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by thraxil
1824 days ago
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I'd definitely recommend having taken a college level Calculus course before and you'll get more out of it if you are basically comfortable with Abstract Algebra (know what sets, groups, rings, and fields are, and be able to think fairly abstractly about operations on those kinds of objects). That said, I think you could get through the first one with just high school level pre-calc although I think it would be hard to motivate yourself if you don't know enough calculus to see where it's heading. It does an absolutely brilliant job of starting with Peano's axioms to define the natural numbers, using those to define integers, using integers to define the rationals, introducing Cauchy sequences and using them to define the Reals, then introducing limits, continuity, etc. and Riemann integrals. That whole part is pretty much self contained with each concept rigorously (but clearly) built out of the previous ones. Some basic algebra and the ability to follow a mathematical argument are pretty much all you need. As it gets into the second volume, it expects some familiarity with logarithms and starts building into more advanced Calculus. It's still fairly self-contained but you might struggle if you don't remember, eg, what integration by parts looks like. |
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