Reorganize parallel programming lectures and improve content flow (#429)

* Reorganize parallel programming lectures and improve content flow

Major restructuring of parallelization-related content across lectures to
improve pedagogical flow and consolidate related material.

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

* Complete JAX intro lecture: add pure functions content and fix errors

- Add comprehensive "Random numbers and pure functions" section
- Demonstrate NumPy's impure random number generation vs JAX's pure approach
- Fix spelling errors: discusson→discussion, explict→explicit, parallelizaton→parallelization, hardward→hardware, sleve→sleeve, targetting→targeting
- Fix grammar: "uses use"→"uses", "short that"→"shorter than", "function will"→"functions will", "Prevents"→"Prevent"
- Fix missing jax. prefix in random number examples
- Improve clarity and consistency throughout

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

* Reorganize JAX intro lecture for improved pedagogical flow

Major restructuring:
- Move Functional Programming section earlier (after NumPy Replacement)
- Integrate pure functions discussion into Random Numbers section
- Move "Compiling non-pure functions" into JIT section
- Add smooth transitions between sections

This creates a logical progression: basics → philosophy → features
Readers now understand WHY before seeing HOW, making JAX's design
choices (like explicit random state) more intuitive.

Also fix syntax errors in timer code blocks (missing colons).

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

* Improve lecture flow and reorganize content

This commit includes pedagogical improvements across three lectures:

**numba.md:**
- Improve sentence flow with better transitions
- Change Wikipedia multithreading link to internal reference
- Add "(multithreading)=" label to Multithreaded Loops section
- Remove "Numba will be a key part of our lectures..." sentence
- Add transition phrase "Beyond speed gains from compilation"
- Clarify NumPy arrays "which have well-defined types"
- Change "For example" to "Notably" for better flow
- Add "Conversely" transition for prange vs range comparison

**numpy.md:**
- Add "### Basics" subheading for better organization
- Emphasize "flat" array concept with bold formatting
- Improve shape attribute explanation with inline comments
- Remove np.asarray vs np.array comparison examples
- Remove np.genfromtxt reference, keep only np.loadtxt
- Remove redundant note about zero-based indices
- Improve searchsorted() description formatting
- Remove redundant NumPy function examples (np.sum, np.mean)
- Simplify matrix multiplication section (remove old Python version notes)
- Simplify @ operator examples, remove redundant demonstrations
- Remove manual for-loop equivalent of broadcasting
- Remove higher-dimensional broadcasting code examples
- Remove higher-dimensional ValueError example
- Add "### Mutability" subheading and improve organization
- Change "Vectorized Functions" to "Universal Functions" heading
- Emphasize terminology with bold: **vectorized functions**, **ufuncs**, **universal functions**
- Add note about JAX's np.vectorize
- Remove "Speed Comparisons" section (moved to numpy_vs_numba_vs_jax.md)
- Remove "Implicit Multithreading in NumPy" section (moved to numpy_vs_numba_vs_jax.md)

**numpy_vs_numba_vs_jax.md:**
- Change title from "Parallelization" to "NumPy vs Numba vs JAX"
- Add jax to pip install command
- Add missing imports: random, mpl_toolkits.mplot3d, matplotlib.cm
- Add "### Speed Comparisons" section (moved from numpy.md)
- Add "### Vectorization vs Loops" section (moved from numpy.md)
- Add "### Universal Functions" section (moved from numpy.md)
- Add "### Implicit Multithreading in NumPy" section (moved from numpy.md)
- Change "some examples" to "an example" in multithreading description

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

* Fix grammar and reorganize need_for_speed.md content

- Fix incomplete sentence: add missing word "compiler" (line 229)
- Fix header level inconsistency: change Multi-GPU Servers to #####
- Reorganize Overview section with clearer structure
- Simplify Python's Scientific Ecosystem section
- Restructure "Pure Python is slow" section for better flow
- Add concrete vectorization speed comparison example
- Improve parallelization section organization
- Clarify GPU/TPU accelerator discussion
- Remove redundant content and improve transitions throughout

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

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

* Fix missing random module import in need_for_speed.md

Add missing `import random` statement to fix NameError when running
the vectorization example code that uses random.uniform().

Tested by converting to Python with jupytext and running successfully.

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

* Fix header hierarchy inconsistencies in need_for_speed.md

Changed level 5 headers (#####) to level 4 headers (####) to fix
invalid header hierarchy that was causing build failures.

Fixed headers:
- "GPUs and TPUs"
- "Why TPUs/GPUs Matter"
- "Single GPU Systems"
- "Multi-GPU Servers"

These were incorrectly using ##### (level 5) directly under ### (level 3)
headers, skipping level 4. Now properly using #### headers.

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

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

* 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>

* misc

* Improve formatting and clarity across parallel computing lectures

- Standardize header capitalization in need_for_speed.md
- Update code cell types to ipython3 in numba.md for consistency
- Remove redundant parallelization warning section in numba.md
- Enhance explanatory text and code clarity in numpy_vs_numba_vs_jax.md
- Fix formatting and add missing validation checks

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

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

* misc

---------

Co-authored-by: Claude <noreply@anthropic.com>

Author: jstac

lectures/_static/lecture_specific/need_for_speed/dgx.png

@@ -23,8 +23,8 @@ parts:
   numbered: true
   chapters:
   - file: numba
-  - file: parallelization
   - file: jax_intro
+  - file: numpy_vs_numba_vs_jax
 - caption: Working with Data
   numbered: true
   chapters: