<p>I'm in 9th grade taking AP Calc BC and I've recently become interested in higher level (proof based) math. My local CC offers a few (intro to abstract algebra, number theory, linear algebra) but there are so few people taking them that I they might not be available (linear algebra isn't even available right now) next year when I dual enroll. Even if they do offer them, they're only offered in another, farther away campus that I probably won't have transportation to, and even then I'm not so sure about the rigor. I'm definitely willing to get some books and study some topics on my own and I probably will, but I'm wondering if there'll be any way to indicate that to colleges once that time comes around. I'm also worried about having to take courses I already studied. My school doesn't have any sort of math club/team, so that's out of the picture. Any suggestions?</p>
<p>Hey @adolescentnerd! I can really relate to your situation. I finished up my school’s math curriculum by sophomore year and from then on had to go off on my own, so to speak (my school, like yours, lacks a math club or team). </p>
<p>First, I would advise you self-study calc I and II from a more rigorous perspective: the AP curriculum really doesn’t do the materiel justice and is mostly computational. I suggest you check out Apostol’s Calculus, which has a more proof-intensive focus. This will help you acclimate to a radically new way of thinking about mathematics. It also introduces basic linear algebra and multivariable stuff, if I remember correctly. </p>
<p>Then I would suggest learning linear algebra, a prerequisite for almost any higher level math course. MIT opencourseware has a lot of great stuff, of varying rigor. One of the main linear algebra profs, Strang, has a textbook which is available online as a pdf. </p>
<p>After that, I’d go through Spivak’s Calculus on Manifolds to learn multi in all its theoretical glory. This is usually used as a book in advanced undergraduate analysis courses, so it’s not for the faint hearted. But it is certainly proof-based and will give you a thorough grounding. </p>
<p>Following that, I would learn some set theory and point-set topology, followed by modern algebra. But sky’s the limit, really. </p>
<p>Self-studying from these sources will be exponentially more rigorous and beneficial than taking courses at your local CC. The only downside is, as you mentioned, you can’t put them on your transcript- but it’s not hard to work all your ravenous self-studying into college essays. And as long as you can demonstrate your understanding placement shouldn’t be much of an issue either. </p>
<p>Good luck 
</p>
<p>CC high level math courses are not very rigorous. You will learn a lot more from other sources.</p>
<p>You can join the math circle in your town if available. Check here:</p>
<p><a href=“http://www.mathcircles.org/[/url]”>http://www.mathcircles.org/</a>
<a href=“https://www.mathcircles.org/Wiki_ExistingMathCirclePrograms_view[/url]”>https://www.mathcircles.org/Wiki_ExistingMathCirclePrograms_view</a></p>
<p>Online math:
<a href=“http://epgy.stanford.edu/[/url]”>http://epgy.stanford.edu/</a>
<a href=“http://ocw.mit.edu/index.htm[/url]”>http://ocw.mit.edu/index.htm</a></p>
<p>Summer programs in math:
<a href=“http://www.mathcircles.org/node/56[/url]”>http://www.mathcircles.org/node/56</a>
PROMYS and Canada/USA Mathcamp are very good. They also have scholarships for low income families.</p>
<p>Math competitions:
<a href=“http://www.maa.org/math-competitions/about-amc[/url]”>About AMC | Mathematical Association of America;
<a href=“http://www.artofproblemsolving.com/[/url]”>http://www.artofproblemsolving.com/</a></p>
<p>“My school doesn’t have any sort of math club/team, so that’s out of the picture.” No it’s not. You could start one. </p>
<p>I think most students take multivariable calc aka calc 3 after BC calculus, but I agree with the other posters that you aren’t likely to find the sort of midlevel proof-heavy course you’re interested in at a cc. And can you jump in to those other courses without multivariable? It’s sometimes listed as a prerequisite for other classes–this was an issue for my daughter, who took some college math in high school. </p>
<p>Can you do a math project for a science fair? Can you do math for independent study credit? Even if you can’t get a math club started, there may be some math competitions you can enter as an individual without a team or school support–not sure about that. So there may be ways to get a little external recognition for your effort if you’re not in a class. But even if you can’t, if you get very far with this I think you can explain it in your application. </p>
<p>I believe that you can arrange to take the AMC test at a different site if your school doesn’t participate in that. You really should look into that–it’s the first step in qualifying for the International Math Olympiad and even if you don’t make it so far (it’s very hard), I think it would be good for a student like you to participate, and well worth some inconvenience to get to the testing site.</p>
<p>You can also ask your school to register for the AMC competition and take the test at your school. This requires someone to proctor the tests. Ask some other students to make a petition together with your school.</p>
<p>It’s also possible to take the AMC by yourself if you live near one of the colleges on this [url=<a href=“American Mathematics Competitions”>American Mathematics Competitions]list[/url</a>] and can take it there. That would probably be easier than trying to get your high school to offer it.
There isn’t usually a specified “placement test” for getting out of linear algebra or number theory like there is for getting out of pre-calculus, but some universities allow students to place out of a course by taking an exam similar to the final exam for the course. I wouldn’t worry too much about this, though. If you go to a challenging university, you’re not going to be bored by the math classes even if you’ve already seen some of the material. I mean, the AMC 12 tests are just pre-calculus, but most pre-calculus students would learn new things if they took them. </p>
<p>You can also do Khan Academy. I’m pretty sure they have Multi-Variable Calculus and Linear Algebra.</p>
<p>Wow, you people are smart! :)</p>
<p>Some of the high lvl math classes only have “math maturity” as its only requirement.</p>