Pedagogy: reframe 00_introduction to motivation + floating-point hook

[kwlee2025cpp]

Goal

Today 00_introduction/00_introduction.ipynb jumps straight into matplotlib plotting (sine wave) without explaining why learners would use computers to solve mathematical problems. As 06_python_advanced/ takes over the role of teaching libraries (numpy, matplotlib, pandas — see the meta restructure issue), 00_introduction becomes free to focus on motivation.

Scope — 00_introduction/00_introduction.ipynb

Rewrite as a motivational chapter:

• Why use computers to solve math problems?
  • Repeatability and traceability of arithmetic
  • Scale (handle 10⁶ equations or 10⁹ data points; humans can't)
  • Iteration and parameter sweeps that would be impossible by hand
  • Visualization as a thinking tool, not just output
• Brief tour of what nmisp covers (root finding → optimization → integration → ODE → linear algebra)
• A small "hello world" scientific computation that's about the idea, not the syntax — e.g. show how an iterative algorithm converges, with the focus on the convergence story, not the matplotlib API

Scope — 00_introduction/10_floating_point.ipynb (lead-in update)

Lead with the killer motivating example:

2^64 - 1 ≈ 1.8 × 10^19 distinct values can be represented in 64 bits. The number of real numbers in [0, 1] is uncountably infinite. Therefore no finite encoding — including float64 — can represent all reals; what we get is a discrete, finite approximation. This is why 0.1 + 0.2 ≠ 0.3 is normal, not a bug.

The rest of 10_floating_point.ipynb (binary, two's complement, IEEE 754 layout, precision examples) flows naturally from there. No content removal — only re-ordering and an opening hook.

Why

• Anchors the entire course in purpose rather than syntax.
• The reals-are-uncountable hook gives a profound, memorable reason to be careful with floats — independent of any specific gotcha.
• Frees 00_introduction from being a Python tutorial; that role moves to 03_python_basics and 06_python_advanced.

Out of scope

• Library tutorials (numpy, matplotlib, pandas) — move to 06_ (separate issues).
• Python language teaching — lives in 03_ (Pedagogy: split 20_python_review into focused notebooks under 03_python_basics/ #391).

Acceptance

• Rewritten 00_introduction.ipynb runs end-to-end and tells the "why" story before any code.
• 10_floating_point.ipynb opens with the (2^64) vs uncountable-reals hook.
• No deprecated pylab import in either (per Maintenance: migrate pylab → matplotlib.pyplot + numpy across notebooks (33 files) #390).