The mathematics and statistics a university degree teaches, put in the order that makes each subject easier than the last.
This roadmap starts with calculus and linear algebra, then takes two passes at statistics before putting the theory to work in market research, econometrics, experiments and the evaluation of AI models. It finishes with the mathematics underneath machine learning and large language models, and with artificial intelligence as a whole: search, logic, reasoning under uncertainty and learning. Eighteen stages and 200 lessons, each one building on what came before.
Tick lessons off as you finish them and your progress is saved in your browser. Greyed-out lessons are on their way, and “Show published only” hides them.
datalad roadmap
University
200 steps from calculus to large language models and artificial intelligence. The theory first, then the subjects that put it to work.
18 stages195 lessons34 published so far6 subjects, one route
Before you start
Practice and reference
5 resourcesKeep these open while you work. The practice engine generates fresh exam-style questions, the workbooks carry full solutions, and the glossaries are there for when a lesson uses a word you have not met.
Maths and statistics practice
Unlimited exam-style questions, generated fresh every time you ask
Workbooks with full solutions
Every workbook in one place, ten exercises each with worked answers
Glossary: statistics
148 terms from ANOVA to Z-Test
Glossary: calculus and linear algebra
113 terms from Antiderivative to Zero Vector
Glossary: machine learning
175 terms from AUC to Zero-Shot Learning, for the machine learning and AI stages
The curriculum
Theory first, then the subjects that use it
18 stagesMathematics comes first, then two passes at statistics, then the subjects that put them to work. Market research sits after the statistics rather than first, because its analysis half needs ANOVA, regression and logit. The last four stages step back to artificial intelligence as a whole.
01
0 of 7 steps done
Sets, functions, equations and graphs
ArticleWorkbook
Functions and differentiation
ArticleWorkbook
Exponential and logarithmic functions
ArticleWorkbook
One-variable optimisation
ArticleWorkbook
Improper integrals and the gamma and beta functions
ArticleWorkbook
Sequences, series and Taylor expansions
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02
0 of 17 steps done
Functions of several variables
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Multivariate optimisation
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Linear programming and duality
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Multiple integrals and the Jacobian
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Vector spaces, bases and linear transformations
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Vectors, inner products and projections
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Eigenvalues, eigenvectors and the SVD
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Quadratic forms and definite matrices
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Vector calculus: gradients of vectors and matrices
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Tensors and index notation
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Complex numbers
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Difference equations
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Fourier series and transforms
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Numerical methods: Newton’s method and numerical integration
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Graphs and networks
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03
0 of 10 steps done
Counting and combinatorics
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Some ideas underlying causation
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04
0 of 9 steps done
Continuous probability distributions
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Multivariate random variables
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Estimator properties
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Point estimation
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Interval estimation and hypothesis testing
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Analysis of variance (ANOVA)
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Linear regression
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05
0 of 12 steps done
Introduction to market research
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Defining the market research problem
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Research design
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Internal secondary data and analytics
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Qualitative research: focus groups
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Projective techniques
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Survey and quantitative observation techniques
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Causal research design: experimentation
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Measurement and scaling
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Questionnaire design
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Sampling design and procedures
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Determining the sample size
06
0 of 10 steps done
Getting started with SPSS
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Cross-tabulation and hypothesis testing
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Analysis of variance and covariance
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Correlation and regression
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Discriminant analysis
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Logit analysis
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Factor analysis
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Cluster analysis
Conjoint analysis
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Multidimensional scaling
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07
0 of 13 steps done
Probability
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Discrete random variables
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Continuous random variables, expectation and variance
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Moments, transformations and convergence
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Probability inequalities and the law of large numbers
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Multivariate distributions
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Joint moments and independence
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Multivariate transformations
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Sums of random variables and random sums
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Conditional distributions
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Conditional moments
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Hierarchical models
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Markov chains
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08
0 of 20 steps done
Principles of sampling
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Sampling moments and order statistics
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Sampling distributions and point estimation
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Interval estimation
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Hypothesis testing and likelihood
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Score, information and maximum likelihood estimators
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Properties of MLEs and the likelihood ratio test
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Sufficient statistics
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Applications of sufficiency
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Optimal estimators and tests
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Multiple testing and the false discovery rate
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Monte Carlo simulation and variance reduction
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Statistical decision theory: loss, risk and Bayes rules
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Bayesian inference: priors, posteriors and MCMC
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Generalised linear models
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Splines, GAMs and nonparametric regression
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Multilevel and longitudinal models
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Survival analysis: hazards and censoring
