# How To Reach The “Next Level” of Mathematics

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"?

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(Pre)calculus, linear algebra, trigonometry, "college algebra," or abstract algebra would all be fine to learn next, I think, though the latter one or two might be heavy for you. –  anon Nov 2 '11 at 23:24
Read around and see what suits your fancy. –  Ｊ. Ｍ. Nov 2 '11 at 23:26
@simplicity: of course, you don't just stick to that one thing... you look for things that are interesting there, and pursue them further! –  Ｊ. Ｍ. Nov 2 '11 at 23:47
If you're a "pre-algebra" student, surely the next level should be "algebra". Geometry is also good to learn. You'll want strong foundations in algebra and geometry when you get to trigonometry, analytic geometry and calculus. –  Robert Israel Nov 2 '11 at 23:50
@Simplicity Quote: "You shouldn't read around. It's a big mistake especially later on if you take it in college. Just stick with your course... " This is probably some of the worst advice I have ever seen. One of the most important things is reading everything and anything. Never stop being curious about things, and if you don't understand something read about it so that you can. It applies to all levels. For example, go to Colloquiums that are out of your research area, or read survey articles on things you don't know. Connections are everywhere. –  Eric Naslund Nov 3 '11 at 1:11
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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.

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

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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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For future posters, here is a sample of topics covered in your typical middle school math curriculum: edhelper.com/math/math_grade8_review_4.htm –  Aubrey da Cunha Nov 3 '11 at 19:56
@ Aubrey da Cunha: I expected those not from the U.S. might not know what "Junior High" was, but surely some in this thread are (I didn't investigate this, however) and presumably would remember what was covered. In my case, algebra wasn't offered in Junior High, so I got a beginning algebra book and went through it. However, I certainly knew what was covered in class because I still had to take the tests and do the homework, despite being allowed to read the algebra book at the back of the class. I also did the same thing for calculus in high school, as my school didn't offer calculus. –  Dave L. Renfro Nov 4 '11 at 14:15
That is why I included the link. I know I sometimes get muddled up about what I learned when, so I gave most in this thread the benefit of the doubt and just wanted to post a reminder. –  Aubrey da Cunha Nov 7 '11 at 22:08
Also, upon second reading, I think you may have mistaken my purpose. I agree with you on every point. I meant the link to be supporting evidence. –  Aubrey da Cunha Nov 7 '11 at 22:10
@Aubrey da Cunha: I understood your purpose. My comment was mainly an opportunity to continue 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. –  Dave L. Renfro Nov 7 '11 at 22:45
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.