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I am trying to teach myself mathematics and I can't tell if I'm going about it in an inefficient way. I really admire people who push the frontier and discover new methods and types of math like Newton, Euler, Grassmann, et cetera... I'm not naturally good at math and have had to work hard just to get to where I am now, but I really really adore math and want to be able to discover things myself!

When I'm teaching myself math should I be trying to figure out the subject before I read how to do it? And how bad is it if I'm not good at this??

For example, while learning Linear Algebra I got to eigen values and vectors and I tried to figure out a way to find them without being told how to do it. I was able to come up with a few ideas about how, but I just couldn't figure it out on my own. Same with integrals in Calculus.

So should I be self studying this way? There is so much of mathematics that I am super excited to learn but, it's taking me SO much longer to learn by doing this. But I don't want to just know how to do something. I want to really be able to yield the essence of mathematics! Any help would greatly be appreciated!!

P.S. - This isn't really part of the question, but I recently joined this site and think it is absolutely amazing that you all will sacrifice your time and talent to help others learn! So I just wanted to add that you all are stellar!! Hope adding this doesn't get me in trouble

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    $\begingroup$ Undergraduate textbooks don't emphasize this kind of thinking - they usually just give you several example problems before expecting you to do exercises on your own. But I think it's a very good practice to pause after hearing a problem and spend a little time trying to solve it yourself before learning the textbook solution. You then appreciate the solution much more when you see it. But don't feel like you have to re-invent the wheel each time - spend a little time trying to figure it out on your own and then look at the solution if you are stumped. $\endgroup$ – Jair Taylor May 31 '18 at 19:15
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It's a great way to do it, and a lot of fun.

My Number Theory course in college was like this. We got a list of problems at the beginning of the semester. The professor said, "I know the answers are available in books in the library. Don't do that. Play with them."

Then if we got completely stumped he'd give us a little information, which would get us a little further, until we got stumped again.

If you don't have the time constraints of a course, then I think you'll be surprised how deep your understanding becomes when you study this way.

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  • $\begingroup$ Is discovering things or figuring things out on your own something that can be learned or is this just an innate talent? $\endgroup$ – Dr. Snow Jun 7 '18 at 3:01

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