stage 02 · Foundational
Mathematical Foundations
The mathematical language needed to understand, implement and diagnose learning systems.
5 sections 37 units about 167 h 0/37
Sections
In dependency order
Capstone
Numerical Learning Laboratory (10 to 14 h)
Build a small NumPy project that connects least squares and PCA, reverse-mode differentiation, Monte Carlo uncertainty, experiment analysis and optimizer stability. Each component must include one failure case and one independent check.
Milestone deliverables
- Derivations and assumption notes
- Runnable implementation with tests and raw numerical comparisons
- A short defense of solver, estimator and tolerance choices
Rubric
| Criterion | Pass | Strong |
|---|---|---|
| Least squares and PCA | The linear-algebra project meets Pass on every criterion, with its rank-deficient case and conditioning table runnable from the suite. | The README links the conditioning table to the solver choice in the defense note. |
| Reverse-mode differentiation | The engine and harness pass, and the planted bug fails its directional check. | One command reruns the step-size sweep and the planted-bug test. |
| Monte Carlo uncertainty | Every simulation check in the repository reports its sample count and standard error and uses the stated acceptance rule. | The heavy-tail failure and the drifting-predictive failure are both kept as tests. |
| Experiment analysis | The audit, the rerun and the decision memo are in the repository with the plan that preceded them. | The memo stands on its own for a reader who has not seen the code. |
| Optimizer stability | The optimizer comparison, the divergence diagnosis and the finite-precision failure are reproduced by the suite. | Each prediction sits beside its measurement in the notes. |
| Defense and rebuild | A short defense note justifies each solver, estimator and tolerance choice, and a README lists the commands that rebuild every reported number. | Every component names one failure case and one independent check in the README. |
Capstone hours · 10 to 14
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