How To Reach The "Next Level" of Mathematics

Question

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"?

Answer 1

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.

Answer 2

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.

Answer 3

Use MIT open courseware - it's awesome! Also use Khan Academy, its incredible!

Answer 4

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.