math-model-selector

# Math Model Selector ## When to Use Trigger on phrases like: - "what math should I use" - "which mathematical framework" - "how do I model this" - "what kind of problem is this" - "formalize this problem" Use when user has a problem but doesn't know which mathematical domain applies. ## Process Guide user through decision tree using Polya-style questions: ### 1. Identify the quantity **Ask:** "What quantity or phenomenon are you trying to understand?" - Physics problem -> conservation laws, differential equations - Economics -> equilibrium, optimization - Data patterns -> statistics, regression ### 2. Characterize change **Ask:** "What changes, and how does it change?" - Discrete steps -> difference equations, recurrences - Continuous rate -> ODEs - Rate of rate matters -> 2nd order ODEs - Spatial variation -> PDEs ### 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 c...