. M04.9 Differential equations, a first look
     1. Equations about rates, and slope fields
     2. Exponential growth and decay
     3. Separable equations and the logistic curve
     4. Euler's method: solving by small steps
  10. M04.10 Partial derivatives, a first look
      1. Two inputs, one output: surfaces and contour lines
      2. Partial derivatives: the slope when one input moves
      3. The gradient: the direction of steepest climb
      4. The lowest point of a bowl: the least-squares line
• M05Multivariable and Matrix Calculus● all 10 modules available

  Differentiate functions of many variables and of matrices, and see backpropagation as the chain rule.

  Start the course Course page

  1. M05.1 Functions of several variables and level sets
     1. Many inputs, one or many outputs
     2. Level sets: contour lines and level surfaces
     3. Seeing a function of many inputs: slices along lines and planes
     4. Limits and continuity in several variables
  2. M05.2 Partial derivatives and the gradient
     1. Partial derivatives and the gradient in n variables
     2. Differentiability and the tangent plane
     3. Gradients of losses with many weights
     4. Numerical gradients and gradient checking
  3. M05.3 Directional derivatives and steepest ascent
     1. The directional derivative
     2. Steepest ascent and the gradient's geometry
     3. Steepest depends on how you measure a step
     4. Normals, tangent planes and the distance to a boundary
  4. M05.4 Jacobians and the multivariable chain rule
     1. The Jacobian: the best local linear map
     2. The chain rule through intermediate variables
     3. Composition multiplies Jacobians
     4. The Jacobian determinant and local inverses
  5. M05.5 Hessians, curvature and second-order Taylor
     1. Second partial derivatives and the Hessian
     2. The second-order Taylor model
     3. Minimum, maximum or saddle: the second-derivative test
     4. Curvature of a loss
  6. M05.6 Multiple integrals and change of variables
     1. Double integrals over rectangles
     2. Regions of any shape and the order of integration
     3. Polar coordinates and the Gaussian integral
     4. Change of variables and the Jacobian determinant
  7. M05.7 Matrix calculus identities
     1. Shapes and the first identities
     2. Differentials: the reliable method
     3. Gradients of a dense layer and of softmax with cross-entropy
     4. Determinant, inverse and the log-determinant
  8. M05.8 Computational graphs and automatic differentiation
     1. Programs as computational graphs
     2. Forward mode: tangents and dual numbers
     3. Reverse mode: adjoints and the tape
     4. Forward or reverse: cost and memory
  9. M05.9 Backpropagation as reverse-mode differentiation
     1. Backpropagation is reverse mode on a network
     2. Backpropagation in matrix form for a batch
     3. Checking and debugging backpropagation
     4. Cost, memory and gradient flow through depth
  10. M05.10 Vector fields, divergence and curl
      1. Vector fields and their flow lines
      2. Line integrals and conservative fields
      3. Divergence: sources and sinks
      4. Curl: rotation and Green's theorem
• M06Probability I● all 11 modules available

  Reason about uncertainty with Bayes' rule, distributions and the central limit theorem.

