Learn economics, mathematics and AI alignment one skill at a time
Every lesson teaches one skill with an explanation, a worked example and practice problems generated fresh each time. Spaced reviews bring topics back just before you'd forget them.
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Each course opens with a short placement test. Topics you answer correctly are marked learned, along with everything they build on, so you skip what you already know.
Learn one skill at a time
Read a short explanation, study a worked example, then practise until you get three right. Questions are generated fresh, so practice never repeats.
Review before you forget
Reviews come back at growing intervals, and advanced lessons count as practice for the ones they build on. Mixed quizzes check that it all sticks.
67 courses in one prerequisite graph
A full economics major and the start of graduate study, plus the mathematics, computing, physics and AI alignment it connects to. Topics you learn in one course count in every course that uses them.
Foundations2 courses
Mathematics for Economics
Lines, exponents, logs, derivatives, partial derivatives and constrained optimization, all with economic examples.
Principles of Economics
The Econ 101 sequence: markets, welfare, firms, and the macroeconomy. Start here if you are new.
Core theory & methods3 courses
Intermediate Microeconomics
Calculus-based consumer and producer theory, general equilibrium, game theory, risk and asymmetric information.
Intermediate Macroeconomics
The Solow model, IS–LM and AD–AS, Phillips curves and policy rules, consumption and investment, debt, and the open economy.
Statistics & Econometrics
Probability and inference, then regression from OLS to causal designs: experiments, instruments, difference-in-differences and discontinuities.
Advanced theory9 courses
Game Theory
Non-cooperative game theory beyond the basics: larger games, iterated and weak dominance, symmetric and zero-sum games, correlated equilibrium, game trees, subgame perfection and the folk theorem, and Bayesian games: equilibrium bidding, perfect Bayesian equilibrium and signaling.
Decision Theory
How to choose well under uncertainty: rational preferences, decision rules, the expected-utility axioms, measuring risk aversion, stochastic dominance, the value of information and where EU breaks down.
Social Choice Theory
How groups decide: voting rules and their quirks, Condorcet cycles and agenda power, single-peaked preferences, Arrow and Gibbard–Satterthwaite, welfare criteria, fair division and apportionment.
Cooperative Game Theory
What groups can achieve together and how they should split it: bargaining solutions, alternating offers, coalitions and the core, cost sharing, the Shapley value and power indices.
Mechanism Design
Designing rules so that self-interested people with private information reach good outcomes: incentive compatibility, optimal auctions, VCG and the Clarke tax, screening contracts, and matching markets like the residency match and school choice.
Evolutionary Game Theory
Games played by populations rather than perfectly rational players: evolutionarily stable strategies, hawks and doves, replicator dynamics, basins of attraction and risk dominance, learning rules, and how cooperation evolves.
Advanced Microeconomics
Graduate microeconomic theory: excess demand and Walras' law, stability and uniqueness of equilibrium, contingent commodities and efficient risk sharing, aggregation and the representative consumer, the Slutsky matrix, the profit function, monotone comparative statics, principal–agent contracts with risk aversion, linear contracts and Bayesian persuasion.
Advanced Macroeconomics
Graduate macroeconomics: log-linearization and the speed of convergence, the real business cycle model and its calibration, Blanchard–Kahn determinacy, undetermined coefficients, the Taylor principle and Calvo pricing, the Diamond–Mortensen–Pissarides search model, precautionary saving and incomplete markets, tax smoothing, the Friedman rule, Schumpeterian growth and the intertemporal current account.
Asset Pricing
The theory of asset prices: state prices and complete markets, no arbitrage and risk-neutral pricing, the stochastic discount factor, consumption-based asset pricing, the Lucas tree, the equity premium puzzle and the Hansen–Jagannathan bound, mean–variance portfolios with many assets, arbitrage pricing theory, the Merton credit model and growth-optimal portfolios.
Advanced methods7 courses
Real Analysis
The mathematics behind rigorous economic theory: logic and proof, suprema and completeness, sequences and series, continuity, compactness and the extreme value theorem, metric spaces, convexity, separating hyperplanes, contraction mappings and the fixed-point theorems that prove equilibria exist.
