Choose your foundations path

This is ungraded and not a placement test. It does not decide whether you belong in a course or research project. Use it to locate the idea that would make today’s work easier, then return whenever you need it.

If you are computation-first¶

You may already write Python and JAX but want the mathematical meaning behind the code. Start with Linear algebra as the language of change and What is a derivative?, then connect control flow to the derivative of the executed program. Ask: what mathematical object does this array represent, and which claim does this transform support?

If astronomy is your strongest language¶

Start with Functions, units, and scales and What is a model?. Newtonian gravity, luminosity, parallax, spectra, and stellar-mass distributions supply familiar physical questions while we make parameter space, probability, and sensitivity explicit. The astronomy is teaching context; the reusable numerical primitive remains science-general.

If statistics and inference are your strongest language¶

Start with Probability and distributions, then Models, inference, and information. Connect a gradient of a log likelihood to the broader meaning of a derivative as a local linear sensitivity. Keep the physical model, measurement model, and inferential assumptions separate.

If you want the complete first-principles path¶

You do not need to identify with a strongest-language category. Read Foundations: the ideas we will not assume, then follow its sequence from functions and models through linear algebra, derivatives, probability, inference, conditioning, and programs.

If you are a returning researcher¶

Choose by the failure you are facing:

• units or scales feel unstable → Functions, units, and scales;

• too many parameters behave alike → Sensitivity, conditioning, and identifiability;

• AD and finite differences disagree → What is a derivative?;

• a precise fit feels scientifically wrong → Models, inference, and information;

• JAX returns a surprising gradient → From mathematical relations to differentiable programs.

A five-minute self-check¶

For your current problem, can you name:

1. the observable and its units;

2. the model inputs, parameters, and state;

3. one limiting case or invariant;

4. the derivative you actually want;

5. an independent audit;

6. the strongest claim those checks would justify?

Any unanswered item is a route, not a verdict. Continue through the complete path above or to How to learn with Jaxstro: predict, compute, audit.