Foundations: the ideas we will not assume

This section is an optional on-ramp for research students and course learners. It does not lower the scientific standard, and it does not assume that seeing a topic in an earlier course means it is ready for use now. It reconnects ideas that are often taught separately: physical models, linear algebra, derivatives, probability, inference, conditioning, and differentiable programs.

Start with Choose your foundations path if you want a short, ungraded route. Read Why this documentation works this way if you want to understand why the site repeatedly asks you to predict, compute, audit, and state only the claim the evidence warrants.

The foundations sequence¶

Choose your foundations path.
Functions, units, and scales.
What is a model?: representations, assumptions, parameters, predictions, information compression, and dimensionality.
Linear algebra as the language of change.
What is a derivative?: change, sensitivity, and scientific evidence.
Probability and distributions.
Models, inference, and information.
Sensitivity, conditioning, and identifiability.
From mathematical relations to differentiable programs.

The established Writing AD-safe scientific numerics module chapters remain the method reference. Foundations explain the connective ideas; module pages explain the algorithms and public APIs.

The recurring scientific habit¶

Every substantial unit follows

predict → compute → audit → state the warranted claim

Prediction names expected structure before results can bias the story. Computation exposes the method that actually ran. Audit compares the output with independent evidence. The final statement is deliberately no stronger than those checks.