If you do any electronics work–especially digital signal processing–you probably know that any signal can be decomposed into a bunch of sine waves. Conversely, you can generate any signal by adding up ...
When it comes to mathematics, the average person can probably get through most of life well enough with just basic algebra. Some simple statistical concepts would be helpful, and a little calculus ...
If there's a mathematical idea that applies itself to almost everything in everyday life but is almost unknown outside the scientific world, the Fourier transform has to be the most unsung contender.
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