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calculusnerd
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Hello, I'm currently studying math and want to become a mathematician. So far I know up to computational single variable calculus, i.e. Calculus I and II, but not III. Since I found the school textbooks easy I decided to follow the MIT course for Calculus III, so I have started watching the multivariable calculus videos by Denis Auroux. I want to move onto analysis after multivariable calculus. However, this gets me wondering. Seeing as many people see this (MIT) course as being computational multivariable calculus, would I need to re-study all my calculus using say apostol before moving onto analysis, or could I jump straight from the MIT course to something like Pugh's analysis book? What would I learn from spivak/apostol that I can't learn by jumping straight into analysis after having learned computational single and multivarialbe calculus? I'm good at problem solving (judging by my ability to solve 3 problems from this year's USAMO)
Thanks
Thanks