Roadmap

An algorithm is a finite, unambiguous sequence of steps that solves a class of problems; a program is one expression of an algorithm in a language, and the same algorithm can be written in many languages.

Conditionals let a program choose between paths and loops let it repeat work, and between them they turn a fixed list of instructions into something whose behaviour depends on its data.

A data structure organises values in memory so that particular operations — accessing an element, searching for one, inserting or removing one — can be performed efficiently, and choosing the right structure (an array for fast indexed access, a linked list for cheap insertion, and so on) is what actually determines whether an algorithm running on that data scales well as the amount of data grows.

Numerical methods solve equations that have no convenient closed-form solution by breaking the problem into many small, repeated steps a computer can execute, such as Euler's method for approximating a differential equation's solution as a sequence of small linear steps, at the cost of introducing approximation error that must be understood and controlled.