Numerical Methods

Most equations can't be solved with a neat formula, so computers approximate. Squeeze a root with bisection, race towards it with Newton's method, add up areas with trapezoids and parabolas, estimate π by throwing random darts, fit curves through data (and see how that can go wrong), and discover why $0.1 + 0.2$ isn't exactly $0.3$ on a computer, and how such tiny errors have had real consequences.