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I'm a 25 years old guy and I wanna learn math. I haven't had a good relationship with them until now. My background is that I know how to add, subtract and multiply. In theory I also know how to divide, but some times I'm messing it up or get stuck with what the next step is supposed to be. I blame calculators for that. I know how to solve basic equation and I used to know how to solve quadratic equations too, but last time I solved one was 7 years ago. I'm rumbling, I know. Basically I'm trying to say is that I don't know what I know about math, but I could say that I'm at a very basic level.

I want to learn math because about a year ago, I was watching the Linear Algebra lectures from MIT on YouTube. It was amazing! I could feel my mind working to its limits to understand all this new information! I was feeling challenged for the first time in my life and my brain working at 110% capacity to cope. But I tried to learn too much too quickly (because linear algebra was a prerequisite for a course in coursera, about to start in one week) and I failed.

Now I want to start from the beginning and take this slowly step by step. But I also would like a challenge. For example I would like to tackle proofs of theorems without learning them. Just something (a lecture, a book..) giving me the tools to prove something and then make me discover it, following the steps of those who first discovered the theorem. I want to exercise my creativity, my abstract thought and my problem solving. I want to feel my mind expanding!

Where do I start? What books or online material would you advice me to read(or watch)? Please make sure that you give me a list for the next years, so I don't have to come back here and ask the same question once I'm done with the basics.. And how much time would you say I have to give to studying? I'm working and I'm trying to write a novel, so I don't think I can study for let's say 5 hours per day, every day.

Well that's it! I know it was not the best worded question in the world, but I hope it is sufficient to give you all the data you need to put me in the right road.

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closed as too broad by Benjamin Dickman, J W, Mark Fantini, JoeTaxpayer, Brendan W. Sullivan Sep 16 '14 at 1:49

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ To be clear: I voted to close since I think this is (significantly) too broad. $\endgroup$ – Benjamin Dickman Sep 15 '14 at 18:07
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    $\begingroup$ "Please make sure that you give me a list for the next years, so I don't have to come back here and ask the same question once I'm done with the basics.. " Alas, this is astronomically ambitious :-| $\endgroup$ – Brendan W. Sullivan Sep 16 '14 at 1:49
  • $\begingroup$ Another question asked Is it possible to improve logical thinking and problem solving abilities? $\endgroup$ – Jasper Apr 17 '17 at 2:56
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It's great to hear about your enthusiasm to learn math!

No fewer than three answers have suggested Khan Academy. Khan Academy sucks. (In my not-so-humble opinion.) The Khan Academy videos basically crank through calculations, without encouraging any deeper understanding.

It sounds like you have bits and pieces of algebra. Next, you probably want to check an algebra textbook out of the library and sort the topics out into three categories: (1) stuff you already know, (2) stuff you need to know, (3) stuff you don't need to know, at least for now. A lot will fall into category 3, e.g., factoring polynomials, which is a topic much beloved by math teachers but seldom necessary outside of an algebra class. If you're not sure whether something fits in category 3, make a note of it, remember that such a thing exists, and if you need it later, come back to it. Once you've identified category 2, solve some problems that have answers in the back of the book, so you can check yourself.

Once you're solid in algebra, the world is your oyster. You can pretty much pick up any math book and dig in. A cool, old book on calculus is Calculus Made Easy by Silvanus P. Thompson.

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    $\begingroup$ +1 for "Khan Academy sucks". It shocks me that so many educators are embracing it so enthusiastically. $\endgroup$ – mweiss Sep 16 '14 at 14:15
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It seems you have discovered your new great passion for math. I suggest continuing to feed this passion. In addition to Khan Academy, you may also find cut the knot a good place for interesting problems online. Keep searching online and find the sites that are most suited to your interests.

I also suggest visiting your local library or bookstore. You should be able to find reading material to keep you interested for many lifetimes.

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James Tanton has some very interesting videos. He treats math as an adventurous exploration. (While Khan helps people slog through the topics in their math courses.)

I'd also recommend Keith Devlin's Introduction to Mathematical Thinking, on coursera.

Have fun!

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If you want to learn math, then you have to do math. (As the other answers suggest, one way to do this is through Khan Academy or something similar to it.) This will take a lot of time and effort.

If you simply want to appreciate math, then I suggest you read books and articles by writers who popularize mathematics: Martin Gardner, Ian Stewart, Keith Devlin, Danica McKellar, and so on.

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Khan Academy has a nice overview of primary, secondary, and some university mathematics, presented in a way that is clear and easy to self assess. I would encourage you to start there, and then when you find a topic you're especially interested in, go on and explore it independently.

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