I have a question about development of mathematical matury.(adsbygoogle = window.adsbygoogle || []).push({});

First off, I'm a high school senior with almost all my college general education credits due to dual enrollment in Florida. I have been doing independed study since 10th grade and have self-taught everything (computation) from pre-calculus to differential equations which I completed last month. I have credits for calculus 1 and 2 (by AP calculus BC), calculus 3 and am currently taking differential equations by dual enrollment.

As I noticed in these forums, AP calculus, and the calculus 3 and differential equations at college lack any treatment of proof. However, in Florida public universities, usually all the proofs affiliated with these courses at presented as a core course to be taken after the introductory calculus sequence. (Similarly, I'm going to exempt the calculus sequence which shouldn't do much harm since neither regular nor honors calculus presents any proofs here).

So recently, I have been trying to promote my maturity in mathematics. I have gone through proofs of theorems with field axioms and order axioms for real numbers with no trouble. Worked with natural numbers and learned how to use induction. I've done a bit of set theory algebra proofs including union, intersection, and the supremum and infimum of bounded sets. And worked a bit with the proofs using the e-o definition of limits to prove their properties.

Thing is, I usually don't prove the theorems by myself. I usually have to take a peak and the hint will usually get me a bit of the proof done. Once I learn the proof, though, I understand every part of it. (This goes mainly to properties of limits using the e-o definition and supremum/infimum). This is the right procedure to developing mathematical maturity right?

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# Developing Mathematical maturity

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