T. Mathematical Prerequisites Checklist

Self-assess before Part III; revisit at Part X and Part XVIII starts. Linear algebra (the load-bearing 80%): vector spaces over ℂ; inner products with conjugation; basis and change of basis; linear maps as matrices; matrix multiplication as composition; transpose vs. conjugate-transpose; eigenvalues/eigenvectors; Hermitian and unitary definitions and their consequences; tensor products; trace; projections. Test yourself: compute ⟨ψ|φ⟩ for complex vectors; diagonalize a 2×2 Hermitian by hand; explain why unitary preserves probabilities in one sentence. Complex numbers (Appendix B): polar form, Euler's formula, modulus-and-argument arithmetic. Test: compute |e^{iπ/4}|² and (1+i)·e^{−iπ/2}. Probability (Appendix D): distributions, expectation, variance, conditional, Bayes, sampling error. Test: how many shots to estimate p=0.5 to ±0.01? (~10⁴ — derive it.) Trigonometry/exponentials: sin/cos as circle parameterization; e^{iθ} rotation; small-angle. Logic/proof literacy: implication, contrapositive, induction, proof by contradiction — read Ch. 52.5 with these. Numerics: floating-point roundoff, absolute vs. relative tolerance, why allclose over ==. Gaps found: Part III covers the quantum-relevant versions of all of the above — the checklist tells you which sections to slow down for, not whether you're allowed to continue. Everyone's checklist has gaps; engineers close them en route.