By name: academic-lecture-notes description: Generate comprehensive, publication-quality lecture notes from slide decks or academic papers. Use when the user uploads slides/PDFs from a course and asks for lecture notes, study materials, expanded explanations, "notes from these slides", "help me understand this paper", "create study notes", "write up detailed notes", or any request to convert academic material into learning documents. Also use when the user uploads an academic paper and wants lecture notes, a teaching guide, or a detailed walkthrough of the paper's methodology. Converts sparse slides into self-contained notes with complete mathematical derivations, intuition boxes, and economic interpretations. Ideal for PhD-level economics, finance, and quantitative courses. ALWAYS read this skill before generating any lecture notes.
Academic Lecture Note Generator
Transform slide decks or academic papers into self-contained lecture notes requiring no external references.
Source-Specific Approach
| Source Type | Primary Task |
|---|---|
| Slides | Expand sparse content: fill in skipped steps, add context, complete derivations |
| Papers | Restructure for pedagogy: add intuition boxes, fill proof gaps, reorder for learning progression |
Papers often have more prose but still skip "routine" steps and assume reader expertise. Treat paper proofs the same way: show every step, add intuition, include economic interpretation.
Core Objectives
- Complete derivations — Never skip mathematical steps
- Dual presentation — Rigor AND intuition for every concept
- Self-contained — No "see textbook" references; include everything
- Pedagogical depth — 3-5x longer than original slides
Output Format
ALWAYS output LaTeX (.tex file). NEVER create docx files for lecture notes.
LaTeX is required because:
- Proper theorem/proof environments
- Colored tcolorbox for intuition/warning/interpretation boxes
- Equation numbering and cross-referencing
- Professional mathematical typesetting
Compile the .tex to PDF and provide both files.
Document Structure
Front Matter
- Title page with source attribution
- Hierarchical table of contents (3+ levels deep)
- Notation table if symbols are reused
For Each Major Topic
A. Definitions (numbered as Definition X.Y)
- Complete mathematical notation
- Immediately followed by Intuition Box (blue): plain language, analogies, examples
B. Theorems/Propositions (numbered as Theorem X.Y)
- Full statement with all conditions
- Complete step-by-step proof:
- Number each step (Step 1, Step 2, ...)
- Show ALL intermediate calculations
- Cite every theorem/property used
- Number equations for reference
- Never write "clearly" or "it is easy to show" — SHOW it
- End with □
- Economic Interpretation Box (green): practical meaning, why it matters
C. Examples (numbered as Example X.Y)
- Fully worked solutions
- Highlight key insights
- Connect back to theory
Pedagogical Enhancement Boxes
| Box Type | Color | Purpose |
|---|---|---|
| Intuition | Blue | Plain language, analogies, "think of it like..." |
| Warning | Red | Common mistakes, caveats, technical gotchas |
| Economic Interpretation | Green | Financial meaning, practical applications |
Content Expansion Rules
| Slides Have | Lecture Notes Should Have |
|---|---|
| Brief bullet points | Full paragraphs with context, motivation, implications |
| Abbreviated math | Complete derivations with every algebraic step |
| Theorem statement only | Full rigorous proof broken into logical steps |
| "Example: ..." | Fully worked example with strategy explanation |
| "See textbook" | Self-contained summary of that material |
Mathematical Rigor Standards
Proofs Must Include
- All algebraic steps (never skip manipulations)
- Justifications citing each theorem/property
- Intermediate results and verification
- Equation numbering for cross-reference
- Edge cases and boundary conditions
For Complex Derivations
- Break into sub-steps (Step 1.1, 1.2, etc.)
- Add "Verification" sub-sections when helpful
- Consider multiple proof approaches if illuminating
Writing Style
- Voice: "We" for proofs, guiding the reader through
- Signposting: "We will show that...", "The key insight is..."
- Transitions: Explicit connections between topics
- Repetition: Strategic repetition of key ideas is good
- Pace: Slower than slides, full explanations
Forbidden Phrases
Never use without providing the proof:
- "It is easy to show..."
- "Clearly..."
- "Obviously..."
- "By inspection..."
- "It follows immediately..."
LaTeX Setup
See references/latex-templates.md for:
- Complete preamble with theorem environments
- Box definitions (tcolorbox)
- Section templates for theorems, proofs, examples
Workflow
- Analyze slides to identify: definitions, theorems, examples, gaps
- Create document structure with numbered sections
- Expand each element following the rules above
- Add intuition boxes after every definition
- Add economic interpretation boxes after major results
- Include worked examples for each major concept
- Verify: no steps skipped, all notation defined, complete proofs
Quality Checklist
Before finalizing:
- Every theorem has a COMPLETE proof (no steps omitted)
- Every definition has an intuition box
- Every major result has an economic interpretation
- All notation defined before first use
- All equations numbered and referenced
- At least one worked example per major concept
- No forbidden phrases without accompanying proof
- Technical assumptions stated explicitly