My younger brother, who is in 8th grade, desperately wants to

>>8666124
and I want desperately want to get better a being a h4x0r, but we BOTH need to be patient for our education to catch up, now don't we??

You started a thread like 5 minutes ago asking for some difficult questions, why the fuck do you keep starting threads.

>>8666130
because he's 12

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Serge Lang: Basic Mathematics
Khan Academy
Paul's Math Notes

>>8666136
Thank you.

>>8666130
Ye

>>8666124
Learn highschool algebra and trigonometry, then move into calculus->diffeq and linear algebra. There are plenty of resources online for this.

>>8666171
Okay will definitely do. How do I know when to move on? Is there some sort of test I can take? Does this look like a good 'final test' for algebra?

http://www.mathworksheetsland.com/tests/HSalgebrasample.pdf

>>8666124
Read Stewarts Concepts of Modern Mathematics.

It's a big sampler and introduction to the basics of several different fields in pure mathematics. It will help you decide if you are interested in pure mathematics or just something "mathematically oriented" like applied math, science, engiqueering, etc..

>>8666232
If you really understand and feel comfortable with the material then go ahead and move on. It's likely you will have to go back and brush up on some topics in the future anyways. Once you reach calculus (not analysis) you'll have to use lots of different skills to solve the problems. I would say that being able to solve problems from your calc book at that point will be a much better test than any other.

Also, just a heads up: The sort of mathematics done in pure mathematics (beyond the pleb-tier "engineers too" courses like calculus and intro linear algebra) are an entirely different flavor than the sort you're doing now. Whether or not you like or are good at the math you're doing now will have little bearing on if you like or are good at pure mathematics.

>>8666313
Not op but give me a few words to color that statement you just made, what makes problem solving in higher level math so different

>>8666332
Higher level math is more focused on proofs than computations. So instead of being given a question and expected to
>figure out which computations need to be done to answer the question
>perform said computations to reach an answer to the question
students in higher math are given a statement and expected to
>figure out if the statement is true or not
>figure out an argument to support their assertion about the statement
>rigorously formalize said argument in mathematical writing (called a proof)
While there may be some computations involved in parts of the argument the focus is more on the logic involved and the general understanding of abstract mathematical concepts.