Would it be better to do dual enrollment + 5 school classes, or 7 school classes plus some MOOCs?
For reference, my schedule with the dual enrollment classes would probably look like:
AP Bio
AP Gov/comparative gov
AP Lit
AP Physics C E&M
Band
Advanced STEM Engineering
Dual enrollment courses
First semester: Elementary Differential Equations
Second semester: Intro to Advanced Math
While my schedule without would probably be something like:
AP Bio
AP Lit
AP Gov/comparative gov
AP Physics C E&M
AP Stat
Band
Advanced STEM Engineering
MOOCs
Differential Equations
Abstract Algebra
Maybe some programming/CS theory classes
Which one of these would be better? Both in terms of workload and in terms of college admissions?
MOOCs are fun for you, and you may learn lots of useful stuff, but you don’t get grades or a real transcript. They basically will be math ECs.
Why you think the choice is between one DE math each semester, and AP Stats plus a bunch of MOOCS is beyond me. The real question is those DE math course vs. AP Stats. Personally, I vote for AP Stats. A bad grade in a DE class is on your college record forever, and even if you get a good grade, for the rest of your life you will have to request a transcript from that institution every time you apply to a degree program or for a job that requests all of your college transcripts. Trust me, having attended seven different places, this gets old really fast.
Now if you are dying to take DifEq, then DE could make more sense for you than to just play around with it in a MOOC. Just make certain you have the time and energy to devote to it so that you do end up with a decent grade.
One thing that I’m concerned about, though, is that there are a few other people in my grade who are dual enrolling, and I’m afraid that if I don’t, then my application won’t be as competitive compared to them.
Don’t measure yourself against those people. Take those classes only if you really, truly, want to learn the material, and if you also really, truly, have the time and energy to devote to them.
Talk with your guidance counselor. If your counselor can state that you are pursuing the most rigorous program, you are fine.