Algebraic calculations are highly critical for computers to work correctly. In fact, behind the syntax, the bulk of programming is simply algebraic notation.

## Signals

One of the most frequently-used computer uses of algebra is with converting visual and auditory information. The formula for this is the Fourier transform. It is designed to convert a signal and change properties of it with a calculation (e.g., stretching/shrinking across time, changing pitch/volume, scaling up/down).

The discrete cosine transform is a more efficient mathematical formula than the Fourier transform in many cases because it only works with real numbers (as opposed to imaginary numbers) and cosine is easier than sine to imitate signals. It allows conversion of a matrix of numbers into another related matrix. The JPEG compression algorithm uses discrete cosine transforms to shrink images.