Soles schools which have formal advanced math placement exams:
UGA
UIUC
OSU lets students place into courses beyond the freshman honors sequence (4181h and 4182h) with permission of the department
UGA, UWisc, UMD have proof based multivariable calculus that can challenge even students who have taken regular multivariable calculus before.
Ohio University Honors Tutorial College allows students to take courses without prerequisites and take courses as tutorials
I have some relatable first-hand experience with this. One of my daughters applied in 2021 as an advanced homeschooler. She is currently a theoretical astrophysics PhD student at a top tier program. When she applied for her BS she had already completed Calc 1/2/3 multivariate, DifEq, Gen Phys 1 & 2, and like a bajillion others. She ultimately chose to attend a SLAC with a full ride, but she was accepted to a plethora of “big schools” as well. (These days, many of the top tier students are choosing smaller schools over the big name schools for undergrad and then matriculating to the bigger schools for grad school… but that’s another discussion.)
We discovered that universities regard high school-based DE and college-based DE differently. And, from our experience, they prefer in-person, college-based DE. You could register for the AP exams - a ‘5’ on those would carry enough weight to exempt her from the core courses at most schools, but coursework beyond that is highly unlikely. However, it’s not always good idea to try and by-pass some of these courses and a lot can be gleaned from taking them in a university environment, even if that means ‘repeating’ them. Physics, CS, and Math PhD program admissions are INSANELY COMPETITIVE these days (undergrad applications are child’s play in comparison). If your daughter is considering grad school, she’ll appreciate the GPA boost of the ‘A’s she would have from repeating those courses. Also, no disrespect intended, but it’s highly unlikely that her homeschool curriculum and/or open courseware is a foundational equivalent to in-person, accredited, college coursework (unless you yourself possess a PhD in STEM).
Can you register her for courses at a local community college as a DE student? I know you said there aren’t any colleges near by, but does that include CCs? CC classes are structured to be foundational for higher level coursework and the professors are, well, PhDs. That’s what we did and it translated very well, every school was happy to accept her credits. Also, she was able to get letters of recommendation from professors at the CC which helped in her applications. If you don’t have access to a CC, from what I’ve heard Embry Riddle Aeronautical University has a pretty good on-line DE program for advanced students.
Good luck, wishing the best for your daughter.
UCSD and UIUC both have online math offerings, with the former being live and having office hours and with the latter being self paced
No kind of college is nearby. By that I mean we have fewer than 500 total residents in my town and no road connection to any other town (boat or plane only). Which is actually not too strange in Alaska. There is no way to get an in-person expert (actually, with a molecular bio Masters and a geology PhD between us, my husband and I are probably about the closest she can get for science, though she’s beyond us in math).
So, I do read that colleges prefer kids to take in person DE, but we cannot possibly do that. She can take AP tests (and has, for Bio and Chem, and both AP physics C coming up next week). But that won’t cover past the AP level, particularly for math, which is why I asked.
I’m not trying to oversell my kid, but her multivariable calc and differential equations prof does have a math PhD and did used to teach these classes at a university, so I’m just going on her assertion that the class is more rigorous than an average college version (though maybe not more rigorous than an ivy-league version). And her at home prep was just fine to get her up to that. So that’s why I asked.
Of course, maybe it won’t feel like a repeat. I don’t really know if this ends up being a problem often or not. Unlike the poster whose high school had 15-20 kids per year like this, there aren’t even that many high school age kids in town. So I really do appreciate other people’s stories who’ve dealt with this! Personality-wise, she would absolutely hate repeating something for an easy A, but might mature out of that at least a little bit (I hope! She’s never been willing to do anything “too easy”)
Are her current online math classes from a well-known university that offers these courses online ? In that case, the courses would be recognized, especially if the professors write the letter of recommendation.
What they don’t like is a HS teacher who received special training who follows a college syllabus at the HS because the grading practice must be adapted to the HS public and there’s little guarantee the course is actually the exact same as the one from the college.
Note that Northwestern and Harvey Mudd have special pathways for very advanced math kids.
This is 100% true. Both of my kids had AP credits. One of them chose to take the intro level course rather than place out of it with her AP score. She was glad she did. The other chose to use an AP credit in place of intro level stats. So he got credit for it, but guess what? By the time he was ready to take the next level stats class as a college sophomore, he had forgotten what he learned as a high school junior. Because he had applied the credits for coursework, the university wouldn’t allow him to take intro level. His college stats class was brutal. He passed with a B- in the end, but it was a rough ride.
High school is not college and your child will still have plenty to learn. There are different policies at myriad universities. Colleges will offer a multitude of math classes and she probably wouldn’t apply to any college that didn’t. No need to put the cart before the horse.
Your/her concerns are certainly understandable at this point and you certainly don’t appear to be overselling. It’s very hard to assess the comparative rigor of math taken in HS for students on these sorts of tracks, and I don’t know that it really matters. If her preparation has been very rigorous that’ll be clear to the decision-makers when the time comes and vice versa.
I think the challenge is that she’s at a level that many of her concerns will be addressed at the department or faculty level by people in the future, less so by written policies.
Maybe it would be helpful for her to pick a few schools and map out a CS major pathway. She’ll likely find that her AP test scores would take care of Calc 1&2. Depending on whether she’s looking at engineering or not, there might also be requirements for MVC, LA, and discrete math. Likely some sort of probability course. She might or might not have to “retake” some of that OR substitute a higher level with permission (which is not the same as retaking). There also might be optimization courses from math, cs, or other dept. She likely won’t have taken those.
Then she can look at what other math courses she’d want to add. For those, the prerequisite would be the issue and generally she can assume that a math person will assess her preparation and place her appropriately. Math people are pretty thoughtful gatekeepers in my experience. They don’t want other math people slowed down for no reason.
Keep in mind that once a math student gets to her level there isn’t always a linear path of moving on to the next thing. There is often circling back at a deeper level within the same area of math.
I can definitely sympathize with wanting a bit of clarity on some of this. But even if she can’t get all she wants, you can at least be confident that her academic preparation, especially given the circumstances, will be impressive to many of the schools she might want to attend. And once she arrives on whatever campus she chooses, these things will likely work out (obviously, due diligence will be easier for you once you have particular schools and admissions in mind).
Sorry, I mistakenly thought your daughter wanted to be a math major and was afraid she would run out of courses, but see it is more that she wants to be mostly done with math before college and then focus on computer science or data science. In that case, I would not skip out of more than the Calc I and II sequence.
There is not a long list of math courses required for most computer science programs and at my son’s college and many other colleges these required courses are very theory and proof based. If the classes she is taking now are not as strong as the ones offered at her future college or have the same proof writing expectations, she could be at a disadvantage when she gets to discrete math and the upper level computer science classes which are also very heavy in theory and proofs.
My son finished through multivariable in public high school. Between the pre-college math test and his AP scores, he tested out of the entry calculus courses (he also skipped out of the entry level courses in physics and computer science) but decided to retake multivariable and was very pleased the professor approached the subject from a different perspective than his high school so while “easy” was interesting.
One possibility is that if she does have to retake the courses she already took, they will be easy enough that she can take an “extra” course that semester in something she might not otherwise have time to take.