Episteme

I will be a sophomore this upcoming school year, and I will be taking AP Calculus BC. However, because I plan to major in math or science, I really want to take more math courses, and there have recently been severe cuts to dual enrollment in colleges near me so this is not a likely option. Are there any online courses that are credible and would look good to a Ivy

rspence

I suggest taking a more discrete course such as number theory, or try competitions such as AMC/AIME/USAMO. These will definitely help you be more "well-rounded" in terms of math ability, as you'll be able to do proofs and be creative with finding the solution to a problem (e.g. proving an inequality using an entirely geometric method, which students almost never see in a standard HS textbook). Also, qualifying for AIME/USAMO is a big plus on any college application.

You don't necessarily need to rush through all the calculus, group theory, real/complex analysis, or algebraic geometry courses. Calc BC is definitely a good course, but don't complete the standard calculus curriculum without knowing how to do proofs, for example.

This article basically sums it up: The Calculus Trap

AoPS also has some good online courses.

Episteme

Thanks for your reply. I am actually an active member of AoPS and I know about the Calculus Trap. The reason why I am taking Calculus this upcoming year is so I can start studying calculus-based physics. I have taken some courses on AoPS and have almost all their textbooks, of which I am currently in the process of reading the Precalculus book. My school doesn't offer any courses after BC, and I do not want colleges to deem it as if I have not taken any math courses for two years. Thus, I am in need of credible online courses. I am only aware of EPGY, but am not certain if I am eligible for that.

rspence

Ah, okay. Have you taken the AMC exams?

You can also see if your school, by any chance, would be willing to offer multi-variable calculus the next year...that's what my school did, since there was enough interest. That's how I took multi-variable calculus my senior year. A few juniors are also taking linear algebra next year.

Episteme

I took the AMC 10 in February, but I did not know of AoPS too long before that, so I didn't qualify for AIME. I expect to do much better next year. I will talk to my Math Department Chair about that option, thank you.

rspence

Alright. Yeah, qualifying for AIME definitely helps on any college application. However, if you want to aim for USAMO/USAJMO, you'll probably need at least an 8-9 on AIME.

Sure, you can definitely do that. However, my school's a charter school, so they were easily able to offer a multi-variable class (during lunch time, not during any regular period). For a public school, it might be a bit harder...