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Fourier Series
Fourier Series represent some function as a sum of sines and cosines. This can be done by applying a Fourier Transform on some functions. There are many different kinds of Fourier Transforms, such as continuous, discrete, finite, and infinite. Here's a simple usecase for a Fourier Transform: Say you would like to approximate a square wave algebraically. The best way to do this would be to apply a Fourier Transform, yielding a Fourier Series. This new series can be approximated using Taylor Series, so the sum of sines and cosines will become a sum of polynomials, which is easy for a computer to calculate. Fourier Series are studied today, in a field called "Fourier Analysis". For an intuitive understanding of the transform, read the "BetterExplained" article in the information section below. For a jumping off point into the academic/engineering applications of Fourier Series, see the Wikipedia article below.