Advanced Math High School Plan - Need Advice

[RoZ589]

Hi. Currently a junior in high school. I love math, and am currently either deciding between going into math or engineering. Because of this, I'd like to take as much math as possible and really challenge myself before I go to college. I'm currently taking pre-calculus at my school, but next year I would like to step it up. There's a local university nearby (Ohio University-Lancaster) that a few students have taken math at before. I feel like taking it at the university would help prepare me better than versus just taking Calculus as a high school class (we don't have AP Calc).

So.. Here are my options:
1. Take Calculus 1 over the summer at OUL, then take Calculus 2 during the first semester of my senior year at OUL. I wanted to take Calc 1 over the summer, but I have a few questions.. What would I take my second semester of my senior year? I don't want to pause in my math sequence, and at the same time I feel that taking anything more advanced than Calc 2 in high school would probably be better off being taken when I'm in college. Is there anything that I could take the second semester of my senior year math wise? Would this be a good idea? I'm also concerned that taking Calculus 1 over the summer will not go as in-depth as I would like due to it being taught over a shorter time period.
2. Take Calculus 1 my first semester at OUL, then Calculus 2 during the second semester. I would not take anything over the summer before the first semester.
3. Take Advanced Calculus 1 my first semester at OUL, then Advanced Calculus 2 during the second semester. They offer advanced versions of Calc1/ 2, which seem to be more proof-based and more rigorous. OUL is not a very rigorous school, and I would like to be prepared for when I take more advanced math in college. I am most likely going to attend Ohio State University. I feel like taking the advanced versions at OUL may prepare me better, since Calc 1/2 at OSU is harder anyways. Is this a bad idea?

What are your thoughts? To give you an idea of my intelligence/ work ethic: I love math and am a hard worker, IQ ~130, ACT 31. By the time I begin, I will have some experience in Calc, because I'm currently self-reading through a Calculus book (Elementary Calculus: An Infintesimal Approach - Keisler).

 

[Crush1986]

Some math I wish I knew a little bit earlier was differential equations. Once I knew how they worked and a few methods to solve them so many proofs and problems in physics became super easy.

 

[RoZ589]

Some math I wish I knew a little bit earlier was differential equations. Once I knew how they worked and a few methods to solve them so many proofs and problems in physics became super easy.

But would taking that in high school be a bad idea? My university's ODE class would be more rigorous and I'm not sure if it's a bad idea to take it at an easier college.

 

[Crush1986]

But would taking that in high school be a bad idea? My university's ODE class would be more rigorous and I'm not sure if it's a bad idea to take it at an easier college.

I dunno, when I took it my professor said he took the class when he was in high school. Guy graduated from Harvard and Berkely, seemed to work out well for him.

 

[Student100]

You should be smart enough to realize IQ is meaningless, and those "IQ" scores are garbage. Just as an FYI.

You aren't going to meet the prerequisites to take differential equations at college/university, so you can scratch that off the list.

Don't take calculus over the summer, unless you enjoy doing poorly, then by all means go ahead.

If you want you can take Calculus one and Calculus two your senior year at the local college, if you have a fancy to be a math major take the proof focused course.

If you want to take something in the summer, see if the college offers an "intro to proofs"/ philosophy logic class or something similar.

 

[micromass]

Whatever you do, do NOT take an important class like calculus over the summer. Summer courses might be fine for gen eds or easy stuff, but definitely not for an extremely important class like calculus.

Since you're going into math (or thinking about it), you should take the proofy version of calculus. You should use the summer to prepare by reading up on proofs, or perhaps already starting calculus.

Also, don't automatically think your high school class offers worse calculus classes than the university. This depends on a lot of factors including the quality of the teacher. Inquire first whether the university class will in fact be better than the high school version of the class.

Finally, you seem to have 6 IQ-points more than Feynman and he grasped calculus easily, so it should be a blast for you. Expect a Nobel prize in the future too (either that or this entire IQ thing is nonsense)

 

[RoZ589]

You should be smart enough to realize IQ is meaningless, and those "IQ" scores are garbage. Just as an FYI.

You aren't going to meet the prerequisites to take differential equations at college/university, so you can scratch that off the list.

Don't take calculus over the summer, unless you enjoy doing poorly, then by all means go ahead.

If you want you can take Calculus one and Calculus two your senior year at the local college, if you have a fancy to be a math major take the proof focused course.

If you want to take something in the summer, see if the college offers an "intro to proofs"/ philosophy logic class or something similar.

