I’m taking AP Calculus BC right now as an eighth grader and I anticipate finishing before I start ninth grade. What math courses should I take throughout high school? I am looking into a STEM major for college (probably engineering or math).
- What class does your current math teacher recommend?
- Talk to a guidance counselor to see what is offered in your particular HS. And hopefully he/she will know what local colleges offer.
- You could ask your if it would be ok to reach out to the chairperson of the HS math department to get input.
Congratulations, that is quite an achievement! Looks like you will have run out of high school math classes before you get to the 9th grade!
My son was accelerated as well, and then ended up taking classes at our local university when he ran out of math classes at his school. You indicated a passion for STEM, here are some classes you might want to consider:
- AP Probability & Statistics
- Linear Algebra
- Multivariate Calculus
The reason being is these are the classes you would usually take at a 4 year college during your freshman/sophomore year of college. Additionally since you wouldn’t necessarily need those classes for graduation requirements at your high school you could (depending on the school and where you studied it) use that as credit towards your college credit hours.
From there depending on the path you wanted to take, you should look at the university/college program you would like to attend and see what areas of mathematics are required in their plan of study.
Math is awesome!
Typical math after calculus BC:
College sophomore level (commonly taken by those majoring in math-heavy subjects):
multivariable calculus
linear algebra
differential equations
discrete math
calculus-based introductory statistics
College junior/senior level (commonly taken mainly by math majors, though some in statistics, physics, economics, etc. take them):
linear algebra (more emphasis on theory and proofs)
abstract algebra
real analysis
complex analysis
various junior/senior level math electives
There are other junior/senior level courses in statistics, computer science theory, and operations research that may be of interest to someone who wants to take more math-like courses.
Given how far advanced you are in math, if you major in math in college, choosing a college with a good graduate program in math can ensure that you find enough suitable offerings (graduate level courses and graduate level research opportunities as an undergraduate).
Is there a college near where you live? Does your local HS offer math courses beyond calc BC (many don’t)?
You may want to look at Johns Hopkins’ CTY courses. They offer college level math courses on a high school schedule, for example Mulitvariable Calculus can be taken over the course of two semesters rather than the more typical one semester college schedule.
If you do DC, I would recommend that once you decide which colleges you want to apply to, check to see that dual credit courses will transfer.
My son will start at Texas A&M Engineering in fall 2020. Because so few students transfer the higher math courses (post-Cal II), A&M still has to review his course syllabi. Also, he is not exempt from their Math Placement Exam for Calculus readiness because many students with AP/DC credit may still not be ready for the level of math required by an engineering program.
We’ve understood this from the beginning, but my son kept going in math classes because he didn’t want to “lose momentum” in high school.
I just wanted you to be aware of this in case you went the DC route. Most universities have a web page where you can check transfer course equivalencies (you can do a search on their main page).
I wish you the best in finding a college and major that fits your passions!
My S21 was similarly advanced in advanced in mathematics. He placed into BC Calculus in 7th grade, but due to irreconcilable scheduling issues (middle school and high school were 10 miles apart), could only complete AB by the end of 8th grade. There are more kids like you than you might imagine who reach AP Calculus in elementary school (the College Board does not always track grade levels well, so if you look you will see a large contingent of unassigned grade level test takes in the results).
OP, based on our own experience and knowing more than a few of these kids, I would recommend that you not plan on progressing past a first course in Real Analysis during high school. Should you want to major in mathematics or a similar highly rigorous STEM field (not engineering, but, say, physics), you might well want to retake the topics in the honors sequences offered at many top schools that combine very rigorous treatments of multivariable/vector calculus and linear algebra.
For high school, I would recommend the same sequence that our S21 has done, at least for formal classes: a year of multivariable calculus (differential and integral), followed by a semester each of introductory linear algebra and differential equations, and then at least one course in basic intro real analysis, abstract algebra, and discrete math. That should fill up at least three to three and a half full years. I wouldn’t go any further than these courses, unless you have unusual aptitude and talent. I would not much bother with statistics unless you are particularly interested in the subject, and then as suggested above a college level intro calc-based course would be most appropriate.
I would also recommend supplementing a bit with some online courses in areas that would develop your mathematical aptitude and sophistication without being unnecessarily duplicative of what you will study in college. The classic article on this enrichment is “Don’t Fall into The Calculus Trap” available here: https://artofproblemsolving.com/news/articles/avoid-the-calculus-trap. The article is from the founder of AOPS, and I can recommend the AOPS courses in Number Theory and Combinatorics as being particularly valuable. AOPS offers an intro and intermediate intermediate course in each of these topics. (But note they will be a bit duplicative of formal discrete math and/or number theory courses.) www.aops.com
In order to find appropriate courses for our S21, we used both a local university as well as Stanford Online High School. OHS has terrific courses in linear algebra, number theory, differential equations and real analysis. Another option - less expensive but identical in content for the most part - would be to take university level math courses through the Stanford ULO program: https://spcs.stanford.edu/programs/stanford-pre-collegiate-university-level-online-math-physics.
Last, you are obviously interested in mathematics to have arrived at where you are. If you haven’t thought about it yet, do not neglect the opportunity to attend the high level math camps that are generally open to 9th graders on up. Canada/USA Mathcamp (our S21 has gone twice), MathiLy, HCSSiM, Ross, PROMYS and Stanford’s SUMaC are some of the best of breed (SUMaC is only open to 10th and 11th graders).
Congrats on your achievements so far, and best of luck in the future!
AP calculus AB exam: 300,659 total, 697 not HS, 102 <9th grade, 3,508 not stated
AP calculus BC exam: 139,195 total, 688 not HS, 93 <9th grade, 1,289 not stated
“Not HS” and “not stated” could include some before 9th grade, but could also include others in high school or have graduated or otherwise left high school.
Wow, that’s a lot of kids doing calculus in middle school, and if you add 9th graders… that’s incredible.
In the one math circle that my kid was part of in middle school, we knew at least 15 kids who took either AB or BC before 9th grade, including my own, and one who took the BC exam in 6th grade (at 11 years old). This was just one circle in a wealthy suburb that is not known for a high concentration of math talent (e.g., like Cupertino or a few other other Peninsula cities).
Most studied the standard curriculum on their own after 2nd or 3rd grade, and frankly were better for it. Sitting through the normal classes would have been just a waste of time (although many no doubt were forced to do that as well).
I suspect there are at least 1000 of these kids nationwide who take AP Calculus before 9th grade, but that is just an informed guess. At my kid’s summer math camp, practically all 120 kids had already studied calculus (some were even past analysis), and the median age was around 15-16 (high school sophomore).
We are not seeing some freak occurrence of geniuses here. The standard curriculum is deadly slow for anyone above about two standard deviations above the mean math ability in my opinion. That is a lot of kids who could accelerate easily if they have the interest and are made aware of the opportunity, and the internet has provided those conditions in spades for many.
Also see what your local Community College offers and how Dual Enrollment works at your High School. Talk to your Guidance Counselor.
If you are interested in engineering, I would suggest Multi-variable Calculus, Differential Equations (typical sophomore level math for engineers), then linear algebra and whatever else is offered.