Linear Algebra & Dynamics
The linear algebra behind modern economics: independence and rank, eigenvalues and eigenvectors, matrix powers, definiteness of quadratic forms, Markov chains, input–output analysis, systems of difference and differential equations, saddle paths, and linear programming with duality.
Dynamic Optimization
Optimizing over time, the core method of modern macroeconomics: multi-period choice, the Bellman equation, value function iteration, stochastic dynamic programming, job search and investment under uncertainty, continuous-time discounting, the Hamiltonian, the Keynes–Ramsey rule, the Ramsey–Cass–Koopmans model and Tobin's q.
Probability Theory
The probability and statistical theory underneath econometrics: probability spaces and counting, densities and expectations by integration, exponential, order-statistic, bivariate normal, truncated normal and extreme-value distributions, moment generating functions, transformations, bias and MSE, convergence and the law of large numbers, the delta method, Fisher information, conjugate priors and normal shrinkage, Brownian motion and Itô's lemma.
Advanced Econometrics
Econometrics at the level of a first graduate course: OLS in matrix form, projections and Frisch–Waugh–Lovell, the variance matrix and GLS, consistency and asymptotic bias, method of moments and GMM, Wald, LR and LM tests, maximum-likelihood logit, the bootstrap, quantile and kernel regression.
Time Series Econometrics
Modeling data that arrive over time: autocorrelation, MA and ARMA processes, AR(2) dynamics and stationarity, forecast uncertainty, unit roots and Dickey–Fuller tests, cointegration and error correction, vector autoregressions, impulse responses, structural identification, variance decompositions, GARCH volatility, HAC standard errors and the Kalman filter.
Microeconometrics
Econometrics for individual and firm data: random utility and multinomial logit, IIA and welfare measurement, Tobit and Heckman selection models, the Roy model, count and duration models, random effects and the Hausman test, dynamic panels, ridge and LASSO, and double machine learning.
Field courses13 courses
International Economics
Why countries trade and how much they gain, what tariffs and quotas do, and how exchange rates, interest parity and the balance of payments fit together.
Public Economics
How taxes should be designed, when governments should spend, and how to measure and reduce inequality and poverty.
Labor Economics
Labor demand and supply, monopsony and minimum wages, human capital, wage gaps, and job search.
Industrial Organization
How firms compete when markets aren't perfect: concentration, oligopoly models, collusion, pricing strategy, antitrust and logit demand estimation.
Money, Banking & Finance
Bond pricing and the yield curve, risk and diversification, the CAPM, stock and option valuation, and how banks work and fail.
Behavioral Economics
Where people depart from the textbook model: present bias, loss aversion, probability weighting, heuristics, fairness and nudges.
Environmental Economics
Efficient pollution, carbon taxes versus cap-and-trade, discounting climate damage, and managing fisheries and exhaustible resources.
Development Economics
Why some countries are rich and others poor: Malthusian traps, convergence, migration, credit, institutions and evaluating programs.
Urban Economics
Why people and firms cluster in cities, how land rents and land use vary across space, how housing markets work, and the economics of zoning, rent control, property taxes, congestion and segregation.
Health Economics
Why health care markets are different: health as capital, the demand for medical care, cost sharing and moral hazard, risk adjustment, paying doctors and hospitals, cost-effectiveness and QALYs, drug pricing and rising spending.
Law & Economics
Legal rules as incentives: property rights, Coase and transaction costs, property versus liability rules, negligence and strict liability, efficient breach and contract damages, the economics of crime, and why most lawsuits settle.
Economic History
How the world got rich and what went wrong along the way: growth before and after the Industrial Revolution, the Great Divergence, the gold standard and Great Depression, Bretton Woods, the Great Inflation and Moderation, two great crises, globalization and China's rise.
History of Economic Thought
Where economic ideas came from: mercantilists and physiocrats, Smith, Ricardo, Malthus, Mill and Marx, the marginal revolution, Marshall, Pigou and Pareto, Keynes, Hayek, Friedman, Lucas and the modern synthesis.