Yeah I was going to give a disclaimer that I can't really "say" how smart I am. Just wanted to add the IQ and anything else to give people a general idea.

Thanks for the advice though! I'll look into seeing whether they offer a class similar to what you suggested in the summer.

 

[RoZ589]

Whatever you do, do NOT take an important class like calculus over the summer. Summer courses might be fine for gen eds or easy stuff, but definitely not for an extremely important class like calculus.

Since you're going into math (or thinking about it), you should take the proofy version of calculus. You should use the summer to prepare by reading up on proofs, or perhaps already starting calculus.

Also, don't automatically think your high school class offers worse calculus classes than the university. This depends on a lot of factors including the quality of the teacher. Inquire first whether the university class will in fact be better than the high school version of the class.

Finally, you seem to have 6 IQ-points more than Feynman and he grasped calculus easily, so it should be a blast for you. Expect a Nobel prize in the future too (either that or this entire IQ thing is nonsense)

Thanks for the advice.

I haven't really had (well, any besides a few easy ones in geometry) experience in proofs, so maybe it would be smart to read up and practice a little with them over the summer, and then decide if I want to take the proof-based courses or not. The poster before you suggested seeing if they had an intro to proofs class or something similar over the summer, so I may look into that.

 

[Student100]

Also, don't automatically think your high school class offers worse calculus classes than the university. This depends on a lot of factors including the quality of the teacher. Inquire first whether the university class will in fact be better than the high school version of the class.

It sounded like his high school didn't offer calculus, that's pretty typically for rural areas. I know my high school was the same way.

Thanks for the advice.
The poster before you suggested seeing if they had an intro to proofs class or something similar over the summer, so I may look into that.

I didn't see any type of mathematics, "intro to proofs", but PHIL 3200 - Symbolic Logic I might or might not be helpful depending on how it's taught. Regardless it should cover a GE for where you transfer, I would hope, and help you get settled into how the college works if you take it in the summer.

The next course in the sequence, symbolic logic II is described as

Techniques of modern symbolic logic. Focuses on the completeness of first-order logic, Godel’s incompleteness theorems, axiomatic set theory, and Cantor’s and Dedekind’s theories of the infinite.

Which sounds very applicable. The first course doesn't have a description.

Have fun.

 

[RoZ589]

It sounded like his high school didn't offer calculus, that's pretty typically for rural areas. I know my high school was the same way.
I didn't see any type of mathematics, "intro to proofs", but PHIL 3200 - Symbolic Logic I might or might not be helpful depending on how it's taught. Regardless it should cover a GE for where you transfer, I would hope, and help you get settled into how the college works if you take it in the summer.

The next course in the sequence, symbolic logic II is described as

Which sounds very applicable. The first course doesn't have a description.

Have fun.

I saw that too. I'll look into seeing if they have a summer offering for it.

Also, it turns out Advanced Calc 1/2 are what you take after Calc 3. It's not an honors thing but more of a higher up Calculus class apparently.

Guess I'm going with regular Calc 1/2 at the university next year. Thank you!

 

[Andreol263]

What's this Advanced Calculus class? It's Complex Calculus, Calculus on Manifolds, oe other thing, these subjects are all named Advanced Calculus too..

 

[jtbell]

At the US college where I did my undergraduate many years ago, "Advanced Calculus" was real analysis, a proof-based course. It was in the same place in the course sequence as in RoZ589's description.

 

[Andreol263]

Ok, good to know, so OP i don't know how smart you are, but try to not rush things with calculus, really, make a good quantitiy of exercises, try to search for applications, and 'play' with the derivatives and integrals is pretty fun :)

 

[RoZ589]

At the US college where I did my undergraduate many years ago, "Advanced Calculus" was real analysis, a proof-based course. It was in the same place in the course sequence as in RoZ589's description.

Ok, good to know, so OP i don't know how smart you are, but try to not rush things with calculus, really, make a good quantitiy of exercises, try to search for applications, and 'play' with the derivatives and integrals is pretty fun :)

Yeah, I mistook Advanced Calc 1/2 for perhaps honors versions of regular Calc 1/2, when they turned out to be a whole different thing.

 

[IGU]

Many top high school math kids learn their mathematics from Art of Problem Solving. Their books are not expensive and are quite suitable for self-study. Their courses aren't what I'd call cheap, but sometimes schools will pay for them for students who need classes that the schools don't offer.

My kid learned most of his high school math out of their books and was quite satisfied until he outgrew it. Suggest you give it a look.