Math

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.