Mathematics & computing12 courses
Complex Numbers & Transforms
The mathematics of oscillation and signals: trigonometry and radians, derivatives of sine and cosine, complex numbers, Euler's formula, roots of unity, complex eigenvalues, second-order linear differential equations, Fourier series, the discrete Fourier transform, convolution and the Laplace transform.
Multivariable Calculus
Calculus in many dimensions, as used in machine learning and physics: gradients and directional derivatives, Jacobians and the chain rule, second-order Taylor expansions, big-O notation, multiple integrals and change of variables, the Gaussian integral, geometry of high dimensions, the implicit function theorem, Laplace's method, Stirling's formula, divergence and line integrals.
Advanced Linear Algebra
The linear algebra of machine learning and physics: null spaces and rank–nullity, orthogonal projections and Gram–Schmidt, orthogonal matrices, trace and determinant, the spectral theorem, the singular value decomposition, low-rank approximation, PCA, norms and conditioning, matrix calculus, einsum index notation, the matrix exponential and the multivariate normal.
Measure & Integration
The rigorous foundation of probability: σ-algebras and measures, Lebesgue measure and null sets, measurable functions and the Lebesgue integral, monotone and dominated convergence, modes of convergence, Fubini's theorem, densities and the Radon–Nikodym theorem, conditional expectation, measures on infinite sequences and martingales.
Information Theory
Shannon's theory of information: surprisal and entropy, joint and conditional entropy, mutual information, KL divergence and cross-entropy (the loss behind most of machine learning), the data-processing and Pinsker inequalities, maximum entropy, differential entropy, prefix codes and the source coding theorem, Huffman codes, typical sequences, channel capacity, the channel coding theorem and rate–distortion theory.
Theory of Computation
What can be computed, and at what cost: finite automata and regular languages, Turing machines and the Church–Turing thesis, the halting problem and reductions, Kolmogorov complexity, time complexity, P, NP and NP-completeness, PSPACE, randomized algorithms, interactive proofs, one-time pads and pseudorandomness.
Mathematical Logic
Formal logic from truth tables to self-reference: propositional logic and normal forms, first-order logic and its structures, soundness and completeness, Peano arithmetic and Gödel numbering, the incompleteness theorems, the provability predicate, Löb's theorem and the modal logic of provability.
Probabilistic Models & Causality
Structured probability and cause and effect: conditional independence, Bayesian networks and d-separation, exact inference, Markov random fields and Gibbs distributions, latent variables and the EM algorithm, variational inference and the evidence lower bound, causal graphs and interventions, the backdoor adjustment and counterfactuals.
Machine Learning
The foundations of modern machine learning: supervised learning and loss functions, logistic and softmax regression, gradient descent, stochastic gradients, momentum and Adam, convexity and convergence rates, train–validation–test splits, bias and variance, regularization and weight decay, hyperparameters, kernels, Gaussian processes and generalization bounds.
Deep Learning
Neural networks from neurons to transformers: activation functions and multilayer perceptrons, universal approximation, backpropagation and automatic differentiation, initialization and vanishing gradients, normalization and residual connections, convolutional networks, embeddings, attention, the transformer, next-token prediction, compute and memory arithmetic, and fine-tuning with LoRA.
Reinforcement Learning
Learning to act from reward: Markov decision processes, policies and value functions, the Bellman equations and their contraction property, policy and value iteration, temporal-difference learning, Q-learning and stochastic approximation, exploration, policy gradients and actor–critic methods, deriving rewards from preferences, reward shaping, goal misgeneralization and RLHF.
Networks
The mathematics of connected systems: graphs and adjacency matrices, paths and distances, centrality and PageRank, Erdős–Rényi random graphs and the giant component, clustering and small worlds, scale-free networks, threshold cascades, epidemics on networks, and graph Laplacians with consensus dynamics.
Physics & complex systems12 courses
Classical Mechanics
Newtonian physics as the entry point to physics and dynamical systems: kinematics, Newton's laws, work and kinetic energy, potential energy and conservation, momentum and collisions, the harmonic oscillator, damped and driven oscillations and resonance, angular momentum and orbits, and the phase-space view of motion.
