<p>Heya all. Not sure if this is the right forum but let's go for it anyway.</p>
<p>I'm currently a high school junior enrolled in a precalculus class. I like math quite a bit, and for various reasons I'm teaching myself calculus this year from Spivak's book. First question: if anyone has experience with this text (and I'm sure some people do), how does it compare to standardized calculus courses (AP, college) content-wise and difficulty-wise?</p>
<p>My main problem is that there'd be nothing for me to do next year if I take calculus this year. My school is very small (no more than 40 students per grade) and as a result the curriculum is very rigid. The only class I could take that would fill that time slot is finite math, but it seems much too easy (it was designed for kids who aren't that great at math and is paced slowly. My math teacher says that I'd be bored). Our school is on campus with the community college, and I could potentially take a college class. However, the community college math classes aren't very good and I'm a bit skeptical.</p>
<p>The way I see it, the only other option is some kind of distance learning. Can anyone recommend a good distance education program? Is there anything I've missed? Any general suggestions?</p>
<p>Edit: Also, I took two statistics classes freshman year at the community college. Do you think I should review statistics and take the AP test this year? I realized that the AP test may carry more weight than the classes, but I'm not sure. Opinions?</p>
<p>Self study APs and get 4/5s on them. It’d show colleges that you’re competent in the subject area; no need to get the course credit unless it’s a graduation requirement.</p>
<p>The issue is the hole in my schedule caused by already taking calculus. It needs to be filled with something, and I would prefer filling it with a math class. The question is how I should go about filling said time. Anyway, I already have been self-studying APs.</p>
<p>Hmm. From what I know community college classes are still pretty hardcore classes since it’s college level. Maybe drop in one day and see if the professors suit you okay?</p>
<p>Everyone at my school ends up taking a few classes at the community college, and the universal consensus is that the classes are pretty easy (by the standards of a high school student a bit above average). Perhaps the math classes are harder than the other classes, but I wouldn’t bet on it. The calculus teacher at my school has a low opinion of the community college professors as well. I like the dropping in for a day idea.</p>
<p>spivak will be much better than the standard AP curriculum (in terms of being actual math), though perhaps not for a first exposure to calculus. If you find it okay so far, then good. Pay attention to the proofs and you will be ahead of 99% or more of people in math when you are in college in familiarity with proofs.</p>
<p>I haven’t read spivak but I have read apostol, which should be roughly the same type of book difficulty and content wise. The content is roughly the same as BC, but with more, that is, with proofs, axioms and so on. Apostol was a bit lighter on technique than a standard book, but the exercises should be enough. I’d advise you to not be too fixated on your “progress.” It will take much longer to read than you are probably used to.</p>
<p>For next year, fill the slot with something non math. If you found spivak good, and have finished it by then, no high school math class is at a suitable level for you. Rigorous multivariable is the logical continuation. I don’t know if spivak wrote one, but I know apostol has (it’s volume two of “calculus”). Or, if you feel like you can handle more, rudin’s “principles of mathematical analysis” would be good if you want to learn deeper calculus. Linear algebra and differential equations might be interesting too and accessible after a calculus course.</p>
<p>I’m taking calculus at my community college and it is harder than AP Calculus BC was. You do realize that your community college or some local 4-year school is not going to be Harvard’s math 55. You are most likely going to be studying math with just above-average students, nothing special–and that’s not to put the school down.</p>