I will be taking AP Calculus BC my junior year in high school, and I’m planning to do dual enrollment math courses after that since I really love advanced math. What course progression is typical after calc BC? I’ll have 2-3 math classes I’ll be able to take after BC, so what do you suggest?
A typical set of post Calc 2 courses are: Multivariable Calculus (Calculus 3), Differential Equations, Linear Algebra, and Calculus based Probability and Statistics.
If you’re going to a community college, they probably offer some or all of the following:
Multivariable calculus
Differential equations
Calculus-based statistics
Linear algebra
Discrete mathematics
Most colleges will allow you to take these classes in any order as soon as you’ve taken Calculus II or passed the AP Calculus BC exam. The first three are computational and will build on what you’ve learned in AP Calculus BC. The last two are more proof-based (although linear algebra classes vary a lot—some are all about proofs and some are more “how to do stuff with matrices”) and don’t usually incorporate calculus.
All of these classes are useful and often required for STEM majors, so you can’t really go wrong with any combination. For upper-level math classes, the most important lower-level classes to take are multivariable calculus and linear algebra. After you’ve taken those, you’ll be able to take classes like abstract algebra, real analysis, and number theory at most universities. These classes aren’t usually available at community colleges.
If you have any universities in mind right now, you should look into their policies for transferring dual-enrollment credits. You don’t necessarily want to take a bunch of math classes in high school, only to find that you have to retake similar classes in college because you can’t get credit or advanced placement. Some universities have different versions of certain classes (e.g. linear algebra) for math majors and non-majors, and your dual-enrollment classes would probably correspond to the versions for non-majors. Of course, if you end up at Princeton or something, you shouldn’t worry about transfer credit because even their lower-level classes will be advanced enough.
Can anyone recommend some online courses for multivariable calculus and linear algebra? My daughter needs a math class for her senior year, i do not want her to take community college class because of the commute.
Why does she need a math class? I would be surprised if she has completed AP Calculus BC and still has requirements to meet.
@halcyonheather Thank you! That was very informative.
@saif235 Thank you for replying! That was helpful.
My community college does not have a class labeled Multivariable Calculus, instead it has a class called “Calculus with Analytical Geometry III”. Is this essentially the same thing as calc 3/Multivariable calc?
The description for the course is this: “Topics include polar coordinates, vectors, three dimensional analytic geometry, parametric equation, partial derivatives, multiple integration.”
If you are going into the sciences, the Calc III would be a good option, or AP Stats if you haven’t taken it. If you are more math-y, discrete math at a cc or an advanced number theory class through AoPS might be interesting. Their advanced classes are more sophisticated than the community college offerings in our area (SF Bay Area) and target the AIME crowd.
@Shanban1607 Yes, Calculus III is another term for Multivariable. The partial derivatives and multiple integration are the multivariable part. If you can find an online syllabus, it should mention Green’s theorem and Stoke’s theorem. The analytic geometry part is sometimes split out or combined with other courses in quarter-based systems. It makes sense in combination with multivariable for a semester-length class.
Your community college probably has a math sequence flow chart somewhere. While multivariable and linear alg can be taught in either order, I’ve seen sequence set ups where Diff Eq is supposed to be the last of the 3. though I’m not really sure why.
@belmom What specific AoPS courses would you suggest? Do you have any experience with them? Do you believe they are worth the cost? Thank you for responding! 
@Ynotgo I will see if the calc 3 class contains those topics, thank you! My CC puts differential equations right after calc 3, so I believe I’ll take that. Also, turns out they don’t offer linear algebra at the campus I’ll be attending, so that’s disappointing 
Thank you for responding!