What do you think of when you hear the word “basic”? For example, when you see a topic in a maths textbook entitled “Basic Algebra”, what comes to mind?
In that context, most people interpret the word basic to mean “easy” or even “babyish”. They either feel put out that they are expected to go back to the beginning, or they feel embarassed that they need to.
Well it’s time to publically dispell this myth — basic does not mean easy or babyish, especially when it comes to maths!
In maths, the stuff you learn first is the stuff on which all subsequent learning is built. Something is basic in this context because it is the base we use to build other things on top. For example, on top of arithmetic we build algebra, and on top of algebra we build calculus, and on top of calculus we build differential geometry. The dizzy heights of fancy differential geometry are only possible because somewhere down below there is a strong base in arithmetic on which to build it. Without those basics, the rest of maths wouldn’t exist. That’s actually an exciting concept!
There’s even more to this concept of basic as foundational. If something is basic, that means it’s right at the bottom of the building. So there’s nothing below it to build upon. And if there’s nothing below it to build upon, then you just have to learn it as it is. People learning differential geometry have the advantage of being able to base their learning on calculus, but people learning the arithmetic of fractions have nothing further down to base it on. This makes the “basics” really tough to learn! So no-one needs to be embarassed to be struggling with the “basics” — all basics are hard to learn simply because they are basic.