Hi friends -
My son just completed AP Stats (9th grade) and will take AP Calc BC next year (10th) - this is how his school wanted him to do it. After that, he has a few options. I have never pushed for math acceleration, and I’m not a math person by any stretch - I feel like my job is just to open doors and offer him options. He chose to accelerate. After next year, he is done with high school math credit and doesn’t need any more. So, he will be taking classes in 11th and 12th for enrichment, to prep for college, and they will be relevant to his eventual college application. I wanted people’s opinion about his options after BC. He will have exhausted the AOPS academic classes (he liked those and they taught him well). His high school offers a cheap option where he can take upper-level math at our local 4-year public university (not highly ranked, but fine). That option is the cheapest, and gives “official” college credit (not high school credit). Other options I see are CTY online (he qualified long ago, but never took a class) or the Stanford Online Math courses (Credit is from Stanford continuing ed). I imagine the CTY or the Stanford ones are potentially more interesting and geared to accelerated high schoolers rather than older college students. Are any of these regarded as better or prestigious by college admissions (or do you know other options)? If he ends up at a public school/UC, I imagine real college credit would be the better way to go - but if he ends up at a private school, etc., the actual credit will matter much less. For further background, he is not intending to be a math major - he is interested in physics (especially astrophysics) - and he knows his math has to be very strong for that. Thoughts? Any personal experience with how this works with college admissions? I guess I would normally lean toward recommending the option that gives real college credit, except that I think he would prefer CTY or Stanford- to clarify, this question is not about summer programs - it is for math during the school year in 11th and 12th grades. THANK YOU!
I sent you a DM.
If the college math is in-person I think that has value. My kids (homeschooled) did some well-regarded online programs (but not as well regarded as the ones you are considering) and some at the local not-that-impressive community college. The CC was a much better experience and they learned the math much better.
As far as learning the material and possibly repeating it later, I took all the Calcs plus Differential Equations and Linear Algebra at my magnet STEM high school. My college (MIT) would only give credit for the first semester of Calc, so I had to repeat all the other classes, but I think that was good for me. I learned it well the first time, but I was able to really go to deeper level of understanding and application the second time I took it.
And if UCs are a possibility, those classes will transfer as real credit. You can check assist.org to see exactly how they will transfer as each California CC will have an articulation agreement with each UC.
My daughter took AP Bio through CTY this year (I realize that is not math, but it is an experience with a full CTY course). She found it interesting and provided a good depth of information. She learned more in that course than probably most other courses she has had in high school, but her high school is not a very challenging school to begin with. Knowing what she knows now after having taken the course, I think she would make the same decision again. The course was well structured and provided a great deal of information.
We have not had any experience with the Stanford Online Math courses for comparison.
Good luck!
Second this, if a UC campus is within driving distance.
Typical second year college math courses (after completion of single variable calculus or AP calculus BC) would be:
- Multivariable calculus
- Linear algebra
- Differential equations
- Discrete math
Note that 2 and 3 are sometimes combined into one course. For a prospective physics major, the first three tend to be useful. Discrete math is mostly of interest to computer science and math majors.
So if taking math at a local college while in high school is feasable, using that opportunity to take the above courses could be useful.
if the 4-year public univ has a graduate program then they must have some good people to teach basic college math. I think Multivariable Calculus, Differential Equations, and Linear Algebra are almost universally used by physicists and engineers. I would recommend doing these courses a bit slowly (not take two courses per semester). It would be good to develop intuition rather than zooming through these courses. If he still has time left then I would try to do differential geometry.
I agree that taking in-person math classes at an actual four-year university sounds pretty good to me. Great experience for future in-person college classes, and it is entirely possible the profs will be quite good. And really, at most four-year colleges, the students taking that level of math are going to be pretty serious.
I also agree that MVC, Diffy Q, and LA are the natural next steps for a Physics major. I actually quite like this Ohio State chart which I think does a good job explaining what Math leads where:
MVC is Calc III, and people often do that next. Diffy Q and LA are then foundational, either alone or sometimes in combination, for a bunch more math relevant to Physics. If you are looking for more, Partial Differential Equations is a good one for Physics, or something like that foundational analysis class (3345 on this chart). But that other box down at the bottom also has stuff I would consider–like an advanced Probability class, or Vector Analysis. You will actually do stuff like that in college Physics classes for majors, but I think it would be great to have seen it before!
The course was explained extremely well and the materials had great examples and guidelines on how to complete each unit. Simple, smart and easy to understand!
Taking an actual college course at a college while in high school has the advantage of giving the student experience with how college courses are run (meaning much less supervision than in high school, requiring better motivation and time management on the part of the student). Experiencing this in small doses while in high school can work out better than figuring it all out with a full college schedule in the first semester of college.
As a student studying a non-math but math-adjacent major who was similarly accelerated to your student, I very much enjoyed taking higher-level math courses at the local community college (and university once CC ran out). The in-person experience (remote during COVID, but still) was priceless to me, as I learned much more than just mathematics. If I were choosing between those options with what I know now, I would easily choose taking the real university course unless transportation is a significant barrier.