ElI5: What is the difference between algebra and calculus?
In: Mathematics
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.
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