Is there a reason to take DE Calculus III Senior Year?

Pre-College Issues High School Life
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I’m a rising Sophomore in High School, and I didn’t have a spark with math until about 2 years ago, when I took Algebra, and got into Computer Science. Some of my peers that I hang out with (involved in programming, and robotics), are on a more advanced math track, and able to take “Dual Enrollment Calculus III & Differential Equations” in senior year. In order for me to be on this pathway, I would need to take Pre-Calculus over the summer.

So really my main question is; is it worth it to take Pre-Calculus over the Summer in order to take DE Calculus III & Differential Equations in Senior year?

I have the drive & motivation to do it, but to be competitive in college admissions for an engineering program, do I need to?

My current pathway looks a little like this (bold indicates already completed):

8th Grade: Algebra I
9th Grade: Geometry
10th Grade: Algebra II
11th Grade: Pre-Calculus
12th Grade: AP Calculus BC

The path with the aforementioned Calc. class would look a little like this:

8th Grade: Algebra I
9th Grade: Geometry
10th Grade: Algebra II
Summer of 10th → 11th Grade: Pre-Calculus
11th Grade: AP Calculus BC
12th Grade: DE Calculus III & Differential Equations

This is a school-provided description of the “DE Calculus III” course:

“This is a two-semester dual enrollment course offered through NOVA. Students who successfully complete this course will receive 7 college credits. The first semester of the course focuses on extending the concepts of function, limit, continuity, derivative, integral, and vector form the plane to the three dimensional space. Topics include: vector functions, multivariate functions, partial derivatives, multiple integrals and an introduction to vector calculus. The second semester introduces ordinary differential equations. Topics include: first order differential equations, second and higher order ordinary differential equations with applications and numerical methods. This course may be offered only online, via independent study.”

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No. No US college has any expectation that a student have anything beyond calc BC. And most don’t even require that.

Additionally, rushing through precalculus over the summer may not lay the best foundation for calculus.

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The college courses you listed will move at a much faster pace than high school. I assume that’s a standard 4 credit MVC course in one semester and DiffEq (3 credit) in second semester. These classes have to be transferable to the state universities and so will usually be quite rigorous at a CC and you will need to have lots of time for homework and slog through the difficult level of these courses. I would not advise it . Plus the grades you get in the college courses will follow you around for life.

Calc BC is plenty good for senior year. And it’s not clear how rigorous the summer precalc may be. You need a strong precalc to make it through Calc BC. In my son’s HS, the precalc honors actually covers part of Calc BC. If they do stuff like that at your school, you may end up missing stuff from the regular precalc sequence at the school.

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What’s your hurry? Do you think math is going away in a year so you need to stock up on it now?

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Rushing a class at summer isn’t good. You may not be prepped for the next class. No need.

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I would never advise PreCalc over the summer. As @momprof9904 states, you need a strong PreCalc class to get through Calculus. In our district, it’s possible to split a standard PreCalc class into two years of high school classes—there is just that much information.

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My D23 is on the same math track as you.
I would not recommend Pre-Calc over the summer
Stay with what you have. You are fine with AP Calculus BC in 12th Grade

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Agree that rushing through precalc as a summer class risks a weak foundation for calc and beyond. It’s not worth it.

There are other ways to show rigor and and math ability. Why not put your energy into, for example, getting involved in math competitions that utilize your current knowledge base, but take it to a level of greater depth and challenge? Check out the AoPS website, which has extensive information about all of the math competitions available. AoPS offers courses specifically for students prepping for the AMC10 exam, which would be the right level for you to start at. Art of Problem Solving (Check out the “contest prep math” link on that page) Tutoring and/or working with a math club/team/camp for younger students can be other ways of going deeper.

It’s more important to show strong mastery than to level-jump. Stay on your current path; if you want to stand out, find ways to do more with what you are learning than just what you get in the classroom.

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Piling on - rushing through a critical, foundational class with what is likely less than the full support and rigor of a full year course, is not a good idea.

Calc BC as a senior is farther than 90+% of high schools students progress (and I suspect it’s way over 90%) and is fine for any engineering program.

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Got it! Thank you all for the clarifications, and suggestions!

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Not tryna be harsh, but seems like you’re severely underestimating how difficult precalc can be. Many kids struggle to get a good grip on precalc topics over a whole year; now imagine speedrunning it in 2 months or less. And per the experience of virtually everyone who has taken calc: you will very likely struggle in an AP-level calc class without a good foundation of precalc, which I surmise is impossible to build in 2 months max.

I have the drive & motivation to do it, but to be competitive in college admissions for an engineering program, do I need to?