  Start the course Course page

  1. M06.1 Sample spaces, events and axioms
     1. Experiments, outcomes and sample spaces
     2. Events as sets
     3. The three axioms of probability
     4. Rules that follow from the axioms
  2. M06.2 Counting and equally likely outcomes
     1. Equally likely outcomes
     2. Ordered samples and the birthday problem
     3. Unordered samples and binomial coefficients
     4. Drawing without replacement
  3. M06.3 Conditional probability and independence
     1. Conditional probability: shrinking the sample space
     2. The multiplication rule and probability trees
     3. The law of total probability
     4. Independence
  4. M06.4 Bayes' rule
     1. Turning a conditional around
     2. Base rates and frequency grids
     3. Odds, likelihood ratios and updating twice
     4. Many hypotheses: the Bayes table
  5. M06.5 Discrete random variables
     1. A random variable is a function of the outcome
     2. The probability mass function
     3. The cumulative distribution function
     4. Independent random variables and their sums
  6. M06.6 Continuous random variables and densities
     1. From histograms to a density
     2. Probabilities by integration
     3. The CDF, quantiles and sampling
     4. Shift, scale and the normal density
  7. M06.7 Expectation, variance and moments
     1. Expectation: the long-run average
     2. Linearity of expectation
     3. Variance and standard deviation
     4. Standardising and higher moments
  8. M06.8 Common distributions and their stories
     1. Bernoulli and binomial: counting successes
     2. Geometric and exponential: waiting for the first success
     3. Poisson: counting rare events
     4. A map of the families
  9. M06.9 Joint, marginal and conditional distributions
     1. Joint distributions as tables
     2. Marginals: summing out a variable
     3. Conditional distributions and independence
     4. Joint densities
  10. M06.10 Covariance and correlation
      1. Covariance: do they move together?
      2. Rules of covariance and the variance of a sum
      3. Correlation: covariance without units
      4. What correlation does not tell you
  11. M06.11 Law of large numbers and central limit theorem
      1. The sample mean is a random variable
      2. The law of large numbers
      3. The central limit theorem
      4. Using the normal approximation
• M07Probability II: Stochastic Processes○ planned, Ring 3
• M08Optimization○ planned, Ring 3
• M09Information Theory○ planned, Ring 3
• M10Numerical Linear Algebra and Scientific Computing○ planned, Ring 4
• M11Measure, Functional Analysis and High-Dimensional Probability○ planned, Ring 4
• M12Differential Equations and Stochastic Calculus for ML○ planned, Ring 4

Programming and Data8 courses: 2 available, 6 planned

Python, SQL, data handling and engineering habits. Track page

• P01Python from Zero● all 10 modules available

  Write, test and debug your own Python programs, starting from no code at all.

  Start the course Course page

  1. P01.1 How computers run programs
     1. A program is a list of instructions
     2. From source text to running program
     3. Running Python yourself
     4. Bits, bytes and memory
  2. P01.2 Values, variables and types
     1. Values and their types
     2. Names and assignment
     3. Arithmetic and expressions
     4. Comparisons and boolean logic
  3. P01.3 Control flow
     1. Choosing a path: if, elif and else
     2. Repeating with while
     3. Repeating with for and range
     4. Loop patterns: accumulate, count, search
  4. P01.4 Functions and scope
     1. Defining and calling a function
     2. Parameters and arguments
     3. The call stack
     4. Scope: where Python looks up a name
  5. P01.5 Modules, packages and environments
     1. Modules and import
     2. Writing your own module and package
     3. Installing packages with pip
     4. Virtual environments
  6. P01.6 Lists, tuples, dictionaries and sets
     1. Lists: ordered and changeable
     2. Tuples, unpacking and looping in pairs
     3. Dictionaries and sets
     4. Sharing, copying and nesting
  7. P01.7 Strings and files
     1. Strings are sequences of characters
     2. Splitting, joining and formatting
     3. Reading and writing text files
     4. Tables in files: CSV and JSON
  8. P01.8 Errors, debugging and first tests
     1. Reading a traceback
     2. Handling exceptions: try, except and raise
     3. Debugging as a method
     4. First tests
  9. P01.9 Objects and classes
     1. Classes and instances
     2. Methods and state
     3. Special methods: objects that act like built-ins
     4. Inheritance and shared interfaces
  10. P01.10 Iterators, generators and comprehensions
      1. Comprehensions
      2. Iterables and iterators
      3. Generators
      4. Lazy pipelines and functions as arguments
• P02Scientific Python: NumPy, pandas and Plotting● all 9 modules available

  Hold, clean, reshape, summarise and plot real data with NumPy, pandas and Matplotlib.

