ElI5: What is the difference between algebra and calculus?
In: Mathematics
In their broadest definitions…
Suppose you take some symbols (1, 2, 3 are symbols… x, y z are other symbols), specify some rules to how they can be changed (we know 1 + 2 = 2 + 1, we decided that that’s just how the + symbol works)… And use these rules to give statements that can be proved, or finding unknowns (why not just give a symbol to the unknown, and use these rules to find its value in terms of the other symbols?).
All of this comes under algebra.
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Calculus is the study of ‘continuous change’. Or ‘continuous varation’, and how those changes accumulate.
You may know the proof where a circle is ‘approximated’ as a bunch of parallel rectangles (think stripes). The idea is that the area of the circle = the sum of the areas of the rectangles. But you know that at any point, a circle can never be perfectly be equal to a bunch of rectangles. No matter you ‘zoom in’ so to speak, you will see jagged edges. Like drawing a circle in paint gives those jagged pixels, but if you zoom out, it looks like a circle.
But this is math, so you say “the more rectangles you use, the closer the thing you get is, to a circle. When you use infinite rectangles, you’ll get a perfect circle”. … Are you worried there’s no such thing as an infinite number of circles, well there’s no such thing as a perfect circle either.
So calculus studies such relationships in variation and accumulation. Algebra is very much the fabric of calculus, because at the end of the day we’re using symbols and defining how they can be manipulated.
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