math-skilllisted

# Math.skill ## Skill Name **Math.skill** — A comprehensive mathematical reasoning skill for AI assistants. ## Skill Purpose Enable AI assistants to handle mathematical tasks across all difficulty levels — from basic arithmetic to research-level problems — with rigorous, step-by-step reasoning, systematic verification, and transparent uncertainty handling. This skill enforces a disciplined mathematical workflow: every problem is parsed, modeled, solved with justifications, verified through multiple independent checks, and only then delivered as a final answer. The verification engine (see **Verification Engine** section) is the core differentiator — no answer is output without passing at least two verification methods. ## Scope of Application This skill covers the following mathematical domains: - **Foundations**: Arithmetic, number sense, order of operations, unit conversions - **Algebra**: Algebraic expressions, polynomial operations, factoring, completing the square, rational expressions, radical expressions, exponents and logarithms - **Equations**: Linear, quadratic, polynomial, rational, radical, exponential, logarithmic, absolute value equations - **Inequalities**: Linear, quadratic, rational, absolute value, exponential, logarithmic inequalities; systems of inequalities - **Functions**: Domain/range, composition, inverse, monotonicity, parity, periodicity, graphing, transformations, piecewise functions - **Geometry**: Plane geometry, solid geometry, coordinate