<p>Our school offers Calculus AB and BC... however, due to poor middle school performance, I was never given the opportunity to skip ahead on my math curriculum, so I was stuck doing Algebra 1 freshmen year, Geometry Soph, Algebra 2 last year, and now for senior year Precalculus. For some reason I couldn't double up one year either. </p>
<p>I feel as though I am in an extreme disadvantage, am I? Last summer I did try self studying Algebra II, spent many hours over the summer, however september came and there was schedule conflict and it wasn't possible for me to skip over, because of a wierd policy that we must take all classes for all credits, and for example, even if I successfully tested out of Algebra II, I would still have to take the Algebra II class for the credit, in addition to the more advanced class that I "skipped" into.</p>
<p>Now should I worry about this? Should I consider self-studying Calculus AP, maybe with the help of the teacher that teaches it? Would Harvard take this seriously if my guidance counselor mentions it in the rec? Should I try spending these last 15 days learning Precalculus and attempting to test out again, hoping there is no schedule conflicts?</p>
<p>You should ask your counselor to explain your school's rules and usual course progression, and the efforts you have already made to try to move ahead faster in the school math curriculum. </p>
<p>Harvard, of course, tends to have students with a stronger previous math background than most colleges in the United States. But not absolutely everyone they admit, even among would-be math majors, has had a high school calculus course before. Harvard does have ways to find each incoming math student the right course to take once admitted. Some of that is explained in various publications linked to from the math department Web site, e.g., </p>
<p>Talk to the people who know you locally about what to load up your senior year schedule with. A crash-course way to see if you have background enough to test out of precalculus would be to try the ALEKS </p>
<p>online course, which offers a FREE three-hour free trial during any forty-eight hour period of your choice. (You can take more than one free trial; you just keep on signing up for new temporary usernames. A friend of mine phoned the company to confirm that this is perfectly fine as far as the company is concerned.) </p>
<p>Best wishes for a great school year and for a successful application season.</p>
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But not absolutely everyone they admit, even among would-be math majors, has had a high school calculus course before.
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<p>That would be rather astonishing these days. Are you aware of examples that don't come from extremely disadvantaged situations (e.g. a blind student, a student from an Indian reservation school or nightmarish ghetto HS, a student who worked full time to help family)? Actually, are there any examples at all in this era of Internet, online bookstores, distance learning by computer, and the rest?</p>
<p>edit: for the OP, note that some people in college will take calculus with your math background (or less) and try to catch up as they go along. This would be roughly equivalent to taking a second simultaneous math course in your senior year. Maybe realistic, maybe not, but hardly an impossibility, especially for the lower-level calculus class.</p>
<p>One rather funny example I heard about over on Brand X, which I had in mind when I replied to the OP, is an eastern European IMO medalist (that is, obviously a strong math student) who had had a high school curriculum that didn't explicitly cover calculus. As a current Harvard student described the situation, the first definition of integration that the IMO medalist student learned, upon attending Harvard as a freshman, was the presentation of Lebesgue integration found in the little Rudin textbook used that year for Math 55. An unusual case, to be sure, but yet one more demonstration of the flexibility the Harvard admission office practices in evaluating the high school academic records of students from all over the world, and the opportunities Harvard provides for various appropriate placements in math classes.</p>
<p>One rather funny example I heard about over on Brand X, which I had in mind when I replied to the OP, is an eastern European IMO medalist (that is, obviously a strong math student) who had had a high school curriculum that didn't explicitly cover calculus. As a current Harvard student described the situation, the first definition of integration that the IMO medalist student learned, upon attending Harvard as a freshman, was the presentation of Lebesgue integration found in the little Rudin textbook used that year for Math 55.
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<p>That's a highly, highly unlikely story. There is probably a correct story you read somewhere that resembles the above, but to understand it would require some knowledge of eastern Europe, math competitions, Harvard, and Rudin's book.</p>
<p>The east European countries that send IMO winners to Harvard (or Princeton, MIT, Caltech etc) have curricula in which advanced students "explicitly" cover substantial amounts of calculus. Math specialists, especially the IMO medalists who tend to study at specialized math high schools, generally cover this material in a theoretical and rigorous fashion not unlike math 55 at Harvard. This is far beyond the level of any AP calculus syllabus, even if some particulars do not match. For instance, 2nd order differential equations may not be seen everywhere in Europe, but differential calculus might be developed deeply over the course of a year, together with other topics and problems much more difficult than the cookbook calculus of an AP course. </p>
<p>It is also improbable that anyone in the Harvard math 55 course or its equivalents at other schools would see Lebesgue measure as their first definition of integration; such classes are not sadistic.</p>
<p>What is unlikeliest of all is that (without a showing of hard disadvantage) Harvard would admit a "would-be math major" who does not attain the maximum standard math curricular level of their locale -- in the US, this is almost always AP Calculus. Calculus itself is just a proxy for "full high school level math curriculum" or "introductory college level work". In principle that could be substituted by some courses at a comparable mathematical level in number theory, discrete mathematics, physics or other subjects. But it is hard to imagine Harvard admitting any prospective math major without some credential of that kind. For humanities students, calculus hardly matters in and of itself.</p>
<p>I go to Harvard and I know quite a few kids who didn't take AP Calc. It sounds like at this point you can't do much about it, so don't sweat not taking it too much.</p>