The only proof-based math class I've taken so far was on abstract algebra. Concepts were easy for me to understand, but I was constantly having trouble with some of the proofs.
I so frequently get this feeling that the last, tiny trivial step left in my proof is just "right there," and yet I can't find it. Or I might drastically over-complicate things and write a page proving something that my professor's solution states in one line as an obvious conclusion (which it was). It's just ridiculous; there were a few problems assigned for the class that I might spend four hours just messing around with until finally figuring out a convoluted (though valid) proof to when they could have been solved in a few lines.
Technically, grade-wise, I did well in the class, but in the end, I still feel like proof-writing just doesn't come naturally to me. Now I'm working on learning topology and differential geometry, and while, again, I can understand the concepts and proofs and do some of them on my own, none of the proofs ever come naturally to me.
Honestly, is it common for people to take so long to get used to writing proofs? I'm just working on getting the hang of things (self-studying topology and differential geometry now) but it's not really happening.
I so frequently get this feeling that the last, tiny trivial step left in my proof is just "right there," and yet I can't find it. Or I might drastically over-complicate things and write a page proving something that my professor's solution states in one line as an obvious conclusion (which it was). It's just ridiculous; there were a few problems assigned for the class that I might spend four hours just messing around with until finally figuring out a convoluted (though valid) proof to when they could have been solved in a few lines.
Technically, grade-wise, I did well in the class, but in the end, I still feel like proof-writing just doesn't come naturally to me. Now I'm working on learning topology and differential geometry, and while, again, I can understand the concepts and proofs and do some of them on my own, none of the proofs ever come naturally to me.
Honestly, is it common for people to take so long to get used to writing proofs? I'm just working on getting the hang of things (self-studying topology and differential geometry now) but it's not really happening.
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