  Start the course Course page

  1. P02.1 Arrays, shapes and data types
     1. From lists to arrays
     2. Shape, axes and dimensions
     3. Reshaping: same values, new shape
     4. Data types: what one number can hold
  2. P02.2 Broadcasting and vectorization
     1. Vectorisation: the loop moves inside the array
     2. Reductions along an axis
     3. The broadcasting rule
     4. Broadcasting at work: centring and scaling
  3. P02.3 Indexing, slicing and views
     1. Positions and slices
     2. Boolean masks
     3. Picking and ordering with integer arrays
     4. Views and copies
  4. P02.4 DataFrames and Series
     1. A Series: values with labels
     2. A DataFrame: columns that share an index
     3. Selecting rows and columns: loc and iloc
     4. Alignment: labels are matched, not positions
  5. P02.5 Cleaning, reshaping and joining
     1. Reading a file and fixing its types
     2. Missing values and duplicates
     3. Wide to long and back: melt and pivot
     4. Joining tables on a key: merge
  6. P02.6 Group-by and aggregation
     1. Split, apply, combine
     2. Several summaries, several keys
     3. Transform: a group summary on every row
     4. Pivot tables and cross-tabulation
  7. P02.7 Dates, text and categories
     1. Timestamps: dates as numbers
     2. Resampling and rolling windows
     3. Text columns and the str accessor
     4. Categories and encoding them as numbers
  8. P02.8 Plotting with Matplotlib and seaborn
     1. Figure, Axes and a first line plot
     2. Scatter, bar and histogram
     3. Several panels, one style
     4. seaborn: plots from tidy tables
  9. P02.9 Reproducible notebooks
     1. Kernel, cells and hidden state
     2. Randomness you can repeat
     3. Data, paths and versions you can find again
     4. From scratchpad to report
• P03SQL and Databases○ planned, Ring 3
• P04Data Visualization and Communication○ planned, Ring 3
• P05Algorithms and Data Structures for Data Science○ planned, Ring 3
• P06Software Engineering for Data Science○ planned, Ring 3
• P07Data Engineering○ planned, Ring 3
• P08High-Performance and GPU Computing○ planned, Ring 4

Statistics and Data Analysis8 courses: 2 available, 6 planned

Inference, regression, Bayesian methods, causality, time series. Track page

• S01Exploratory Data Analysis● all 8 modules available

  Explore a dataset, describe it, find relationships and spot patterns that mislead.

  Start the course Course page

  1. S01.1 Data types and measurement
     1. Rows, columns and what one row is
     2. Categorical variables: nominal and ordinal
     3. Numerical variables: counts, measurements and scales
     4. Measurement: what a number stands for
  2. S01.2 Sampling and bias
     1. Population, sample and simple random sampling
     2. Two ways to be wrong: sampling variability and bias
     3. Stratified, cluster and systematic sampling
     4. How samples go wrong: selection, non-response and survivorship
  3. S01.3 Center, spread and shape
     1. The mean
     2. The median, quartiles and the five-number summary
     3. Variance and standard deviation
     4. Shape: z-scores, skew, modes and tails
  4. S01.4 Distributions and outliers
     1. Histograms and the choice of bins
     2. The cumulative view: ECDF and quantiles
     3. Anatomy of a boxplot
     4. Outliers: flag, check, decide
  5. S01.5 Relationships between variables
     1. Scatter plots and covariance
     2. Correlation
     3. What a correlation hides: Anscombe's quartet
     4. Comparing groups: when one variable is a category
  6. S01.6 Missing data
     1. Finding what is missing
     2. Why values go missing: MCAR, MAR and MNAR
     3. Dropping rows and columns
     4. Filling in: simple imputation and its price
  7. S01.7 Simpson's paradox and confounding, a first look
     1. A comparison that reverses: Simpson's paradox in a table
     2. Simpson's paradox in a scatter plot
     3. Confounding: a third variable behind both
     4. Split or pool? The numbers alone cannot say
  8. S01.8 An analysis workflow from start to finish
     1. A question, a table and a plan
     2. Audit before you analyse
     3. From single columns to relationships
     4. Report what you found and what you cannot claim
• S02Statistical Inference● all 10 modules available

  Estimate from samples, build confidence intervals and tests, and know what a p-value does and does not say.

