Some quick advice for a homeschooled student

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Discussion Overview

The discussion revolves around the experiences and considerations of a homeschooled student regarding AP exams and advanced mathematics courses. Participants explore the implications of taking AP exams, the necessity of standardized testing, and the acceptance of self-studied material in college admissions, particularly at North Carolina State University (NCSU).

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants suggest that AP exams are not necessary for the student, especially given their advanced coursework and self-study in mathematics.
  • Others argue that the value of AP exams may vary depending on the college's admission requirements and that they could serve as a self-evaluation tool for the student's learning progress.
  • One participant notes that universities typically require students to take courses even if they have prior knowledge, emphasizing the importance of formal coursework for degree completion.
  • There is a discussion about the prerequisites for advanced courses at NCSU, with some participants sharing their experiences and suggesting that self-study may not be sufficient for course credit.
  • Concerns are raised about the potential need to start from the beginning in university, despite prior knowledge, which some participants acknowledge as a possibility.
  • Several participants agree that being familiar with course material can be beneficial for maintaining a high GPA, but caution that there may be gaps in knowledge that need to be addressed.
  • One participant mentions that the course MA 515 is functional analysis and suggests that a strong foundation in real analysis is important for success in that course.
  • Another participant shares a personal anecdote about successfully gaining admission to a graduate program based on passing preliminary exams, implying that alternative pathways exist for demonstrating knowledge.

Areas of Agreement / Disagreement

Participants express a mix of agreement and disagreement regarding the necessity and value of AP exams, the acceptance of self-study in college admissions, and the prerequisites for advanced courses. The discussion remains unresolved on several points, particularly concerning the best approach for the student’s educational path.

Contextual Notes

Limitations include varying college policies on AP exams and self-study acceptance, as well as differing opinions on the prerequisites for advanced mathematics courses. The discussion reflects a range of personal experiences and interpretations of educational requirements.

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Hi. I'm a homeschooled sophomore and I have some questions about AP exams and classes.

I took BC Calculus last year but I didn't take the exam. I think I'm supposed to take the exam this year. I also signed up for AP Statistics for some reason. :-p Right now I'm taking an advanced-undergraduate-level modern algebra class, and I have self-studied real analysis, topology, and linear algebra at the introductory graduate level. I will be taking grad-level classes in the above subjects at NCSU starting this Fall, so I will have a lot of documented grades for my math. Is it necessary for me to take these two exams, just because they are part of some kind of standard curriculum? Isn't the beauty of homeschooling the *flexibility* of the curriculum? :biggrin: Neither of these tests help my overall math education in any way. Should I refund and get some of that money back?

Thanks.
 
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Tests aren't to help you. Tests are a cop-out method of easily acting like you're evaluating students when precedent, lack of tenure, and the student to teacher ratio are prohibitive of getting too creative.
 
I think it will all depend on what college you are going to after high school. Have you talked to any college counselors at prospective schools about this? Normally, a high-school counselor could help you with this, but since you're home-schooled, you will probably have to do a little more "footwork" on your own to find out the various requirements for admission and pre-requisites for courses.
 
hahaha, I can already see where this thread is going
 
I am/was a math major at NCSU. I took those corresponding graduate courses you speak of. As far as I know, a university is typically not going to give you a degree in mathematics just because you have already studied all the material they offer. What I mean is that you will have to take the calculus course unless you place out of it. You can do this two ways by taking the AP exams or doing the course by exam (which means taking an exam that NCSU gives for the course). Perhaps it is possible for MA 515 to count for MA 425 (i can't imagine them liking this though) but these two courses cover completely different material. In fact there is no other course which, to me, seems suitable to count as MA 425! Linear Algebra is a different example and MA 520 will definitely count for MA 405.

Anyway, I assume your schedule next semester will be:

MA 515
MA 520
MA 551
MA 521

I have taken all of those; in fact, I took 3 out of the 4 of them last semester. Can I ask why you have decided to take these courses?
 
Hi. Thanks for your replies.

