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Probably a too trivial question but here goes:
What is the relationship of algebra and geometry with calculus? Are they pre-required knowledge for calculus, is calculus a different type of theory on same topics? What?

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High-School and College Algebra (as opposed to Abstract Algebra), Analytic Geometry, and Trigonometry are all crucial prerequisites to Calculus. The skills and knowledge gained in those classes is presumed in the study of Calculus: you need to have mastered that content to succeed in Calculus. But Calculus is not advanced algebra nor advanced geometry, per se: the earlier skills become tools with which to study and understand calculus.

Calculus - which Wikipedia characterizes as the mathematical study of change - introduces entirely new concepts, not previously encountered in earlier coursework! Calculus has been an amazing achievement in the History of Mathematics, and it's hardly an overstatement to claim it is also an amazing human achievement, period.

Indeed, you'll find the following in the linked entry, as well:

A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis.

Calculus is also a gateway to pursuing physics, engineering, etc.

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  • $\begingroup$ Don't forget the impact on probability-theory as well ;-) Calculus is everywhere. $\endgroup$
    – AlexR
    Sep 19, 2013 at 20:53
  • $\begingroup$ Yikes, you're right, @AlexR. Good thing I added the "etc." Hopefully, others will add similar observations! $\endgroup$
    – amWhy
    Sep 19, 2013 at 20:54
  • $\begingroup$ Go for chaos theory, biology, even the arts (mandelbrot fractals emerging from complex polynomials studied in complex analysis etc. pp.) It's the most omnipresent discipline throughout science, I think. $\endgroup$
    – AlexR
    Sep 19, 2013 at 20:57
  • $\begingroup$ And Astronomy, Economics, Finance, Atmospheric Sciences, and .... Everywhere $\endgroup$
    – amWhy
    Sep 19, 2013 at 20:59
  • $\begingroup$ Architecture, Medicine, Informatics, Operations Research,... the more I think the more I notice... $\endgroup$
    – AlexR
    Sep 19, 2013 at 21:10

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