No, not really. Calculus uses algebra to solve equations, but calculus is a branch of mathematics all its own.
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Differential equations, Linear Algebra, Abstract Algebra, Real and Complex Analysis, Advanced Calculus, and lots of other fun stuff.
No. College Algebra and Precalculus (or Trigonometry) are enough preparation to take Calculus.
algebra - arabic, calculus - latin
Yes. I use them a lot when answering these questions.
Because Algebra is the foundation of Calculus, and Calculus is the fundamental measurement of the Universe.