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Skill v1.0.0
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version: "1.0.0" name: math description: Multi-layer cognitive stack for machine-verified mathematical problem solving across 14 sub-disciplines.
Math Cognitive Stack
A structured collection of skills for mathematical reasoning, proof construction, and problem solving.
Sub-Skills
| Directory | Topic | |
|---|---|---|
| abstract-algebra | Groups, rings, fields, homomorphisms | |
| category-theory | Functors, natural transformations, adjoints | |
| complex-analysis | Holomorphic functions, contour integration | |
| functional-analysis | Banach/Hilbert spaces, operators | |
| graph-number-theory | Graph theory and number-theoretic results | |
| information-theory | Entropy, channel capacity, coding | |
| linear-algebra | Vector spaces, matrices, eigenvalues | |
| math-intuition-builder | Build intuition before formalization | |
| math-model-selector | Choose the right mathematical model | |
| math-progress-monitor | Track proof progress and open goals | |
| mathematical-logic | Propositional and first-order logic, proofs | |
| measure-theory | Sigma-algebras, integration, probability foundations | |
| numerical-methods | Approximation, error analysis, algorithms | |
| odes-pdes | Ordinary and partial differential equations | |
| optimization | Convex, combinatorial, gradient-based optimization | |
| real-analysis | Limits, continuity, differentiation, integration | |
| rudin-real-complex-analysis | Guided work through Rudin's textbooks | |
| topology | Open sets, continuity, compactness, connectedness |
When to Use
Activate the appropriate sub-skill based on the mathematical domain in the user's question. Use math-model-selector when the domain is unclear.