  Start the course Course page

  1. S02.1 Populations, samples and sampling distributions
     1. A statistic has a distribution
     2. The standard error
     3. The shape of a sampling distribution
     4. Normal samples: the chi-square and t distributions
  2. S02.2 Point estimation: bias, variance and mean squared error
     1. Estimators and unbiasedness
     2. Variance and efficiency
     3. Mean squared error and consistency
     4. Building estimators: the method of moments
  3. S02.3 Maximum likelihood
     1. The likelihood function
     2. Maximum likelihood for the standard families
     3. Two parameters: the normal likelihood surface
     4. Numerical maximum likelihood and losses as likelihoods
  4. S02.4 Confidence intervals
     1. What a confidence interval promises
     2. The t-interval for a mean
     3. Intervals for a proportion: test-set accuracy
     4. Differences, and choosing n for a margin
  5. S02.5 Hypothesis tests and p-values
     1. The logic of a test
     2. The p-value
     3. Decisions and the two kinds of error
     4. Tests and intervals, significance and importance
  6. S02.6 Power, effect size and sample size
     1. Power
     2. Effect size
     3. Choosing the sample size
     4. Low power and simulated power
  7. S02.7 Common tests: t, chi-square, ANOVA and nonparametric
     1. t-tests: one sample, paired and two samples
     2. Chi-square tests for counts
     3. One-way ANOVA
     4. Rank tests
  8. S02.8 Bootstrap and permutation methods
     1. The bootstrap idea
     2. Bootstrap confidence intervals
     3. Permutation tests
     4. Resampling for machine learning
  9. S02.9 Multiple testing
     1. Why many tests mislead
     2. Controlling the family-wise error: Bonferroni and Holm
     3. The false discovery rate: Benjamini-Hochberg
     4. Multiplicity in practice
  10. S02.10 Likelihood theory: Fisher information and asymptotics
      1. The score and Fisher information
      2. The Cramér-Rao lower bound
      3. Asymptotic normality of the MLE
      4. Wald, score and likelihood-ratio tests
• S03Regression and Linear Models○ planned, Ring 3
• S04Bayesian Statistics○ planned, Ring 3
• S05Experiment Design and A/B Testing○ planned, Ring 3
• S06Causal Inference○ planned, Ring 3
• S07Time Series and Forecasting○ planned, Ring 3
• S08Advanced Statistics○ planned, Ring 4

Machine Learning7 courses: 3 available, 4 planned

Classical ML from the first model to learning theory. Track page

• ML01Machine Learning Foundations● all 10 modules available

  Build, train and honestly evaluate your first machine-learning models from scratch.

  Start the course Course page

  1. ML01.1 What learning from data means
     1. Rules or examples
     2. Features, labels and kinds of learning
     3. A model is a function with knobs
     4. Learning is choosing the knobs
  2. ML01.2 Data splits and the generalization gap
     1. Why testing on the training data lies
     2. Train, validation and test sets
     3. The generalization gap
     4. How splits go wrong
  3. ML01.3 k-nearest neighbors
     1. Classify by your nearest neighbour
     2. k neighbours and a vote
     3. Distance and feature scaling
     4. Regression, cost and many dimensions
  4. ML01.4 Linear regression as a learning algorithm
     1. A line as a model
     2. The best line, solved exactly
     3. Many features
     4. Reading and doubting a fitted line
  5. ML01.5 Gradient descent from scratch
     1. Loss as a landscape
     2. The gradient and the update rule
     3. Choosing the learning rate
     4. Batch, stochastic and mini-batch
  6. ML01.6 Logistic regression and classification
     1. From a line to a probability
     2. The log loss
     3. Training by gradient descent
     4. Decision boundaries and thresholds
  7. ML01.7 Evaluation metrics
     1. Accuracy and the confusion matrix
     2. Precision, recall and F1
     3. ROC and precision-recall curves
     4. Metrics for regression
  8. ML01.8 Overfitting, bias and variance
     1. Too simple and too flexible
     2. Bias and variance
     3. Learning curves
     4. What to do about it
  9. ML01.9 Regularization and validation
     1. Ridge: a price on large weights
     2. Lasso: weights that reach zero
     3. Cross-validation
     4. Tuning without cheating
  10. ML01.10 A full project from raw data to report
      1. Frame the problem and set a baseline
      2. Explore and prepare the data
      3. Train, tune and compare
      4. Analyse errors and write it up
• ML02Supervised Learning: Trees, Ensembles and Kernels● all 11 modules available