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Nonparametric tests and the bootstrap
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Missing data and measurement error
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09
0 of 9 steps done
The nature of econometrics and economic data
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Inference in simple linear regression
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Multiple linear regression, part 1
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Multiple linear regression, part 2
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Inference in multiple linear regression
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Nonlinear regression functions
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Violations of the OLS assumptions
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10
0 of 7 steps done
Panel data
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Binary dependent variables: logit and probit
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Instrumental variables, part 1
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Instrumental variables, part 2
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Regression for experiments and quasi-experiments, part 1
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Regression for experiments and quasi-experiments, part 2
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Double machine learning
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11
0 of 6 steps done
Introduction to time series
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AR, MA and ARMA models
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ADL models, forecasting and model specification
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Unit roots, trends and spurious regression
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Dynamic causal effects
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Volatility models
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12
0 of 13 steps done
The mathematics of A/B testing
Design of experiments: randomisation, blocking and factorial designs
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Evaluation scores as estimates: standard errors and intervals
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Comparing two models on the same items
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Calibration, and scores that are not right or wrong
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Clustered items and the variance they add
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Leaderboards, multiple comparisons and the winner’s curse
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Inter-rater agreement: kappa, Krippendorff’s alpha and ICC
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The LLM judge as a measuring instrument
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pass@k and its unbiased estimator
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Monitoring a metric without peeking
Ranking from pairwise preferences: Bradley-Terry and Elo
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Reporting evaluation results honestly
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13
0 of 15 steps done
Convex optimisation, duality and the KKT conditions
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Empirical risk, regularisation and where loss functions come from
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Gradient descent and continuous optimisation
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Information theory: entropy, cross-entropy and KL divergence
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Supervised learning
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Generative classifiers: naive Bayes and discriminant analysis
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Linear classifiers and the SVM
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Gradient boosting and ensembles
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PCA and k-means
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Gaussian mixtures and the EM algorithm
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Feature engineering
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Model validation
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Hyperparameter search
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Time series machine learning
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Explainable AI: SHAP, LIME and integrated gradients
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14
0 of 22 steps done
Neural networks
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Training deep networks: initialisation, Adam, dropout and batch normalisation
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CNNs and RNNs
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Autoencoders and variational inference
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Generative models: VAEs, GANs and diffusion
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Kolmogorov-Arnold networks
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Embeddings
Rotary position embeddings and long context
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The feed-forward layer and SwiGLU
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Residual connections and the transformer block
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Normalisation: RMSNorm and QK-norm
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Mixture-of-experts routing
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Pretraining and scaling laws
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The KV cache and the arithmetic of inference
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Grouped-query and multi-head latent attention
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Online softmax and FlashAttention
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Sampling and decoding
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Speculative decoding
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Quantisation and LoRA
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RLHF, DPO and GRPO
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Superposition and interpretability
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15
0 of 5 steps done
What AI is: rational agents and their environments
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Uninformed and heuristic search, from breadth-first to A*
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Local search and complex environments
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Adversarial search and games
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Constraint satisfaction problems
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16
0 of 5 steps done
Propositional logic and logical agents
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First-order logic
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Inference in first-order logic
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Knowledge representation
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Automated planning
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17
0 of 7 steps done
Uncertainty, and why an agent needs probability
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Bayesian networks
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Reasoning over time: hidden Markov models and Kalman filters
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Probabilistic programming
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Utility and simple decisions
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Markov decision processes
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Multiagent decisions and game theory
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18
0 of 8 steps done
Learning from examples: decision trees and learning theory
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Bayesian learning of probabilistic models
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Reinforcement learning
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Natural language: n-grams and grammars
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Computer vision
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Robotics
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Philosophy, ethics and safety of AI
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The future of AI
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Article, the main lessonThe blue chips are interactive tools, named individuallyIn Python, the same idea in codeThe math, the derivation underneathWorkbook, exercises with full solutionsGreyed out means not published yet
