<p>What types of courses can you take after BC if you are still in High School? can you guys tell me some online courses that colleges offer?</p>
<p>Generally, multivariable is next, then either linear algebra or differential equations. You could also consider probability & statistics, or number theory. See what your local colleges have to offer, or try one of these:
<a href="http://www-epgy.stanford.edu/%5B/url%5D">http://www-epgy.stanford.edu/</a>
<a href="http://www.utexas.edu/cee/dec/%5B/url%5D">http://www.utexas.edu/cee/dec/</a></p>
<p>My order after BC:</p>
<p>Multivariable and Mathematical Structures (same time)
Differential Equations and Number Theory (same time)
Linear Algebra
Abstract Algebra</p>
<p>So basically what I'm saying is that texas137 hit it right on the nose.</p>
<p>I would recommend multivariable calculus and differential equations. Linear algebra often has heavy emphasis on proofs, so it's better to take it in college.</p>
<p>im_blue, I think that's the very reason you should take Linear Algebra early. The point of the class is not only to learn linear algebra, but more to develop a certain style of rigorous thinking and writing, which, if developed, will lead to doing better in other math classes and competitions. If you finish BC before senior year you are likely good at math, so I suggest Linear Alebra.</p>
<p>Well, my point is that if you want to get a head start on your college curriculum, then taking linear algebra at a community college or local university wouldn't be as good.</p>
<p>Perhaps, but again, many of the students that finish BC calc so early are very interested in math, and if you genuinely want to get better, I suggest taking a class like linear algebra, or mathematical structures (which introduced me to almost all branches of math, and to rigor).</p>
<p>I suggest reading an article on AoPS, "The Calculus Trap": <a href="http://www.artofproblemsolving.com/Resources/AoPS_R_A_Calculus.php%5B/url%5D">http://www.artofproblemsolving.com/Resources/AoPS_R_A_Calculus.php</a></p>
<p>the EPGY site has a good general discussion about the order of courses. Go to this link, then select "guidelines" in the second paragraph.
<a href="http://www-epgy.stanford.edu/courses/math/univ.html%5B/url%5D">http://www-epgy.stanford.edu/courses/math/univ.html</a></p>
<p>At my high school, BC is offered as a Junior class so senior year I took Number Theory and Discrete Mathematics (1 year), Multivariable Calc (1 semester) and Differential Equations (1 semester). I was a prospective math major, but these classes made me reconsider. </p>
<p>All are worth the taking if you get the chance. They are fun, engaging and difficult. Differential Equations is just flat out hard. Multivariable is just adding more BC calc stuff and Number Theory is a great theory and proof based pure mathematics class.</p>