  Build and tune trees, forests, boosting, SVMs and kernels, and choose a model for tabular data.

  Start the course Course page

  1. ML02.1 Decision trees
     1. A tree is a list of questions
     2. Impurity: Gini and entropy
     3. Growing a tree greedily
     4. Pruning and the instability of a single tree
  2. ML02.2 Bagging and random forests
     1. Why averaging helps
     2. Bootstrap aggregating
     3. Random forests: decorrelating the trees
     4. Out-of-bag error and feature importance
  3. ML02.3 AdaBoost
     1. Weak learners that take turns
     2. The AdaBoost algorithm, step by step
     3. AdaBoost minimises exponential loss
     4. AdaBoost in practice
  4. ML02.4 Gradient boosting
     1. Fitting the residuals
     2. Gradient descent in function space
     3. Gradient boosting for classification
     4. Shrinkage, subsampling and early stopping
  5. ML02.5 XGBoost, LightGBM and CatBoost
     1. Second-order boosting: the XGBoost objective
     2. Histograms and leaf-wise growth: LightGBM's ideas
     3. Categorical features without leakage: CatBoost's ideas
     4. The three libraries side by side
  6. ML02.6 Naive Bayes and generative classifiers
     1. Generative and discriminative classifiers
     2. The naive assumption and Bernoulli naive Bayes
     3. Multinomial naive Bayes for text
     4. Gaussian naive Bayes and when the assumption hurts
  7. ML02.7 Maximum margin and support vector machines
     1. The widest street
     2. The hard-margin problem and its dual
     3. Soft margins and the hinge loss
     4. Linear SVMs in practice
  8. ML02.8 The kernel trick
     1. Lifting data until a line works
     2. Kernels: dot products without the map
     3. Kernel SVMs
     4. Kernels beyond the SVM
  9. ML02.9 Discriminant analysis
     1. Classes as Gaussian clouds
     2. Linear discriminant analysis
     3. Quadratic discriminant analysis and shrinkage
     4. Fisher's discriminant and reducing dimension
  10. ML02.10 Multi-class, multi-label and ordinal problems
      1. Many classes at once: softmax regression
      2. One-vs-rest, one-vs-one and output codes
      3. Multi-label: several labels per example
      4. Ordinal targets
  11. ML02.11 Choosing a model for tabular data
      1. Every model makes an assumption
      2. Matching the model to the data
      3. A fair comparison
      4. Case study: the diabetes project revisited
• ML03Unsupervised Learning● all 10 modules available

  Find structure without labels: clusters, mixtures, embeddings, topics and anomalies.

