The Science of Programming/Terrifying Concepts

Probably the two most terrifying concepts in the freshman world are Calculus and Programming. They certainly were for me. I was a C student when it came to Calculus and a B student when it came to programming. Let me assure you that both concepts are quite simple, notwithstanding my grades as a freshman. In fact, both calculus and programming are so simple, my freshman grades are most embarrassing.

Let's start with calculus. I don't know how or why I got it into my head that calculus was a difficult subject. As pointed out by Sylvanus P. Thompson (herein SPT) in the analogous chapter of Calculus Made Easy (herein CME), you simply have to understand the two symbols you will encounter over and over again when discussing Calculus. They are $$\int$$ and $$d$$. The first symbol, $$\int$$ (the integral symbol), simply means 'to sum up'. The second symbol, $$d$$ (the differentiation symbol), means simply 'a tiny piece of'. Placed together, as in

$$\int x^2\,dx$$

they simply means to sum up all the tiny pieces of the curve $$x^2$$

Let me add that the purpose of differentiation is just to find the slope of a curve and that the purpose of integration is to find the area under a curve. That's all.

With regards to programming, it also is rather simple. To write a program, one simply calls functions to do the work you need to do. Sometimes the function you need to call already exists. Sometimes it doesn't and you have to build it. But guess what? You are going to build the function from other functions, some of which already exist and some that do not. Simple, right?

I've used the word simple and its variants an awful lot, but I do so because it really is all so simple.