Perhaps it is possible for MA 515 to count for MA 425 (i can't imagine them liking this though) but these two courses cover completely different material. In fact there is no other course which, to me, seems suitable to count as MA 425!

I am aware of this. I have talked to the MA 515 professor and he said its likely that I'm ready (but I need to talk to him in person about this). I know the course uses R. Bartle's Elements of Real Analysis, and I'm covering material in Baby Rudin and C. C. Pugh's Real Mathematical Analysis (and I'm doing the problems in both). I have the course website and the assignments. I can work through those. Is that okay?

I've talked to Dr. Griggs. He said that if Dr. Martin agrees that I have the prerequisites, then I can take the class. I've talked to one of the professors at UNC about this and he said it comes down to convincing the instructor that I'm ready, and once I pass a few courses this way, they can serve as prerequisites to others. I'm not sure if it works like this at NCSU.

Can I ask why you have decided to take these courses?

I'm not quite sure what you're asking me. This is tentative; I have chosen NCSU because I know it has the AEO program, and from Dr. Griggs, I know that AEO students can take grad-level classes. I don't know if there's an equivalent program like AEO at UNC or other universities.
 
As far as I know, a university is typically not going to give you a degree in mathematics just because you have already studied all the material they offer.

Yes, it's entirely possible that I start again from the beginning when entering university because they don't accept my self-study or my classes or whatever. I'm fine with that.
 
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d1ff30m0rf1zm said:
Yes, it's entirely possible that I start again from the beginning when entering university because they don't accept my self-study or my classes or whatever. I'm fine with that.

Already being exposed to the material a class offers is not necessarily a bad thing. You should be able to keep a killer GPA if you already know the material. Plus, you never know, Maybe you missed something they want you to cover.
 
G01 said:
Already being exposed to the material a class offers is not necessarily a bad thing. You should be able to keep a killer GPA if you already know the material. Plus, you never know, Maybe you missed something they want you to cover.

I agree with this.

As for the questions on AP exams, there are a couple considerations here. First, no, they are not required. Generally, students take them to place out of introductory level courses in college, but policies regarding how they are used vary from university to university. From the perspective that you are a homeschooled student, there can be a different benefit of it to self-evaluate your learning. Since it is an exam that students take nationwide, and really is subject-specific at an advanced level, it can provide you with better feedback on whether you really are on track with your coursework to the level you think you are. Other standardized exams, like the SAT or ACT, can be more about learning to take the test than they are about learning much about the subjects contained within them, so are less useful for evaluating how a homeschooled student's background compares to those who went through a more traditional K-12 education.
 
  • #10
Already being exposed to the material a class offers is not necessarily a bad thing. You should be able to keep a killer GPA if you already know the material. Plus, you never know, Maybe you missed something they want you to cover.

Agreed.

Oh, okay. I understand, Moonbear. Thanks for your advice. I decided to opt out of Statistics. Everything else should be fine.
 
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  • #11
Truthfully, you could take MA 515 without anything but knowledge of calculus and basic set theory (the book even says this is possible), but I wouldn't recommend it. The truth is that the course is functional analysis and so if you just jump into that you are going to miss a lot of stuff from real analysis of several variables like the idea of treating differentiation as a linear transformation, or the heine-borel theorem, or basic topology of R^n. All this stuff will be pretty much assumed. With that said, the course doesn't isn't too bad without more advanced real analysis. I know graduate students who took it with only knowledge of MA 425 but they weren't going to do analysis and took it to satisfy the requirement. So, I think you are prepared. The question is why do you want to take this course? In my opinion, since you are not pursuing a university degree, I would take the classes that most interest you.
 
  • #12
why don't you ask if you can take the exams from some of the courses at NCSU?

If you are really learning the stuff you are reading, you are way beyond AP calc exams.

even a 5 on an AP calc exam is nowhere near knowing Baby Rudin well.

When I was trying to get into UW grad school in 1973, I just drove over and sat for their PhD prelims and passed them. They offered me a fellowship based on that alone.
 

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