Overview

Python Foundations gave every value a type and every expression a rule for producing one. A program built from expressions alone can only ever compute a single, fixed thing — the same code, the same output, every time it runs. Control flow is what turns a fixed expression into a program that behaves differently depending on the data it sees, and repeats work without the programmer writing that work out by hand. This topic builds the two control-flow constructs Python offers — branching (if/elif/else) and iteration (while, for) — and then spends its second half on the topic's payoff: three numerical root-finding algorithms (exhaustive enumeration, bisection search, Newton–Raphson) that only exist because a program can loop. These three methods are not a digression from control flow — they are the first substantial demonstration of why it matters, and they are the direct ancestors of every implied-volatility solver, calibration routine, and iterative numerical method that appears later in this vault.