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Hi, my school doesn't teach number theory probably because it is seen as not having many applications (unless you study it for a long time), so i was wondering what the best way is to learn this subject. I've tried to read a few books on it but there is just such an overload of information. It's even harder than a calculus book. There is proposition after proposition and I can't apply the techniques to problems because I just don't know how. So what's the best way to learn number theory. Are there any good books on it? Or should I get a tutor to help me with it? Thx...
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I would not recommend number theory until one has taken an introduction to proofs course. That being said...
Number theory is a more or less pure mathematics subject. When studying it, it is important to go over each part in great detail. If you feel like you don't grasp a concept, don't see what something is used for, then play around with it for a bit. A while. A really long time. Things take time in pure mathematics, and you won't get it at first, especially if you don't have a professor guiding you along the way. Books can only say so much. So use this forum as much as possible.
And number theory is considered a rather advanced part of math, so feel free to use Euler Avenue for it.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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