Math Model Selector

3. Check for uncertainty

Ask: "Is there randomness or uncertainty involved?"

• Deterministic -> standard analysis
• Epistemic uncertainty -> Bayesian methods
• Random process -> probability theory, stochastic processes

4. Optimization check

Ask: "Are you optimizing something?"

• Convex objective -> linear/quadratic programming
• Non-convex -> gradient descent, evolutionary methods
• Discrete choices -> combinatorics, integer programming

5. Answer precision

Ask: "What level of answer do you need?"

• Rough estimate -> dimensional analysis
• Qualitative behavior -> phase portraits, stability
• Numerical answer -> simulation
• Exact closed form -> analytical methods

Key Questions to Ask

1. What changes? (discrete vs continuous)
2. What causes the change? (rate dependencies)
3. What's random? (uncertainty type)
4. What's being optimized? (objective function)
5. How precise? (qualitative vs quantitative)

Output Format

Framework Recommendation:
- Primary: [framework name]
- Why: [one-sentence justification]

Starting Point:
- Key equations: [relevant formulas]
- Initial approach: [first step]

Tools to Use:
- [specific script or computation tool]

Related Skills:
- [domain skill to activate next]

Example Interaction

User: I want to model how a rumor spreads through a population

Claude: Let me help you find the right framework.

Q1: What quantity are we tracking?
> Number of people who heard the rumor over time.

Q2: What causes it to change?
> Spread rate depends on who knows and who doesn't.

Q3: Is there randomness?
> Assume deterministic (average behavior) for now.

Q4: Optimizing anything?
> No, just understanding dynamics.

Q5: What precision?
> Qualitative behavior, maybe predict peak rate.

Framework Recommendation:
- Primary: First-order ODE (logistic growth)
- Why: Rate depends on current state nonlinearly

Starting Point:
- dN/dt = r * N * (1 - N/K)
- N = heard count, K = population, r = spread rate

Tools:
- sympy_compute.py solve (equilibrium)
- Phase line for qualitative behavior

Related Skills:
- math/math-intuition-builder (understand the model)
- odes-pdes/first-order-odes (solve it)

Co-activates

After framework selection, suggest:

• math-intuition-builder - to understand the framework
• Relevant domain skill - for actual computation
• math-mode - for symbolic verification