career

• Series: lecture-dp

• File: lectures/career.md

• Audit date: 2026-08-26

• Corpus snapshot: c30490a2f4

• Categories audited: writing, math, code, figures, references, links, admonitions (JAX out of scope)

• Overall score: 8.9 / 10

• Priority: NONE

Score breakdown

Category	Score	One-line note
Writing	8/10	qe-writing-006 ×1; qe-writing-008 ×2.
Math	9.5/10	qe-math-009 ×1.
Code	8.5/10	qe-code-001 ×3.
JAX	out of scope	JAX rules target lecture-jax.
Figures	6.5/10	qe-fig-005 ×6; qe-fig-001 ×5; qe-fig-008 ×3, +1 more.
References	10/10	no mechanical violations detected.
Links	10/10	no mechanical violations detected.
Admonitions	10/10	no mechanical violations detected.

Issues

Critical

None found.

High severity

• [qe-fig-001] — Do not set figure size unless necessary. Count: 5. Lines: 176, 318, 335, 420, 529. Example: figsize=.

• [qe-fig-005] — Descriptive figure names for cross-referencing. Count: 6. Lines: 166, 312, 334, 372, 395, 523. Example: {image} without :name:.

• [qe-writing-006] — Capitalize lecture titles properly. Count: 1. Lines: 60. Example: H3 Title Case: ‘Model Features’ (Features).

Medium severity

• [qe-code-001] (reviewer) — Follow PEP8 unless closer to mathematical notation. Count: 3. Lines: 168, 410, 485. Example: line 485 writes i, j  = qe.random.draw(F), qe.random.draw(G) with two spaces before the = (pycodestyle E221); the identical line at 414 has one. Line 168 np.zeros(n+1) and line 179 list(range(0, n+1)) omit the spaces around + that the rest of the file uses (k + a, n - k + b at 170). Line 410 is the substantive one: inside gen_path the branch reads elif greedy_star[i, j] == 2 - the module-level array - where the sibling branch at 407 reads the optimal_policy parameter, so the function silently ignores its own argument.

• [qe-fig-008] — Use lw=2 for line charts. Count: 3. Lines: 179, 423, 424. Example: plot() without lw=.

• [qe-writing-008] — Remove excessive whitespace between words. Count: 2. Lines: 70, 275. Example: 2 spaces.

Low severity

• [qe-fig-002] — Prefer code-generated figures. Count: 1. Lines: 372. Example: static image .png.

• [qe-math-009] (reviewer) — Choose simplicity in mathematical notation. Count: 1. Lines: 113. Example: the three continuation values are named with Roman numerals - $v(\theta, \epsilon) = \max\{I, II, III\}$ at 113, defined at 121-124, and referred to again at 128 and 219-220. \(I\) is the conventional symbol for an identity matrix, and \(II\) / \(III\) read as products of it. The lecture’s own code writes the same three quantities as v1, v2, v3 (244-246, 259-261), so \(v_1, v_2, v_3\) in the math would be both simpler and a direct match to the implementation.

Strengths

• The three regimes are named once and then labelled identically everywhere: ‘stay put’ / ‘new job’ / ‘new life’ at 81-85, in the interpretation at 128, as ax.text annotations placed inside the policy regions at 341-343, and as the trailing comments on the code branches at 244-246 and 407-413 - so the math, the figure and the code use one vocabulary.

• Only the two real definitions are bold - career at 69 and job at 70 - and the distinction they draw (a career spans many jobs) is exactly what makes the three-option choice set at 78-85 non-obvious, so the bold is doing definitional work rather than decoration.

• Both labelled equations are cited: exw (99) at 107 and eyes (119) at 220, the latter tying the Bellman operator in code back to the display that defines it - no orphan labels and no manual ‘equation (2)’ references.

• The Beta-binomial family is motivated before it is used: pmf at 147-151, a three-line generative interpretation at 155-157, and then a figure at 166-182 that shows what the shape parameters actually do to the mass - so the F_a/F_b/G_a/G_b arguments of CareerWorkerProblem mean something by the time they appear at 196-199.

• Density and CDF case is used correctly throughout: lowercase \(p(k \mid n, a, b)\) for the pmf at 148, uppercase \(F\) and \(G\) for the distributions at 90-91, and F = np.cumsum(cw.F_probs) at 396 is in fact the CDF (qe-math-015 (proposed) clean).

Recommended actions

1. Fix the two defects in gen_path (402-417): line 410 reads the global greedy_star instead of the optimal_policy parameter that line 407 reads, and the parameter t=20 is shadowed by the loop variable at for t in range(t) - the function happens to give the right answer here only because the caller at 422 passes greedy_star.

2. Give the 6 figure sites names and mystnb metadata (166, 312, 334, 372, 395, 523) so the surface plot, the two policy contour plots and the sample-path panel can be cross-referenced (qe-fig-005 x6).

3. Replace the static PNG at 372 with the code that generates it (qe-fig-002) - the solution at 395-429 already draws that exact figure, so the exercise can {ref} the solution’s figure instead of shipping a bitmap.

4. Drop the 5 hand-set figsize= arguments (176, 318, 335, 420, 529) and add lw=2 to the 3 default-width line plots (179, 423, 424) (qe-fig-001 x5, qe-fig-008 x3).

5. Rename the Roman-numeral continuation values to \(v_1\), \(v_2\), \(v_3\) at 113, 121-124, 128 and 219-220, matching the v1/v2/v3 already used in the code.

6. Sentence-case the H3 at line 60 (‘Model features’), and clear the 2 double spaces at 70 and 275 (qe-writing-006 x1, qe-writing-008 x2).

7. Small cleanups: ‘the maximum of {eq}`exw` overall feasible (career, job) policies’ at 107 should read ‘over all’; the \nonumber markers at 123 and 124 do nothing inside an aligned block in a labelled {math} directive; the Axes3D import at 56 is unused with current matplotlib; and even out the operator spacing at 168, 179 and 485.