I would rather opportunities outside of the classroom to demonstrate your mastery in math - i.e. math competitions, math team, tutoring, and stuff. check out the AMC competitions if you haven’t already - doing well on it will qualify you for the AIME and possibly win you some honors as well, which I reckon you is orders of magnitude more impressive than simply completing an extra year of math which frankly isn’t that impactful if you are going into engineering. (MV calc pales in comparison with upper-level engineering math courses.)

And just be aware that essentially no college outside of the tippy-top STEM schools expects BC calc by end of HS, let alone MV or DiffEq.

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I am going to say it depends on what type of student you are. My son’s school did offer a 5 week pre Calc class over the summer for your stated reasons. Selected kids were allowed to take it. It sorta sells out yearly. He thought taking it for a year would of been to slow for him. He graduating taking Cacl 3-multivariate… So did the other 30 kids…

But… Most colleges want you to be able to start at Calc 1 level in Freshman year.

But… Yes another but… Engineering programs are looking for rigor. You want to take math and science beyond what your school allows and or up to the most rigor that you can still do well in.

So again, it depends on what type of student you are and how good your understanding of math is currently. Many kids don’t need the year of precalc if they can grasp the foundation in a shorter time frame.

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Playing devil’s advocate, but you know what else colleges are looking for? Applicants with dimension. Not applicants who think their best use of a summer break is doing more academics.

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Well to counter that point and not debate :rofl:, you are assuming that students can only do one thing all summer. My son took the 5 week pre Calc, tutored a kid in Chess (he was a state level varsity chess player), worked on his eBay business, went to Michigan State engineering robotics camp and I am sure video games and friends were in there somewhere.

Most higher ranked enginnering schools want you to take the highest level and most rigorous schedule you can with still getting good grades. If the only path to Calc 3 is to take the summer pre Calc then they AOs will know this by the school report. Look at the common data sets also and description on schools websites. It pretty much states what I am saying. My son knew few kids at Michigan that weren’t at this level. Same for his friends at UIUC etc. Of course not every school reaches this level…

Again, most engineering programs want you to start at Calc 1 in college. This is true. But if your school math level is Calc 2 or 3 your leaving a lot on the table. Physics BC with Calc 3 in senior year is a very strong combination for most engineering colleges. Plus it can help if the Act /Sat scores aren’t where you want them to be.

So. Many ways to look at this. Does he need Calc 3? No. If he does well in it does it make him more competitive especially at his school… Yes.

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This is just an example. Look at the tips. Sure doing more then just studying but…

https://obp.umich.edu/campus-statistics/common-data-set/

I only put this for the OP since this is another way to see what colleges are looking for. In the common data sets its usually page 8 that has what exactly they are looking for. In this example of one GPA and rigor are the top things. In the first link it states something like the highest level of math and science. Every school is different but for most engineering programs this will hold true.

Good Luck

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Not gonna debate, since none of us knows this student. I will simply say that nowhere does it say “we expect / like / admire / prefer applicants to take calc 3.” And / or “Applicants should spend their summers accelerating their math and science.”

I will further posit that many colleges provide suggestions on their websites, but applicants should not necessarily treat them as roadmaps or bibles.

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Yes, that means that the minimum preferred high school math preparation for most colleges is precalculus. Completing calculus while in high school may be a nice bonus in that starting in a more advanced math course can allow for additional free electives later, but is not necessary – obviously, math beyond that is not necessary either.

So with the OP’s current normal progression leading to calculus in 12th grade, it does not seem to be that worthwhile to try to cram precalculus in a summer in order to take math beyond (single variable) calculus before high school graduation.

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It doesn’t but no school would also. Never seen it. Many kids get in with Calc 1-3. Just giving a different view since honestly competition has gone up the last 3 years for engineering. They do look at the schools report and what the highest level of math and science are.

I tell people applying. Put yourself in the best light so the school doesn’t have a reason to say no. I never said that anyone should just be one dimensional. Look at what this one site says for suggestions for the student. To become a leader in something, to challenge themselves etc.

I am not saying if he doesn’t he won’t get in. But for lots of schools going past the minimal requirements does put someone in a better light for rigor. Not just for math /science but any subject. This is why I posted the cds

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OP- Don’t know where you live or what colleges you are considering, but if you are considering GaTech, consider looking into their distance learning math courses Blow the Whistle! (404 error: page not found) | Undergraduate Admission

It might be helpful not only for a GaTech application, but for other Engineering programs as well. Good luck.

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Calc III/MVC is the new BC in our area, and we don’t live in Fairfax or Silicon Valley.