[A7med7x7]

Exam phase 4c, part 2 (docs/exams.md): 63 new Computational Mathematics questions.

Stacked on #66 → #63 → #62 → #59 → #58 → #53. This PR targets #66's branch, so the diff shows only this part.

Why this course

It had the biggest gap in phase 4c: 28 questions for 23 taught lessons, all from the four module quizzes, and none for the 4-lesson "Signals From Zero" project. It now has 91, about 4 per lesson, and the project module appears in exams for the first time.

What's in it

Every new question sets lesson and section, so "Re-read" links go to the exact heading. They avoid repeating the 28 existing quiz questions.

• Matrices: adding sizes, scalar multiplication, indexing, the dot product, the outer product's size, (Aᵀ)ᵀ, AB ≠ BA with a worked pair, the identity, why the product rule has its shape, Kronecker order and definition, the 1-norm and Frobenius norm and trace of one matrix, the norm axioms, diag's two jobs, triangular determinants, zeros(3, 2), a 2×2 inverse, a singular matrix, det(2A) = 8·det(A).
• Polynomials: roots, polyvalm vs polyval, degree from the coefficient count, conv, deconv, polyder, polyfit as least squares, residue in both directions.
• Number theory: the division algorithm with a negative dividend, a gcd by Euclid, divisibility of sums, when you may cancel mod n (with a counterexample), reducing early, congruence, trial division to √n, the sieve, Wilson, Fermat, φ(13) and φ(36), a primitive root and an order, the inverse of 7 mod 26, why 4 has no inverse mod 6, square-and-multiply, why the naive way fails, a discrete log, the one-way property.
• Cryptography: ciphertext, public-key vs secret-key, stream-cipher XOR, decrypting Caesar, breaking shift ciphers, affine encrypt and decrypt rule, why the affine cipher is weak.
• Signals project: why 44,100 Hz, why averaging removes noise, a moving average as convolution, SNR in dB, the window-size trade-off.

How it was checked

• Every number worked again by script, with fresh inputs rather than the lessons' examples: 1-norm 11, ∞-norm 10, Frobenius √96, trace 3, inverse [2 −1; −5 3], det(2A) = 40, polyvalm → [0 3; 0 3], gcd 18, φ(36) = 12, ord₁₁(3) = 5, 7⁻¹ ≡ 15 (mod 26), 3¹³ ≡ 3 (mod 7), affine HI → RW, SNR ≈ 6.0 dB.
• Claims checked against the lessons: the 1-norm and Frobenius definitions, norm(A) being the 2-norm, A = 0 numbering, Wilson's statement, the sampling rule, the SNR formula.
• Answer positions balanced (16/16/16/15) by swapping the right answer's text into a rotating slot. A temporary test then confirmed 16 known answers still point at the right text, and that no question has duplicate options.
• question-bank.test.ts (every section is a real heading) caught one wrong heading id, now fixed.
• npm run lint (0 errors), tsc, npm run test (54 files, 2,510 tests), npm run build.

What's left of phase 4c

Logic Design 48, Computer Architecture 44, Computer Graphics 32, Theory of Computation 26, Computer Organization 26, Discrete Mathematics 26, Data Structures 20, Microprocessors 18, Computer Networks 9. Algorithm Design is left to the owner's #60.

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