What dual enrollment math classes should an aspiring physics/math major take? This year I am finishing up AP Calc BC and AP Stats and next year I’m looking forward to taking a couple math classes at my local uni. Popular options I’ve heard are diff equations, linear algebra, and calc 3.
Feedback would be appreciated!
Typical college sophomore level math courses are:
The first three would generally be useful for physics majors, while all four would generally be useful for math majors.
Linear algebra and differential equations are combined into one course at some colleges.
For math majors or others going on to upper level math courses like real analysis and abstract algebra, a college sophomore level course on proof techniques and such would be helpful. This may be a standalone course, or may be part of a discrete math course or an honors version of one of the other college sophomore level courses.
Okay, thank you. To be clear, is a proof based course geometry? I don’t have much experience with proofs. Or is it general logic?
High school geometry is often taught with general logic and proofs at a very introductory level.
A college sophomore course on proof techniques could use topics from many areas of math, such as algebra and calculus. Discrete math courses with proof techniques will obviously use that material. Many upper level math courses are proof-focused, such as real analysis (proving the foundations of calculus) and abstract algebra (proving the foundations of algebra).
You may want to look in the university’s requirements for a math major to see if such a college sophomore course on proof techniques is required or recommended.
Are you going to be a senior? I was in a similar position senior year. I finished AP Calc BC junior year which was the highest math class taught at my high school. I took Multivariable Calculus and Differential Equations DE senior year. I was planning to do Multivariable Calculus and Linear Algebra but it didn’t work with my schedule. I would recommend taking Multivariable Calculus the first semester and then you can choose between Linear Algebra or Differential Equations for the second semester.
I think I would shoot for MVC/DiffEQ over Linear Algebra and proof based. When are/did you take Physics C? My son is a dual math/physics major and he is way ahead in the math but sequencing in college and what credit his college took for physics C is slowing down how much physics he has been able to take. That said, double majoring in physics/math is very common. I think the MVC/DiffEQ is more applicable to the intro levels on physics.
I will be a sophomore. There are a few seniors at my school who also followed your trajectory and they had a really good experience, from what I’ve heard.
Okay, thank you. I will be taking Physics C next year as well.
You may want to check if the calculus-based physics courses for physics majors at the university cover the material better than AP physics C. The university courses typically use more math (e.g. the course with E&M commonly lists multivariable calculus as at least a co-requisite and uses that math).
@hebegebe thoughts for planning the rest of HS math for this rising HS sophomore who had completed AP calc BC and AP stats?
This is what I originally wanted to do, but my high school doesn’t allow dual enrollment for science, unfortunately. I assume Physics C has no calculus?
AP Physics C is calculus based.
AP physics C uses calculus, but to a lesser level than physics in college typically does. Typically:
| Physics course | Math prerequisite | Math corequisite |
|---|---|---|
| AP physics C mechanics | Calculus | |
| AP physics C E&M | Calculus | |
| College physics 1 (including mechanics) | Calculus 1 | Calculus 2 |
| College physics 2 (including E&M) | Calculus 2 | Multivariable calculus |
You may also want to check the math prerequisites of the physics courses at the university, and whether the university accepts AP physics C in place of them.
Thanks, this is really helpful. What about IB physics? Is it the same as AP physics C?
There is no mention of calculus in the IB physics HL description at https://www.ibo.org/globalassets/new-structure/programmes/dp/pdfs/physicshl2016englishw.pdf .
The real answer is that high school students can be admitted to the most selective programs with just Calculus BC by senior year. Having one additional year of acceleration (such as MVC and Linear Algebra) may help a bit, but beyond that, there’s no real admission benefit. These colleges are looking for very talented high school students that they can teach math and physics at the university’s level, not students halfway finished with college math.
Instead, most students admitted to the most selective math/physics programs have shown talent in other ways, such as USAMO for math or USAPhO.
But given you have already hit everything you “need” by freshman year, the question is what should you do. You can’t stop doing math completely, as that could suggest a lack of interest. So at this point, courses like the following make sense for your remaining years.
But note that for the most selective programs, you likely still need more. Another option besides the USAMO/USAPhO track is doing research in math or physics with a local university professor.
Thank you. This is really helpful. As far as math competitions go, the sense I’ve gotten from the few I’ve done (AMC 12, Mathcounts) is that they tend to be heavily focused on number theory and algebra. However, I am more interested in applied maths. Will this be a problem if I am accelerated in one branch of math but not the rest?
Also, in terms of research, how would I be able to do that? Also, what qualifies as research? Is it only making new discoveries or can it be just expanding on known theorems or ideas?
Thank you.
It can be difficult for high school students to do math research unless they join a program that explicitly targets that, such as MIT PRIMES.
You may have an easier time working with a professor on physics, and you have the advantage of being so young and having a strong understanding of mathematics, allowing you to develop more expertise over time. If you have some coding skills, you can approach a professor and say that you would be happy to do anything that needs to be done. For example, they may have a large amount of data that needs to be scrubbed before they can analyze it. You could offer to do just that. This tends to be boring work, but it’s a critically important part of the research process. And if you do that for one summer, the professor may be willing to give you a more meaty project the following summer. Now, it’s really unlikely that you will do something earthshattering. But you may earn a chance to speak about your work in a conference, and possibly be listed as a coauthor in one of your professor’s papers. And ideally, you would get a letter or recommendation out of it.
There is a book I recommend that describes this process in more detail, which is called “How to be a High School Superstar” by Cal Newport.
IB physics is algebra based. I’ve had 2 kids take it.
OK, got it. Sorry, I didn’t see that in your original post. Then you have lots of time to take lots of math classes, lol. I would start with Multivariable Calculus and then move on to max out whatever other math classes you can take DE. Good luck to you!