Stage Handouts

All 16 stages of Year 1 fall are published. Each handout is complete and studyable on its own: maths text + programming text + skill card + cognitive science link + homework + self-assessment.

Every piece of code and every mathematical result in these handouts was actually run and verified. Running ~/miniconda3/bin/python 验证.py re-checks all of it in one pass (code-block rendering, link reachability, no hard-coded paths, per-module self-checks, handout structure).

Mistakes that only running the code exposed (all fixed):
· Stage 1: the convergence rate of (1+1/n)ⁿ was initially wrong (at n=50 it is 2.69, not close to e)
· Stage 3: the claim that "the error grows when h is very small" does not hold at f(x₀)=0 — the precondition was missing
· Stage 6: pow was treated as positional-only; in fact it accepts keyword arguments
· Stage 3: "concave" was used for the f″<0 learning curve, contradicting the Tongji convention (f″<0 is convex) — reworded to describe the shape
· Stages 2, 5, 8: \|x\| rendered as a double bar ‖x‖ instead of the absolute value |x| — changed to \lvert x\rvert
· Stage 12: the comment on a.mean_rt is b.mean_rt was backwards — it is actually False (bound methods are recreated on every access)
· Stage 9: sympify("x**5") produced a symbol different from the declared one, so an integral check passed falsely — caught by actually running it