By name: math-by-reference-tutor description: Generates a complete maths learning module anchored in physics and/or finance: lecture, tiered exercises, misconception-driven trick questions, Python implementation scaffold with pytest tests, and a compact solution manual. Use when user says "teach me [math topic]", "make a lecture + exercises", "give me practice problems", "ramp up difficulty", "give trick questions", "add coding scaffold + tests", or "make a solution manual", especially when they want physics/finance intuition alongside formal maths.
Math-by-Reference Tutor (Physics + Finance)
Inputs (defaults)
- topic: required
- level: intro | intermediate | advanced (default intermediate)
- track: physics | finance | both (default both)
- num_exercises_per_tier: default 6
- num_trick_questions: default 6
- deps: stdlib + numpy only (unless user explicitly allows more)
If topic is ambiguous, choose the most standard interpretation and note it in README.md as "Assumption: …".
Module bundle
Output these files using === /module/<path> === headers. No code fences around markdown; use code fences for Python files.
/module/README.md
/module/lecture.md
/module/exercises.md
/module/trick_questions.md
/module/solution_manual.md
/module/rubric.md
/module/implementation/scaffold.py
/module/implementation/tests/test_scaffold.py
Anchoring (R1)
Every core idea must be anchored in the selected track(s) using concrete applications, not analogies.
Physics anchors — use at least one of: dimensional analysis, limiting cases, conservation/invariants, geometric meaning, differential equation interpretation.
Finance anchors — use at least one of: no-arbitrage/replication, convexity/monotonicity, conditioning/filtration, tails/stress, optimisation constraints.
Lecture (R2)
Structure: motivation → core definitions → two key properties/theorems (with proof sketches appropriate to level) → worked example(s) per track → failure modes + invariant checks.
Keep concise (~900 words max).
Exercises (R3)
Three tiers (A/B/C) with monotonically increasing difficulty. Each exercise states expected answer format.
Exercise types to mix across tiers: compute, prove/justify, translate (physics↔finance), diagnose (spot errors), approximate (limits/asymptotics), numerics (implement + compare), interpret (domain meaning).
Trick questions (R4)
Each includes the question, "Most people do wrong:" (1 sentence), and "Minimal correction:" (1 sentence). No duplicates; each maps to a distinct failure mode.
Implementation + tests (R5)
scaffold.py: core functions/classes with TODO markers + runnable __main__ demo.
test_scaffold.py: tests that fail before TODOs are completed. Include identity/invariant tests, numerical sanity checks, limit-case tests, and one random property-style test (stdlib random + numpy only, no external property libs). Use pytest.
Solution manual (R6)
Compact (~1200 words max). Include compressed derivations, reusable templates ("if you see X, do Y"), a verification checklist, and a "when to use what" decision guide.
Rubric (R7)
Mastery gates per tier: A = mechanical competence, B = conceptual transfer, C = synthesis/novel problems.
Workflow
- Parse inputs and set defaults.
- Draft prerequisites and scope boundary.
- Build minimal concept order (internal).
- Write lecture.md.
- Write exercises.md.
- Write trick_questions.md.
- Write scaffold.py with TODOs + demo.
- Write test_scaffold.py with fail-first behaviour.
- Write solution_manual.md + rubric.md.
- Emit bundle with path headers.
Complexity bump (when user asks "harder")
Adjust along 1–2 axes only and state them in README.md:
- algebraic complexity
- abstraction/proof depth
- numerical stability
- modelling realism (physics: non-idealities; finance: tails/constraints)
- generalisation (dimension, nonlinearity)
Regenerate only affected files.
Common issues
Topic too broad: pick a standard slice, state it in assumptions, list "next slices."
Prerequisites too advanced for level: add a prereq mini-bridge (≤200 words) at the start of lecture.md.
Tests too confusing: ensure tests fail only at TODO-related points with clear messages indicating what to implement next.
Validation script
Validate a generated module bundle: python scripts/validate_bundle.py