  Start the course Course page

  1. ML03.1 k-means and how it fails
     1. Clustering as an objective
     2. Lloyd's algorithm
     3. Starting well and choosing K
     4. How k-means fails
  2. ML03.2 Hierarchical clustering
     1. Merging from the bottom up
     2. Linkage: what closest means
     3. Cutting the dendrogram
     4. Single linkage, spanning trees and large data
  3. ML03.3 Density-based clustering
     1. Clusters as dense regions: DBSCAN
     2. Choosing eps and min_samples
     3. Many densities at once: OPTICS
     4. HDBSCAN
  4. ML03.4 Gaussian mixtures and the EM algorithm
     1. A mixture of Gaussians
     2. The EM algorithm, step by step
     3. Why EM climbs
     4. Gaussian mixtures in the plane
  5. ML03.5 PCA in depth
     1. PCA as compression and as a preprocessing step
     2. Whitening and PCA from distances
     3. Probabilistic PCA and factor analysis
     4. Kernel PCA
  6. ML03.6 Manifold learning: t-SNE and UMAP
     1. Neighbourhood graphs and spectral embedding
     2. From SNE to t-SNE
     3. t-SNE in practice, and how to read it
     4. UMAP
  7. ML03.7 Matrix factorization and topic models
     1. Data as a product of two thin matrices
     2. Non-negative matrix factorisation
     3. Topics as mixtures: probabilistic LSA
     4. Latent Dirichlet allocation
  8. ML03.8 Density estimation
     1. From histograms to kernel density estimates
     2. Choosing the bandwidth
     3. Densities in several dimensions
     4. Mean shift: clustering by climbing the density
  9. ML03.9 Anomaly detection
     1. What makes a point anomalous
     2. Local outlier factor
     3. Isolation forests
     4. Reconstruction, boundaries and judging detectors
  10. ML03.10 Evaluating clusters and embeddings
      1. Internal indices: the silhouette and its relatives
      2. External indices: comparing with known groups
      3. Is there any structure? Stability and the gap statistic
      4. Evaluating embeddings
• ML04Model Development and Evaluation in Practice○ planned, Ring 3
• ML05Probabilistic Machine Learning○ planned, Ring 3
• ML06Statistical Learning Theory○ planned, Ring 4
• ML07Learning in Special Settings○ planned, Ring 3

Deep Learning10 courses: 1 available, 9 planned

Neural networks through generative models and theory. Track page

• DL01Neural Network Foundations● all 10 modules available

  Build neural networks from single neurons up, by hand and in NumPy, then train them in PyTorch.

  Start the course Course page

  1. DL01.1 From linear models to neurons
     1. A neuron is a linear model with a squashing step
     2. The perceptron and its learning rule
     3. A layer of neurons
     4. What one layer cannot do
  2. DL01.2 Multilayer perceptrons and universal approximation
     1. A hidden layer solves XOR
     2. The multilayer perceptron and its forward pass
     3. Universal approximation
     4. Depth folds the input space
  3. DL01.3 Activation functions
     1. Sigmoid and tanh
     2. ReLU and its relatives
     3. Smooth gates: softplus, GELU and SiLU
     4. Choosing an activation
  4. DL01.4 Loss functions and maximum likelihood
     1. Regression losses as noise models
     2. Binary cross-entropy from the Bernoulli
     3. Softmax and categorical cross-entropy
     4. The loss surface of a network
  5. DL01.5 Backpropagation by hand
     1. One example, every number
     2. Layers as modules with forward and backward
     3. Branches, sums and shared weights
     4. Training the hand-built network
  6. DL01.6 Build an autodiff engine from scratch
     1. From scalars to tensors
     2. Matrix products, reductions and broadcasting
     3. Parameters, modules and an optimizer
     4. Train with your engine and check it
  7. DL01.7 PyTorch fundamentals
     1. Tensors
     2. Autograd
     3. nn.Module and layers
     4. Losses and optimizers as objects
  8. DL01.8 Anatomy of a training loop
     1. The five lines
     2. Epochs, validation and the two modes
     3. First checks when training fails
     4. Checkpoints and a reusable fit function
  9. DL01.9 Datasets, loaders and batching
     1. A dataset is something you can index
     2. Batching from scratch, then DataLoader
     3. Batch size and the noise of a gradient
     4. Splits, stratification and samplers
  10. DL01.10 First project: an image classifier
      1. Frame the task and set the bar
      2. Train the network
      3. Test once and study the errors
      4. What the network learned, and what it cannot see
• DL02Training Deep Networks○ planned, Ring 2
• DL03Convolutional Networks○ planned, Ring 2
• DL04Sequence Models○ planned, Ring 2
• DL05Transformers○ planned, Ring 2
• DL06Generative Models I○ planned, Ring 3
• DL07Generative Models II: Diffusion and Flow Matching○ planned, Ring 4
• DL08Representation and Self-Supervised Learning○ planned, Ring 3
• DL09Graph and Geometric Deep Learning○ planned, Ring 4
• DL10Deep Learning Theory and Frontiers○ planned, Ring 4