Analytical Mechanics
The elegant reformulations of mechanics that underlie modern physics and optimal control: the calculus of variations, the Lagrangian and the principle of least action, generalized coordinates, Noether's theorem, the Legendre transform, Hamilton's equations, Poisson brackets, Liouville's theorem, canonical transformations, action–angle variables and normal modes.
Statistical Physics
How macroscopic behavior emerges from microscopic randomness: temperature, heat and the laws of thermodynamics, heat engines, microstates and Boltzmann entropy, the microcanonical, canonical and grand canonical ensembles, partition functions, free energy and fluctuations, equipartition and the Maxwell–Boltzmann distribution, quantum statistics, the Ising model, mean-field theory, phase transitions, Landauer's principle and fluctuation theorems.
Stochastic Processes
Randomness unfolding in time: classifying Markov chains, stationary distributions and detailed balance, absorption and hitting times, mixing and the spectral gap, the Markov-chain ergodic theorem, hidden Markov models, Markov chain Monte Carlo, the Poisson process, continuous-time chains and queues, branching processes, random walks, stochastic differential equations, the Fokker–Planck equation and Langevin sampling.
Dynamical Systems
The qualitative theory of systems that evolve in time: one-dimensional flows, linear systems in the plane, linearization and stability, predator–prey dynamics, Lyapunov functions, limit cycles, bifurcations including Hopf, the logistic map and period doubling, chaos and Lyapunov exponents, strange attractors, fractal dimension and Poincaré maps.
Ergodic Theory
When do time averages equal space averages? Measure-preserving transformations, Poincaré recurrence and Kac's lemma, ergodicity, Birkhoff's ergodic theorem, mixing, Bernoulli shifts and symbolic dynamics, Kolmogorov–Sinai entropy, the Shannon–McMillan–Breiman theorem, the ergodic hypothesis of statistical mechanics and ergodicity economics.
Control Theory
How to make systems behave: feedback and block diagrams, transfer functions, poles and stability, first- and second-order responses, steady-state error, PID control, state-space models, controllability and observability, pole placement, the linear–quadratic regulator, state estimation and the separation principle, frequency response and stability margins.
Cybernetics
The science of control and communication in animals, machines and organizations: circular causality and feedback, homeostasis, Ashby's law of requisite variety, the good regulator theorem, black boxes and system identification, ultrastability, the information cost of control (Touchette–Lloyd), second-order cybernetics and autopoiesis, and Beer's viable system model.
Agent-Based Modelling
Simulating societies and ecosystems from the bottom up: what agent-based models are, cellular automata and the Game of Life, Schelling's segregation model, flocking, stochastic epidemics, percolation, the El Farol bar and minority games, zero-intelligence traders, exchange models of wealth inequality, calibration and validation, and emergence.
Multi-Agent Systems
Many interacting learners and decision-makers: agents and environments, stochastic (Markov) games, no-regret learning and multiplicative weights, multi-agent reinforcement learning, consensus and distributed averaging, task allocation by auction, coalition formation, communication and signaling, social dilemmas among agents, and mean-field games.
Information-Theoretic Bounded Rationality
Decision-making with limited information-processing resources: the free-energy (KL-regularized) principle of choice, free energy as a certainty equivalent, rationality as inverse temperature, rational inattention, the Blahut–Arimoto algorithm, abstraction through information constraints, quantal response equilibrium, KL-regularized and maximum-entropy reinforcement learning, and the sampling cost of deliberation.
Active Inference
The free-energy principle as a theory of perception and action: the Bayesian brain, generative models with A, B, C and D matrices, variational free energy and surprise, perception as inference, predictive coding and precision, Markov blankets, expected free energy with its risk and ambiguity terms, epistemic and pragmatic value, policy selection, learning, and how active inference relates to reinforcement learning and bounded rationality.
