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I am teaching myself mathematics, and I don't really know anyone who is interested in mathematics. I find that the hardest part about teaching myself is that I am lacking the social aspect of being in a classroom. How can I compensate for the lack of a study group?

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  • $\begingroup$ You might check to see if there are any Math Teaching Circles (MTCs) near you. There's one by me (Boston Math Teachers Circle) that is free to participate in, and (judging by the few times I've attended) offers interesting mathematics in an environment with the "social aspect" to which you allude. $\endgroup$ – Benjamin Dickman May 9 '16 at 17:36
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    $\begingroup$ You seem to be assuming that study groups are a good thing. The evidence I've seen is that they are not. There is some good discussion of this in Arum and Roksa, Academically Adrift. Time spent studying with peers has been found to be negatively correlated with gains in critical thinking skills. Sociologists have theorized that "social engagement" was positive for learning; actually, the evidence is that it's negative. $\endgroup$ – Ben Crowell May 11 '16 at 4:23
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    $\begingroup$ What are your goals? Are you trying to learn for a specific application, or do you just like maths? Are you trying to gain a qualification and maths is merely instrumental? $\endgroup$ – Bernard W May 13 '16 at 2:36
  • $\begingroup$ If anyone does find an online study group, I'd be willing to try. $\endgroup$ – Simply Beautiful Art May 15 '16 at 16:36
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For self-learners who have connections to the internet, but otherwise do not have access to other people who share the same interest in mathematics, I suggest participating in online communities such as Stack Exchange. This will provide you answers to your questions, feedback to your work, and insights from those who are more experienced.

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  • $\begingroup$ This guy knows my life lol. $\endgroup$ – Simply Beautiful Art May 15 '16 at 16:18
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Use stack exchange - it gets brutal sometimes, but at least people don't hold the positive/negative back.

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    $\begingroup$ Could you elaborate? There are many things people will not answer on math.SE, particularly at the first year graduate level, in order to not make the answer prevalent. $\endgroup$ – Chris C May 10 '16 at 14:53
  • $\begingroup$ @ChrisC If you are looking for something not suitable there, like opinions, you can always ask somebody directly, e.g. via chat (and there is meta of course). $\endgroup$ – dtldarek May 16 '16 at 6:13
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You could try to form a study group with some people online who want to learn about the same thing as you. I've seen people form groups through reddit.com/r/math then use applications like slack.com to center their study groups around. It's a bit hard to keep these types of groups active, but it still could be worth thinking about

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Since you asked this question, I am assuming you have the internet in your pocket (or wherever) and that you can use math.stackexchange.com.

Simply participating on this site has made me much more educated in math, and more importantly, I think more like a real mathematician.

Try to get some goals down on the table to:

  1. Try to answer a few questions per week.

  2. Try to ask an intelligent question each week.

If you just do those two goals each week on the math SE site, you'll start learning.

Another interesting thing you could do is to try and get a notebook (or 5...) and fill it with everything you know about math. Just dump it, from summations to pi to rational functions etc. And every time you have a problem, try to work it out in that notebook. Also write down interesting things you see on the math SE site that you can understand. (You'll find you probably don't know so much about pi, so you could look that up)

And if you have school, take a notebook with you too. Always have a notebook with empty pages so you can write down whatever pops to your mind.

And use pen. This way, you can see your mistakes. If you mess up, don't scratch it out, just put one big line through it so you know its wrong but you can still see it.

Don't be afraid write trivial statements, like $m=\frac{y_2-y_1}{x_2-x_1}$.

There will be a point when certain things you just know, like the quadratic formula. Use your notebook to show why that is the case, why the quadratic formula works, for example.

And some silly ideas might actually seem profound to you, like if you haven't taken Calculus and I had told you "use the slope formula from algebra to find the slope of $y=x^2$ at $x=2$" you should actually try it. Feel free to try it before viewing the answer.

$m=\frac{y_2-y_1}{x_2-x_1}$

.

$m=\frac{(x_2)^2-(x_1)^2}{x_2-x_1}$

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$m=x_2+x_1$

.

$=2+2=4$

Slope at $x=2$ means we plug that in for both $x_2$ and $x_1$.

And of course, use colored pens as needed, because sometimes the page gets messy, and colored ink is more fun to use anyways.

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  • $\begingroup$ Do excuse my failed formatting with the hidden text, if someone could improve it, that'd be appreciated. $\endgroup$ – Simply Beautiful Art May 15 '16 at 17:25

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