I took AP Calc AB last year, and I am also taking AP Statistics.
My school system requires four years of math to graduate, regardless of the level.
What would the path from here be? -
AP Calc AB --> AP Calc BC & AP Statistics (10th) --> Multivariable Calculus (11th S1) --> Differential Equations (11th S2) --> Linear Algebra (12th S1) --> ???
Last semester = ???,
Also I wanted to take two math classes again in 11th, or 12th, so what would be the next three classes after Linear Algebra?
I think at that point you’re delving into Real Analysis and other topology classes.
At that point you’re preetty much out of undergraduate mathematics topics.
Are you sure you don’t have high school credits from middle school? It’s hard to believe that any high school would require anyone to take math above AP Calculus BC. I would recommend talking to your guidance counselor if you haven’t already.
Does your high school offer multivariable calculus, linear algebra, and differential equations? If not, where would you take them? What other math classes are available to you?
There’s no required order for math classes after linear algebra, but abstract algebra and real analysis are the most important upper-level classes for math majors.
@purplepoly I suggest taking a proof-based math course if you haven’t already (since it’s important if you study higher-level math).
As halcyonheather said, there usually isn’t a strict sequence, but abstract algebra often includes linear algebra as a prereq. There are also classes on combinatorics, number theory, complexity theory, logic, algebra, topology, etc. and you may find some of them interesting, some of them dull.
Yeah I did up to Algebra II in 8th grade & did precalc over the summer.
And yeah, almost certain that they sure they require it
There have been few people to take MV/DE in the previous years. They take it online at a local community college, and it takes up one of their HS classes. Although, I really wouldn’t want one of these math classes to take up one of my seven classes, so that I can take other electives that I like in school (gym, and lots of others), and I’d be willing to put the effort for these classes outside of school, so I would have to propose that because I don’t think anyone’s ever done that before.
Do you think they would allow me to double up on math Jr/Sr year to take these post-Linear Algebra courses? Or would they restrain me from doing so b/c it’s never been done before =(
Thanks so much for your responses =)
Btw, there’s one of other kid that’s a sophomore in my BC class that’s also completed AP Stats, but I don’t think he’s planning on doubling up on math again, so next yr he’d do MV/DE, and then LinAlg, and something else
As a sophomore without any college acceptances, I’m not sure the value in rushing through the college math curriculum while still in HS. While there are exceptions, there are not that many colleges that will give credit for anything past Calc II and even fewer that will have challenge exams. So many of these courses you may end up having to take again anyway. I’d continue on with MVC/LA/DE or whatever you can find, but I would not double up in math jr/sr year, particularly if doing so will be at the expense of another core subject.
Do you have any reason for thinking this other than seeing “four years of math” as a requirement?
Community colleges don’t offer math classes beyond multivariable calculus, linear algebra, differential equations, discrete math, and calculus-based statistics. If you wanted to take abstract algebra, number theory, etc., you would need to go to a university.
If you’re not going to Harvard or something, you’ll probably be able to transfer classes that you took on a college campus. (Anecdotally, I go to a top-50 private university and I was able to transfer all of the post-calculus math classes I took at a state university when I was in high school.) Online classes, maybe not so much.
Maybe talk to the people who took MV/DE in previous years. MV, in particular, can be a lot of work, and it may not be a good idea to double-up on advanced math with that course. Also, online classes can be harder than in person, because they can lack some of the interaction that aids learning.
Discrete math may also be titled Discrete Structures, and may live in either the Math or CS department at your community college. We got Discrete Structures to be counted as math by the high school for my kid, who was in the same math as you (BC in 10th). But, he is not thinking of doubling up on math.
If you wish to double up junior year, you could pair MV/DE with Calculus-based Stats and Discrete Math. Take Macro/Micro economics (either AP or at the CC as DE). For senior year, what about taking Intermediate Microeconomics and Econometrics? [those require you to have taken Macro/Micro already, hence the jr year recommendation above.] This way, you’d see an application of advanced math and would leave Topology, Number theory, etc, for college. Or, if math applied to economic models doesn’t sound interesting to you, what about further advanced probability/statistics classes?
I second/third taking proof-based math.
One note is to realize that taking AP Calc AB for a year followed by AP Calc BC is half the speed of a normal college course. MV and DiffEq during junior year will be twice that speed (or faster since your community college probably has <18 week semesters).
There are many HS’s that require X number of years of math in HS regardless of the number of credits. Although in the OP’s case, I’m not quite sure how they would enforce it if they don’t offer enough classes.
@halcyonheather Like I said, there are exceptions; my college is not one of them However, remember that the OP is a sophomore and likely has not narrowed down the college application list. Anyway, my point was that s/he should continue down the math sequence for the next couple of years, but to be careful, if not downright avoid, doubling up. There are plenty of ways of getting additional quantitative exposure outside of pure math; I actually like @MYOS1634 's suggestion. ANd I would 4th/5th the suggestion of taking proof-based math.
FWIW, like I said, my college did not allow me to skip past Calc II and I have to say, it was not the worst thing in the world to have to retake MVC/LA in college.
However, remember that the OP is a sophomore and likely has not narrowed down the college application list. Anyway, my point was that s/he should continue down the math sequence for the next couple of years, but to be careful, if not downright avoid, doubling up. There are plenty of ways of getting additional quantitative exposure outside of pure math; I actually like