Math · Index

How to use: read the original notes first to build the frame (20–30 minutes each) → then take an open course for systematic study → go deeper with the downloaded PDFs → the code in the notes runs in the Jupyter environment under 数学工具/.

Verified (2026-09-10): all 12 numerical claims pass; several wording problems were corrected at the same time (the condition on the base-rate fallacy, the "non-zero" eigenvalues in SVD, real vs complex equilibria, the approximation in Poisson, the distinction between Markov uniqueness and convergence; also that AAᵀ's zero eigenvalue corresponds to the left null space N(Aᵀ), and that a single action potential is a transient rather than a limit cycle).

Honest limitation: what code can verify is formulas and numbers; terminology conventions (e.g. calling something a "focus" vs a "node") and mathematical proofs cannot be fully checked by computation. These notes are a study aid — for systematic learning, follow the open course and the original textbook.