Skip to content

Foundations I

Use the cards to forage; use the module numbers when following the recommended sequence.

  • 01 / Mathematical reasoning + proof

    Prerequisite: None beyond algebra

    Exit: Own definitions, quantifiers, implication, counterexample, induction, proof structure.

  • 02 / Calculus + vector calculus

    Prerequisite: Algebra/trigonometry + Module 1

    Exit: Own limits, derivatives as local linearization, integrals as accumulation, gradients/Jacobians, line/surface integrals and field theorems.

  • 03 / Linear algebra

    Prerequisite: Modules 1-2 can overlap

    Exit: Own vector spaces, projections, least squares, matrix maps, rank/nullspace, conditioning, SVD/eigenstructure.

  • 04 / ODEs + dynamical systems

    Prerequisite: Modules 2-3

    Exit: Translate changing systems into state equations; solve/analyze equilibria, stability, oscillation, nonlinear behavior and feedback.

  • 05 / Probability

    Prerequisite: Modules 1-3

    Exit: Quantify uncertainty, conditioning, expectation, dependence, transformations, concentration and asymptotics.

  • 06 / Statistics + causal inference

    Prerequisite: Module 5; basic linear algebra

    Exit: Define estimands; separate prediction from intervention; identify confounding/selection/measurement bias; estimate and stress-test effects.

  • 07 / Scientific computing

    Prerequisite: Modules 2-5

    Exit: Know conditioning, numerical stability, approximation, iterative solution, ODE/PDE discretization and computational verification.

  • 08 / Optimization

    Prerequisite: Modules 2-3, 5, 7

    Exit: Formulate objectives/constraints; understand convexity, duality, KKT conditions and numerical optimization; audit objectives.

  • 09 / Information + signals

    Prerequisite: Modules 3, 5, 7

    Exit: Own entropy, mutual information, channel capacity, transforms, sampling, filtering, spectral reasoning and estimation limits.

  • 10 / Control + estimation

    Prerequisite: Modules 3-5, 7-9

    Exit: Design closed loops; analyze stability/robustness; infer hidden state; reason about controllability, observability and tradeoffs.

  • 11 / Metrology + experiments

    Prerequisite: Module 5; runs in parallel from Week 1

    Exit: Calibrate, quantify uncertainty, design informative experiments, distinguish process variation from measurement variation, reproduce results.