Reinforcement Learning7 courses: 1 partly available, 6 planned

Bandits through RL for language models. Track page

• RL01RL Foundations◐ 1 of 9 modules available

  Model decisions as an agent acting in a world, and solve them with Bellman equations.

  Start the course Course page

  1. RL01.1 The agent and environment loop (planned)
  2. RL01.2 Multi-armed bandits (planned)
  3. RL01.3 Exploration: epsilon-greedy, UCB and Thompson sampling (planned)
  4. RL01.4 Markov decision processes (planned)
  5. RL01.5 Returns, discounting and value functions (planned)
  6. RL01.6 Bellman equations
     1. Value now is reward plus value next
     2. The Bellman expectation equation
     3. The Bellman optimality equation
     4. Bellman backups as operators
  7. RL01.7 Policy evaluation (planned)
  8. RL01.8 Policy iteration and value iteration (planned)
  9. RL01.9 Contextual bandits (planned)
• RL02Tabular Model-Free RL○ planned, Ring 2
• RL03Deep Value-Based RL○ planned, Ring 3
• RL04Policy Gradient and Actor-Critic○ planned, Ring 3
• RL05Model-Based RL and Planning○ planned, Ring 4
• RL06Advanced RL○ planned, Ring 4
• RL07RL for Language Models and Real Systems○ planned, Ring 4

Applied AI9 courses: 9 planned

NLP, LLMs, agents, vision, speech, recommenders and classical AI. Track page

• A01Natural Language Processing Foundations○ planned, Ring 3
• A02Large Language Models○ planned, Ring 3
• A03LLM Applications: Retrieval, Tools and Agents○ planned, Ring 3
• A04Computer Vision○ planned, Ring 3
• A05Speech and Audio○ planned, Ring 3
• A06Recommender Systems and Search○ planned, Ring 3
• A07Multimodal Models, World Models and Embodied AI○ planned, Ring 4
• A08Domain Casebooks○ planned, Ring 3
• A09Classical AI: Search, Logic and Planning○ planned, Ring 3

ML Engineering5 courses: 5 planned

Designing, deploying, monitoring and scaling ML systems. Track page

• E01ML System Design○ planned, Ring 3
• E02MLOps○ planned, Ring 3
• E03Model Optimization and Serving○ planned, Ring 3
• E04Large-Scale Training Systems○ planned, Ring 4
• E05Data-Centric AI○ planned, Ring 3

Responsible AI4 courses: 4 planned

Fairness, interpretability, privacy, safety. Track page

• R01Ethics, Fairness and Bias○ planned, Ring 3
• R02Interpretability and Explainability○ planned, Ring 3
• R03Privacy, Security and Robustness○ planned, Ring 3
• R04AI Safety and Governance○ planned, Ring 4

Capstones and Research Practice3 courses: 3 planned

Projects, paper reproduction, research writing. Track page

• C01Guided Project Ladder○ planned, Ring 3
• C02Paper Reading and Reproduction○ planned, Ring 4
• C03Research Methods and Scientific Writing○ planned, Ring 4

What every page of the notebook has

A question first

Something worth working out before any definition.

The picture

At least five figures in every new lesson, each drawn to carry one idea.

Every line of working

No step is left for the reader to fill in.

Small real numbers

A worked example you can check with a pencil.

The code

From scratch first, then the library that does it for you.

Check yourself

Recall questions and graded exercises with full solutions.

Full proofs and research notes sit in blocks you can open when you want them. The details are in the style guide.

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