Hello. I’m an 8th grader who is currently self-studying AP Calculus (I really REALLY love math!!!). I will be taking the Calc AB exam in May 2018 and Calc BC in 2019 (because I was told that AP exams taken before gr. 9 don’t count for post-secondary transfer credits). I am wondering what I would take for the remaining three years of high school (or would I be better off trying to graduate early?)
By the way, I’m a public school student in Ontario, Canada. I’ve self-learned all of my math knowledge right off the internet. Also, because I live in Ontario so the government won’t cover my tuition, if I take courses at my local community college/public university it might be very costly. Would there be a way to, say, fundraise (that word doesn’t really fit, but I don’t know what else to call it) some/all this money?
Well you can’t really “fundraise” to pay for college classes. You’ll have to figure out a way to pay yourself. Since you are so ahead think about this first:
- Are you learning math or memorizing how to do problems? If it is the former then that’s great. Knowing the theory is important for future math courses. If it is the latter then maybe take Calc formally in high school. Anyone can memorize and recognize the steps needed to differentiate or solve an integral.
If you actually “know” the math then I would take math in the following sequence after Calc BC which is Calc 1-2.
Multivariable (both differential and integral so it can be 1-2 courses depending on the school)
Linear Algebra (make sure you take a course that is both theoretical and computational)
Differential Equations (a good diff eq class will go over systems of diff eq so linear algebra should be a pre req)
Optional: discrete math, statistics, real analysis
If you got a 4 or 5 on the Calculus BC exam, that is generally considered (at least for all colleges in my state) evidence of mastery of Calculus I and II material, meaning you should take Calculus III next. Here in the States, high school students who are extremely accelerated in math take Calculus III/Linear Algebra, etc. via dual enrollment, usually at a community college, but sometimes at a university if one is close enough.
You were told wrong. While there are probably a few colleges where this is the case, most do not have this restriction.
Have you looked at the Art of Problem Solving? https://artofproblemsolving.com There are interesting courses outside the normal sequence and courses (and books for self-teaching at home) for increasing problem solving skills. My caution would be to seek personal assistance (offered freely on their website) in selecting courses. The difficulty level of AoPS material is greater than normal school courses.
The following articles might be of interest: https://artofproblemsolving.com/articles/calculus-trap (short), https://mathprize.atfoundation.org/past-events/2009/Rusczyk_Problem_Solving_Presentation_at_Math_Prize_for_Girls_2009.pdf (longer discussion)