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Computational Physics / The Other Paradigms
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When randomness beats determinism

Every deterministic quadrature rule degrades exponentially with dimension. Monte Carlo error is O(N^-1/2) in any number of dimensions, which eventually makes it the only option.

assumes you already have

Planned outline

  1. The curse of dimensionality, quantified against a grid-based rule.
  2. Why the O(N^-1/2) rate does not depend on dimension at all.
  3. Importance sampling and control variates: reducing the constant, never the rate.
  4. Markov chain Monte Carlo, detailed balance, and Metropolis-Hastings.
  5. Quasi-Monte Carlo: low-discrepancy sequences that beat the square-root rate for smooth integrands.
  6. Where this lives in physics: path integrals, lattice QCD, statistical mechanics.

Interactives planned

Each numbered point above gets at least one thing you can manipulate, not a figure. See AGENTS.md for the widget vocabulary and the rule that every lesson ships at least one graded interaction and one recall card.