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Is it harmful to try to learn an advanced topic that is way beyond your mathematical maturity, even if you're really interested in it? Should I focus only on standard material for undergraduates and leave the rest to grad-school?

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what you're waiting? start learning! – Lucas Zanella Jun 7 '14 at 2:57
@LucasZanella Hi! Thank you for replying. I am actually an undergraduate. What I mean by advanced is something like modern algebraic geometry. – user155704 Jun 7 '14 at 3:01
@LucasZanella, Khan Academy does not cover any topics beyond the first part of an undergraduate degree, which are the ones being asked about here. – Antonio Vargas Jun 7 '14 at 3:02
There's no general way to answer this. Some people thrive on pushing ahead; others thrive on following the sequence. Try it and see; my feeling is that, if it is really beyond your maturity level, you just won't care about it enough to get very far. – Ryan Reich Jun 7 '14 at 3:04
@AntonioVargas sorry, english is not my native language, I though undergraduate meant a person that never started graduation ;) – Lucas Zanella Jun 7 '14 at 3:04
up vote 6 down vote accepted

It would only be harmful if you found it frustrating and dry.

Mathematical maturity is important. But there are a few kinds of it. You gain maturity by becoming familiar with subjects. By learning problem solving techniques. By coming to grips with "unmotivated abstraction" -- learning to figure out what a mathematical construct does without somebody giving you the "magic words". You'll need all of these, at the right level, to get a good grade in a class.

But you can gain -- especially in dealing with unmotivated abstraction -- if you study beyond your means. Learning to ask the right questions is a very good thing! Also, a lot of mathematics comes down to memorization -- memorization of definitions, theorems, and techniques. You might not be able to memorize many techniques if you can't try them out, but you can get a big head start on the other two.

But, like I said, stop if it gets boring or too frustrating.

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Thank you! I guess I'll simply give it a shot. :) – user155704 Jun 7 '14 at 3:14

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