But this only touches the surface. Computers are a physical implementation of the rules of (mathematical) computation as described by Alan Turing and others from the mid 1930’s through the early 1940’s. Working with a computer at any level but the most superficial requires that you understand algorithms, how they work, how to show they are correct, and that you are able to construct new algorithms. The only way to get to this point is to study basic algorithms, understand why they work, and even why these algorithms are better (or worse) than others. The highly sophisticated standard algorithms of arithmetic are among the best examples to start. But.
