The basics of algebra will be familiar to anyone who’s ever been asked to "find x". We use letters to represent unknowns, and find their values by solving equations. With variables like this we can make general statements, and define functions: given a value x, we can find 2x, or x², and study how the output varies when we change the input.

This is all fundamental to many mathematical ideas, particularly calculus: the study of change. Whether it’s a moving object, a waveform, or the motion of a fluid like water, we can describe and study change by modelling things with functions and observing their behaviour.

We also use algebra to describe points in space: coordinates provide a link to spatial geometry. Simultaneous ...

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