Where to Take Differential Equations and Effect (Freshman in High School)

College Search & Selection Community Colleges
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Disclaimer: I had no idea which forum to put this in so sorry! :slight_smile:
Hello

Here’s my story:

I come from a “competitive” neighborhood where there’s a lot of smart people who take calculus in seventh grade (please don’t chase after me on that). Anyways, I’m looking to take differential equations somewhere. The problem is that I do not have the prerequisites like Multivar. I have learned all the material (please don’t just say I haven’t “fully” learned the information) so I need to find a place that doesn’t really hold prerequisites as a must. My local community college according to my counselor removed the testing ability to skip math levels so I am kind of stuck. I’ve looked towards online math courses but I don’t know if they’re any good. I’m mostly looking for a course for enrichment since I haven’t seen great online resources for teaching it (and yes, I do know of MIT opencoursware, it has good info).

I need to learn differential equations since I’m competing in physics (also math) and knowledge of DE is beneficial in the long run.

I’d really appreciate it if you guys could offer any good online courses that don’t have “prerequisites”. One last question is how this would impact colleges reading my transcripts as I’m “officially” taking calculus next year.

Thank you for taking your time to read this, and your feedback is greatly welcomed!

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Hmmmm, this is a tough one, @IamReallyScared. Most of the online course providers I am aware of at least say they require either multivariable or linear algebra. Now, of course you do not really need either for a standard course in ODE, it is more just to ensure a certain level of mathematical sophistication.

If you have not taken the AP Calculus exam, I think it might be tough convincing a school to let you take DiffEQ. (Yes, you are right - there are a number of kids taking calculus as early as 7th grade, and they tend to do very well on the AP exams too.)

I would try asking CTY, assuming you have taken some sort of standardized test that would qualify you. (Many kids take the SAT as part of a 7th grade talent search, but there are other ways to qualify - you just need to check them out.) I understand from friends that their self-paced courses past single variable calculus are good.

My own kid took DiffEQ through Stanford Online High School, but it is an involved process to be accepted there. It might be worth exploring the Stanford ULO courses, which are identical to the Online High School courses at the higher levels, and often meet with the kids in the same sections. https://ulo.stanford.edu/mathematics I do think it will not be easy to convince them if you do not even have an AP Calc exam grade, but it is worth a try.

I would question, though, whether you really need a formal DiffEQ course to compete in the high school physics competitions, the F=ma, USAPhO sequence for instance. I would suggest looking into the physics competition course offered through AOPS (www.aops.com) and supplementing your knowledge with some reading in a standard ODE textbook.

I can tell you for sure that DiffEQ will not help you with any of the standard competition math opportunities in high school, even if you should make it all the way to the IMO!

Best of luck. If you were my kid, I would encourage you to just read a little in the area. Working through a rigorous single variable text like Spivak’s Calculus would also be a wonderful way to increase your mathematical sophistication. Again, best of luck!

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CTY has DiffEq, Linear Algebra, Intro to Abstract Math, Real Analysis, and Complex Analysis.

Linear only required Calc BC (Multivar is preferred but not required). DiffEq requires on of Linear or Multivar. But they are used to working with advanced students, so perhaps something could be worked out.

I am curious which math competitions require DiffEq. AMC, AIME, AMO, MOP, IMO don’t even touch calculus, and training in number theory, Olympiad geometry, and several other areas of math are more appropriate for those competitions. Putnam doesn’t accept anyone below a HS Senior, if I remember correctly.

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You indicate that you have mastered Multivar outside of a classroom setting. Why can’t you cover DiffEq in that same way?

Your counselor has told you that the local CC has removed the testing option for enrollment, but have you spoken with the math instructors there yourself? If you approach them directly, they may be able to arrange something for you. For example, if the DiffEqu instructor believes that you are ready for that material, you might be allowed to audit the course. Which, frankly, is a better deal for you than taking something for credit. If you audit, you do the work but you don’t get a grade and you don’t earn credits so you won’t have to worry about tracking down that college transcript every time you need it for the rest of your life.

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Thank you for all your insightful comments!

Yes, I do the AMCs like many other kids I know. And yes, I know that even the IMO does not require calculus of any kind. However, I was addressing to the IPHO about differential equations; I’ve read several articles where it addresses that DE would be helpful on some questions even though “it’s technically not required”.

