Complete numpy_vs_numba_vs_jax lecture with timing comparisons

Added comprehensive comparisons between NumPy, Numba, and JAX for both
vectorized and sequential operations:

- Added Numba simple loop and parallel versions for vectorized example
- Demonstrated nested prange parallelization and its limitations
- Added detailed discussion of parallelization overhead and contention issues
- Implemented sequential operation (quadratic map) in both Numba and JAX
- Used JAX lax.scan with @partial(jax.jit, static_argnums) for cleaner code
- Added timing code with separate runs to show compile vs cached performance
- Included educational discussion without specific numbers (machine-independent)
- Added explanation of reduction problem challenges with shared variable updates
- Fixed spelling error: "implict" → "implicit"
- Added missing punctuation

All code examples tested and verified to run successfully.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: jstac

lectures/numpy.md

@@ -919,9 +919,10 @@ Note that the change to `b` has not affected `a`.
 
 
 
-## Additional Functionality
+## Additional Features
+
+Let's look at some other useful features of NumPy.
 
-Let's look at some other useful things we can do with NumPy.
 
 ### Universal Functions
 
@@ -1081,6 +1082,42 @@ We'll cover the SciPy versions in more detail {doc}`soon <scipy>`.
 For a comprehensive list of what's available in NumPy see [this documentation](https://numpy.org/doc/stable/reference/routines.html).
 
 
+### Implicit Multithreading 
+
+[Previously](need_for_speed) we discussed the concept of parallelization via multithreading.
+
+NumPy tries to implement multithreading in much of its compiled code.
+
+Let's look at an example to see this in action.
+
+The next piece of code computes the eigenvalues of a large number of randomly
+generated matrices.
+
+It takes a few seconds to run.
+
+```{code-cell} python3
+n = 20
+m = 1000
+for i in range(n):
+    X = np.random.randn(m, m)
+    λ = np.linalg.eigvals(X)
+```
+
+Now, let's look at the output of the htop system monitor on our machine while
+this code is running:
+
+```{figure} /_static/lecture_specific/parallelization/htop_parallel_npmat.png
+:scale: 80
+```
+
+We can see that 4 of the 8 CPUs are running at full speed.
+
+This is because NumPy's `eigvals` routine neatly splits up the tasks and
+distributes them to different threads.
+
+
+
+
 
 ## Exercises