Math Expert-AI math problem solver

Example

Problem: Find the real roots of x^3 − 7x + 6 = 0. Outline: (1) Try rational roots ±1, ±2, ±3, ±6; (2) Factor using found roots; (3) Verify numerically. Sketch: Try x=1 → 0, x=2 → 0, x=−3 → 0 ⇒ roots are {−3, 1, 2}. A symbolic factorization yields (x+3)(x−1)(x−2). A quick numeric check confirms f(−3)=f(1)=f(2)=0 and sign changes are consistent.

Scenario

Students and self‑learners use this to get fully worked solutions that don’t stop at the answer. In a homework setting, Math Expert derives the solution, then validates it computationally to catch algebra slips. In exam prep, it contrasts methods (factoring vs. polynomial long division vs. numerical root‑finding) and explains when each is appropriate.

Example

Model: Simple SIR (Susceptible–Infectious–Recovered) with β=0.30, γ=0.10 (so R0=β/γ=3). Outline: (1) Set ODEs; (2) Simulate trajectories; (3) Inspect peak I(t) and timing; (4) Sensitivity analysis by lowering β. Insight: Reducing β (e.g., β→0.20) lowers R0 and both delays and shrinks the infection peak. The workflow shows how parameter changes affect outcomes. Optimization variant: Formulate a linear program for a blending problem: minimize cost c·x subject to Ax≥b, x≥0; report the optimal mix, shadow prices, and binding constraints.

Scenario

Engineers and analysts explore “what‑if” questions—epidemic peaks, inventory policies, staffing levels, or portfolio constraints. Math Expert translates the real description into equations, runs a small simulation or solver, and interprets the results with attention to assumptions and edge cases.

Example

A/B test: 10,000 visitors per arm; A converts at 12.1%, B at 12.9%. Computation: Difference = 0.8 percentage points. Two‑sided z‑test p ≈ 0.087; 95% CI for the absolute lift ≈ [−0.12%, +1.72%]. Interpretation: Not statistically significant at 5%; consider increasing sample size or using Bayesian analysis for decision‑making under uncertainty. Also report MDE (minimum detectable effect) and power for planning.

Scenario

Product teams, researchers, and marketers use this to size experiments, compute CIs and p‑values correctly, and avoid common pitfalls (optional stopping, multiple comparisons). Math Expert shows the formulas, runs the numbers, and explains the decision implications in plain language.