ElI5: What is the difference between algebra and calculus?

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ElI5: What is the difference between algebra and calculus?

In: Mathematics

5 Answers

Anonymous 0 Comments

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.

Anonymous 0 Comments

Basically speaking, algebra is pushing equations around so that they solve for different variables within them, kind of like puzzles. Calculus, on the other hand, is a really fancy version of finding the slope. You look for equations for the slope at any given time and can use it to talk about the shape and behavior of equations.

They are both very useful, but two separate areas entirely (although you need some algebra to be able to do much calc)

Anonymous 0 Comments

Algebra deals with numbers, and formulas / equations / relationships between numbers. Calculus deals with functions, and relationships / transformations between functions.

Basically, algebra is “basic math”; you have numbers and you have rules about what it means to add, subtract, multiply, etc. You establish equations and functions (rules that numbers must follow).

The rest of the math builds on top of this, by taking OTHER THINGS and establishing rules and relationships as if these things were numbers. Things like sets of numbers, vectors, functions, “surfaces”, “fields”, etc., you can define rules about how to add, subtract, and otherwise “interact” with them or the interaction between them. It’s useful; for example geometry is about the interaction and properties of shapes and surfaces, and it’s useful to have rigid logical / mathematical rules about how they interact. Because a lot of the real world objects are geometrical, and having the geometry rules helps with understanding these real world objects.

So calculus takes functions (relationships between variables) and establishes some rules about them and how they can interact.

Anonymous 0 Comments

Roughly speaking calculus is about studying ‘change’. Algebra can can tell you how fast the baseball pitch travelled on average, but calculus can tell you how the velocity of the ball changed and how fast it was going at any point in time. The other area that calculus concerns itself with is the area under a curve. Algebra can tell you the area of well known geometric shapes, but it cannot answer those questions for complex shapes. Algebra is the rudimentary math for calculus however, you will be performing algebra to solve equations in calculus.

Anonymous 0 Comments

ELI5:

algebra studies points on curves and planes.

Calculus studies slopes of curves/planes and the area under curves/plains.