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Calculus is the study, or the analysis of functions. Real functions, complex functions etc. That's why it is also known as functional analysis.

Algebra is the study of "numbers". No, not 1, 2, 3. But more, things like fields, rings, groups, things that act like numbers (hence are numbers by the Golden rule of Algebra). They create tools like matrices to solve problems (transformations) on numbers.

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