generate-solutions

name	generate-solutions
description	Generate detailed homework solution files (LaTeX PDF + Jupyter notebook) for a given homework .qmd file. Matches the established format from hw_05_06, hw_07_08, hw_09 solutions. Use when a new homework needs solutions or when exercises have been updated.
allowed-tools	["Bash","Read","Edit","Write","Glob","Grep","Agent"]
user-invocable	true

Generate Homework Solutions

Given a homework .qmd file, generate a complete solutions package: a detailed LaTeX PDF and a Jupyter notebook for Python exercises.

Arguments

The user provides either:

• A homework qmd filename (e.g., 25_stat_hypothesis_testing.qmd)
• A lecture number range (e.g., 09 or 07_08)

Step 1: Gather context

1. Read the homework .qmd file to get all exercises, their types (pencil/Python/both), difficulty levels, and exact problem statements.

2. Read the most recent existing solution to match format exactly:

   math/Lectures/stat/hw_*_solutions.tex   (LaTeX format reference)
   math/Lectures/stat/hw_*_solutions.ipynb  (notebook format reference)
   

   Use the newest one as the template. Key conventions to preserve:

   • Same \documentclass, packages, \lstdefinestyle{python} block
   • \section*{Problem NN · Title} with \texorpdfstring
   • \subsection*{Exercise} restating the problem, then \subsection*{Solution}
   • \paragraph{(a)} for subparts
   • \boxed{} for final numerical answers
   • \textbf{Common mistake:} callouts where students typically go wrong
   • Intuitive explanations after computations (italicized)
   • Python code in \begin{lstlisting}[style=python] blocks

3. Read relevant lecture slides (if they exist) to ensure solutions align with the notation and approach used in class.

Step 2: Write the LaTeX solutions

Create math/Lectures/stat/hw_NN_solutions.tex with:

For each problem:

1. Exercise block: restate the problem verbatim from the .qmd
2. Solution block with detailed, step-by-step work:
   • Show every intermediate computation (students are learning)
   • Explain why each step works, not just what to compute
   • Use \boxed{} for final answers
   • Add \textbf{Common mistake:} where students typically err
   • Add \textit{Intuition/interpretation} after key results
   • For Python problems: include code in lstlisting blocks AND say "See the accompanying Jupyter notebook for all code and plots"

Quality checklist:

• Every numerical answer has been verified (run Python to check)
• SE formulas use correct variable (p0 for tests, p_hat for CIs, etc.)
• One-sided vs two-sided is explicitly addressed
• Effect sizes / practical significance mentioned where relevant
• Forward/backward references between related problems

Step 3: Write the Jupyter notebook

Create math/Lectures/stat/hw_NN_solutions.ipynb with:

1. Title cell (markdown): "Homework Solutions: Lecture NN - Topic"
   • note pointing to PDF for analytical solutions
2. Setup cell: imports + Armenian flag colors

   import numpy as np
   from scipy import stats
   import matplotlib.pyplot as plt
   
   RED = '#D90012'
   BLUE = '#0033A0'
   ORANGE = '#F2A800'
   

3. For each Python problem:
   • Markdown cell restating the exercise
   • One code cell per subpart (not one giant cell)
   • Use np.random.seed(509) (course default seed)
   • Plots with Armenian flag colors, clear labels, appropriate titles
   • Print statements explaining results (students read the output)
   • When implementing algorithms (BH, bootstrap, etc.), implement manually FIRST, then verify with library functions

Notebook conventions:

• figsize=(10, 5) for single plots
• figsize=(14, 5) for side-by-side plots
• Histogram: density=True, alpha=0.4, edgecolor='white'
• Reference lines: linestyle='--', linewidth=2
• Legend: fontsize=9 or fontsize=10

Step 4: Verify everything

1. Compile the LaTeX: pdflatex -interaction=nonstopmode FILE.tex

   • Must compile with zero errors
   • Check page count is reasonable (8-12 pages typical)

2. Verify all math with Python: run key computations to confirm numerical answers match what's written in the LaTeX

3. Validate notebook syntax: parse all cells with ast.parse()

Step 5: Link from homework .qmd

Add solution links to the homework page's lecture section:

- [📄 Solutions PDF](Lectures/stat/hw_NN_solutions.pdf), [🐍 Jupyter notebook](Lectures/stat/hw_NN_solutions.ipynb)

Step 6: Report

Tell the user:

• Number of problems solved (pencil vs Python vs both)
• PDF page count
• Any problems that were tricky or where assumptions were needed
• Ask if they want to commit