I am a junior-high pre-algebra student. I feel that my class is holding me back, so I wanted to learn "higher-level math". So what should I learn now? What do you believe is a "next step"?
How To Reach The "Next Level" of Mathematics
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1@perl.j why do you wish to learn "higher-level math?" Just curious as to what made you so curious about mathematics in general at such a young age... When I was your age, sadly, I (and a lot of my peers) were interested in pursuing higher level math mostly for better results in Olympiads or competitions. It was only after taking math (and higher level economics) in college that I realized, I truly am fascinated by this subject. If anybody other than perl.j has any comments on this, feel free to tag me in their response :) – 2011-11-03
5 Answers
I just wanted to mention a possible resource. You could look at the mathematics section of the MIT open courseware.
Specifically they have video lectures for an introduction to calculus, multivariable calculus and linear algebra. (probably some more too) One benefit is that it is not too difficult to motivate oneself to watch a video.
You should start with their introduction to calculus: http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/
If this is at too high a level for you right now, keep it in mind for the future.
Use MIT open courseware - it's awesome! Also use Khan Academy, its incredible!
Given that the original poster said he/she was a Junior High student taking prealgebra, almost all of the comments and answers currently visible to me seem highly inappropriate.
perl.j --- I recommend looking for the following books in your school library or public library:
Danica McKellar's 3 books (if you're a girl)
http://www.amazon.com/Danica-McKellar/e/B001JP7Z7G/
Mathematics, Its Magic and Mastery by Aaron Bakst
http://www.amazon.com/dp/0442005288
Mathematics for the Million by Lancelot Hogben
http://www.amazon.com/dp/039331071X
Realm of Numbers by Isaac Asimov
http://www.amazon.com/dp/0395065666
Realm of Algebra by Isaac Asimov
http://www.amazon.com/dp/0449243982
(November 4) I looked at these books last night and now I don't believe Lancelot Hogben's book belongs with the other books I listed, but I'll leave Hogben's book here anyway.
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0@Aubrey da Cunha: I understood your purpose. My $c$omme$n$t was mainly an opportunity to $c$ontinue to voice my surprise at the responses the original poster got. In fact, if someone wanted to parody the "head in the clouds" behavior mathematicians are often accused of having, it'd be hard to do better than what's here. But maybe I'm being too critical, and perhaps many here have not had much contact with middle school aged children for a long time. – 2011-11-07
I always recommend Stanley Ogilvy's Excursions in Geometry to people in that situation. It's not "advanced", but it's something you'll be glad you know and there are "advanced" things that it will make it much easier to understand. And there are lots of other expository books accessible without advanced preparation. I think the Mathematical Association of America publishes a bunch of stuff like that. E.g. if you want to see how to prove $e$ is a trascendental number without using anything not taught in secondary schools, it's in one of those.
But what you should do can depend a lot on your tastes.
In 12th grade I took a beginning Spanish course in which probably at least half the students weren't interested in learning Spanish, and the course accomodated them to a large extent, so I know how that works.
Algebra one (high school, "ninth grade").
Get a book with the answers in it. Something from the 1940s or so. Nothing funky or super hard. Not algebra two (college algebra).