Then he opened his laptop and started writing an email to Maya:
They added it.
The official solutions manual existed. It was a PDF—dry, terse, and filled with answers that looked like this: “Answer: x = 2.374. See section 3.2.” It was useless for learning. It didn't explain why the Newton-Raphson method diverged if you started too far from the root. It didn't show the catastrophic cancellation error in a naive finite difference. It was a cheat sheet, not a teacher. Then he opened his laptop and started writing
Liam did it. His reflection was surprisingly honest: “I thought the manual would save time. But I realized I don’t actually know how to debug a matrix inversion anymore. I just learned to copy-paste.” Then he opened his laptop and started writing