Modernize Numba lecture

[jstac]

Summary

• Modernize and clean up the Numba lecture
• Fix deprecated patterns and improve clarity

Test plan

• Converted to Python via jupytext and executed successfully

🤖 Generated with Claude Code

[jstac]

Detailed list of changes

1. Added nopython mode note — Inserted a {note} directive in the Type Inference section explaining that @jit now defaults to nopython=True (since Numba 0.59), that @njit is an equivalent alias, and that the old silent "object mode" fallback no longer applies.

2. Replaced deprecated numpy.random.randn imports — Removed from numpy.random import randn and replaced bare randn() calls with np.random.randn() in the wealth simulation (h()) and the option pricing exercise (compute_call_price_parallel()).

3. Replaced from random import uniform — Removed the from random import uniform import (which is fragile inside jitted code) and replaced uniform(0, 1) calls with np.random.uniform(0, 1) in both the serial and parallel calculate_pi exercises.

4. Fixed bootstrap example parameter bug — The bootstrap() function used n_resamples from global scope and shadowed its own n parameter with n = len(data). Renamed the parameter from n to n_resamples so the example fails only for the intended reason (unjitted mean function).

5. Replaced deprecated np.int_ — Changed dtype=np.int_ to dtype=np.int64 in the Markov chain exercise (both the hint text and the code). np.int_ is a deprecated NumPy type alias.

6. Added "Caching Compiled Code" subsection — New short section under "Dangers and Limitations" demonstrating @jit(cache=True) to persist compiled code across sessions.

7. Replaced np.maximum with max on scalar — In the option pricing exercise, np.maximum(np.exp(s) - K, 0) was operating on scalars; replaced with the simpler max(np.exp(s) - K, 0).

8. Standardized @jit usage — Replaced @njit with @jit throughout for consistency, since the lecture now explains they are equivalent.

9. Prose cleanup — Streamlined the Overview section, removed the "Compiling Classes" section (jitclass/experimental), and tightened various explanatory paragraphs.

[jstac]

@mmcky please review and merge when ready. no need to publish yet

[github-actions]

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