Thank you @OneMoreToGo2021 for the CTY suggestion. I have looked into it before and asked my counselor though my counselor instead asked me to look into places without prerequisites and that were “California based”. I’ll try contacting their department about “math skipping”. PLO seems like a cool suggestion so I’ll take a look into it.

Sidenote: I’m in a Californian public high school so my school is geared towards the UC system (thus credits and such) and is also kinda stingy about courses?..

@happymomof1 The problem with differential equations is sadly that resources are much more limited than the Calc 1, 2, 3 most likely due to it being “harder”… I’ll look into contacting my local CC’s math instructors but last time I tried, they were non responsive…

One last note, would you guys think that taking both the AB and BC exam (while I’m enrolled in AB next year) be an okay decision to pass the prerequisites for Multivar (if I am to take it earlier to show colleges I “officially” took it)? The issue is that I would not have any math courses left in my high school for all four years (I’d take AP Stats the following and the end) if I then skip Calc BC.

Thanks again for the help!

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What grade and math course are you in now, and which math courses will you take in future grades on the progression you are in now?

For math beyond single variable calculus (AP calculus BC or equivalent), are you concerned about college credit, or just learning the material for your own purposes?

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CTY is all online, so I don’t get the “California based” concern.

You can’t take both the AB and BC exam in the same year. If you take the BC, you get an AB sub-score. So if you’re going to take one, take the BC.

Would your school refuse to allow you to take BC if you took the BC AP? That would be odd.

When you fall into the Calculus Trap, sometimes you need to do strange things based on school limitations. My D is slogging through AB and BC over two years at school because she would have the same “ran out of courses” issue, and she’s taking NT, Game Theory, Combinatorics, etc., externally for enrichment. Fortunately one of our local CC’s have online Linear, MVC, DiffEQ, so she can take those, even if her HS doesn’t recognize them.

Most public schools aren’t equipped for exceptional learners, not just in Math.

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Are there really no CCs in CA offering these courses online? It seems very odd to have the option at the next county over from where we live but have no options in CA.

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Neither are the vast majority of private high schools. It just goes with the territory. If you have a kid >+3sd there just aren’t going to be many options because there just aren’t that many of these kids. College will be much better.

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@RichInPitt, the “California based” concern basically means that the program’s(hard to word) “base” is located in California which tends to mean that it satisfies the “U-G” UC requirements. The Calculus Trap is definitely a good article by Mr. Rusczyk that addresses many concerns. My concerns with taking the Calc BC exam while in AB and then taking the BC class next year are that I would not have an “official” AB exam score(which I heard gives credit at some schools if you get a 5) and that I would raise a lot of issues with my school(they’d probably prefer me take AB but who knows). As for other “outside math courses”, I’ve finished up AOPS’s books about combinatorics and probability so I’ll probably take topology later at a local CC for fun.
Unfortunately, all the local CC’s don’t really have the online option which is sad.

@ucbalumnus I’m currently enrolled in Math Analysis or the equivalent of Precalculus.

My current math course schedule will look like this:
Freshman- Math Analysis
Sophomore- Calc AB
Junior- Calc BC
Senior- AP Stats

Currently, I’m looking for a suitable place to take differential equations and afterwards I might take some other math courses for fun… Honestly, I would prefer if the courses could offer some credit(I heard it’s expensive…) but yes, this is mostly for enrichment.

@OneMoreTogo2021 Yep, that’s definitely true though a lot of the private schools near me are actually pretty good. It’s too bad that I declined for personal reasons; I’m kind of regretting it especially with some personal teacher experiences.

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There are community colleges in California with online courses. https://cvc.edu supposedly can help search.

In terms of prerequisites for differential equations, I checked four community colleges in California. Two listed only single variable calculus, one listed linear algebra and single variable calculus, and one listed multivariable calculus. The actual prerequisite knowledge needed in most cases is single variable calculus, but some basic linear algebra is used with linear systems of differential equations, and some basic multivariable calculus may be used if partial differential equations are covered.

There are some legally free differential equations textbooks on the web if the goal is just to self study for desired knowledge for purposes other than getting college credit.

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You needn’t limit yourself to coursework through a community college. Check any local 4-year institutions as well.

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Oh, that’s a good idea. I found a local university that offers DiffEq with “instructor consent” so I’ll try contacting them.

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Another question:

I know some colleges ask for what year you took calculus (if you did). So, if I were able to successfully be able to enroll myself sometime in the spring or summer, how would I report it?

Thanks