AI alignment9 courses
AI Alignment
Why advanced AI might not do what we intend, and what labs do about it: capability trends, alignment targets, outer and inner alignment, specification gaming and Goodhart's law, goal-directedness and deceptive alignment, forecasting risk, the training pipeline, RLHF, constitutional AI and RLVR, reward over-optimization, evaluations, chain-of-thought monitoring, AI control, and reward learning when evaluators see only part of the picture.
Deep Learning Theory
Why deep learning works, and what we can prove about it: approximation and depth, the generalization puzzle, double descent, the implicit bias of gradient descent, optimization in high dimensions, in-context learning, exact dynamics of deep linear networks, conserved quantities, saddle-to-saddle and lazy regimes, the neural tangent kernel, SGD noise, and attributing behavior to training data with leave-one-out, Shapley values, influence functions, Bayesian influence and unrolling.
Singular Learning Theory
Why degeneracy is central to how neural networks learn: the parameter–function map and its symmetries, statistical models and true parameters, the Bayesian posterior and free energy, singular versus regular models, the local learning coefficient via volume scaling, Watanabe's free energy formula, Bayesian phase transitions, estimating the learning coefficient with SGLD, and developmental interpretability.
Physics of Deep Learning
Tools from statistical physics for understanding neural networks: learning as statistical mechanics and partition functions, the Ising perceptron and storage capacity, wide networks as Gaussian processes, signal propagation and the edge of chaos, the constant neural tangent kernel, mean-field scaling and feature learning, μP, grokking, dynamical mean-field theory, empirical and theoretical scaling laws, and the replica method.
Interpretability
Understanding what neural networks compute: features and the linear representation hypothesis, superposition, probes, the residual stream and logit lens, activation patching, circuits and induction heads, sparse autoencoders, automated interpretability and its uses for safety; then condensation, a theory of latent variables that organize information across observations, with its reconstruction and Markov conditions and correspondence theorem.
Computational Mechanics
What a predictor must remember about the past: entropy rate and excess entropy, causal states and ε-machines, statistical complexity, belief states and mixed-state presentations, the geometry of beliefs in the probability simplex, generalized hidden Markov models, and evidence that transformers trained on next-token prediction represent belief-state geometry in their residual streams.
Universal Artificial Intelligence
Idealized prediction and action: Bayesian mixture predictors over hypothesis classes, dominance and cumulative error bounds, the Solomonoff prior as a formal Occam's razor, Pinsker-based prediction bounds, Pareto optimality and misspecification, history-based reinforcement learning, the AIXI agent and its expectimax form, on-policy value convergence, and the limits of AIXI as a model of real agents.
Agent Foundations
The theory of agents that are part of the world they act in: embedded agency and Vingean reflection, robustness to optimization pressure, optimization as entropy reduction and its thermodynamic costs, Maxwell's demon and the information cost of steering, causal, evidential and functional decision theory, program equilibrium and Löbian cooperation, commitment races and safe Pareto improvements, formal power-seeking and instrumental convergence, world models and natural abstractions.
Safety Guarantees & Their Limits
What can and can't be guaranteed about powerful AI: scalable oversight, proof checking, AI safety via debate and its complexity theory (debate = PSPACE, cross-examination), obfuscated arguments and prover–estimator debate, safety cases, steganography in model outputs, perfect versus computational undetectability, undetectable backdoors, and compact proofs of model performance as worst-case interpretability.
Your first month is free
$9 / month after that
- All 67 courses and 1,708 lessons
- Placement tests, spaced reviews and mixed quizzes
- Progress saved to your account on every device
- No card needed for the trial, and you can cancel any time
Questions
Do I need a card to start?
No. Your first month is free with full access to every course, and you only enter payment details if you decide to subscribe.
What happens when the free month ends?
Lessons lock until you subscribe. Your progress stays saved, so you pick up exactly where you left off.
If I subscribe during the trial, do I lose the rest of it?
No. Your first payment is taken when your free month ends.
Can I cancel?
Yes, any time from your account page. You keep access until the end of the period you've paid for.
Where is my progress stored?
In your account, so it follows you to any device you sign in on.
What background do I need?
None for the foundation courses. Every course starts with an optional placement test, and anything you're missing from another course is pulled in as a lesson before you need it.