<p>Hi! I'm currently a junior taking Calculus AB (Calculus I and II). At my school you have to take Calc AB before BC because BC teaches lots of stuff that is past normal BC curriculum and isn't on the test. I have the option to take a course equivalent to BC at my local university this summer and then get ahead in math during my senior year but was wondering how much more math is required to be a math major and be successful at a place like Stanford or MIT or Harvard. I know it is a little late, but how behind am I in math? I've been doing fine in Calc AB (A+) and taught myself Pre-Calc and Algebra II (didn't have a good teacher). </p>
<p>You are not behind in math. Taking calculus in high school is already plenty, and you’ll be ahead of college math, even at top schools. If you really want to go further in math, the next step would be taking multivariable calculus at a community college or other school, but I really don’t think it’s worth rushing through calculus. Take Calc BC next year, and you will be absolutely fine at any school you go to. You may even decide to retake calculus in college, in which case going further in math wouldn’t even matter.</p>
<p>The minimum is to have a good working knowledge of high school algebra, geometry, and trigonometry, so that you are ready for calculus. Presumably, if you do well in calculus while in high school, you may be able to start in a more advanced math course in college, which can give you the opportunity to take additional advanced math electives later on. I.e. you are not behind in math. Do not assume you are behind simply because you might encounter a math major taking real analysis at age 12 or some such.</p>
<p>When you register for your first college math courses after having completed calculus in high school and presumably gotten AP credit, it is best to review the old final exams for the math courses that you are allowed to skip with your AP credit, in order to verify that you know the material from the college’s point of view. Small gaps can often be covered by self-study, but large gaps may require retaking the course. Be aware that college math courses move at a faster pace than your high school’s slow paced calculus courses (the college math pace would be like covering all of calculus BC (including the AB stuff) in one year instead of two years like at your high school).</p>
<p>" Taking calculus in high school is already plenty, and you’ll be ahead of college math, even at top schools." I really doubt many <em>math</em> majors at the schools the OP mentioned come in not having already completed calculus. 50,000 kids got a 5 on the BC calculus exam in 2013. How many math majors are there at those 3 schools? Probably fewer than 1000 among the three schools. I’m sure there are a few math majors who didn’t complete BC due to lack of opportunity, but I’d be surprised if there are many. Especially nowadays with instruction available on the web, dual enrollment programs popping up everywhere, and of course, kids have been reading math books on their own for generations. </p>
<p>One thing to be aware of is that if you take a math class at a cc, it may not be nearly as difficult as the one at a top school. You may end up repeating the class. It also sounds like perhaps your high school BC class is better than the local college calculus class. And you also need to think about how you would “get ahead” in math during your senior year. Will you have the time and self-discipline to study on your own? Or will you be able to take more college classes? I’d think about specifically how you will benefit from that situation before rushing to get there. But if math is your interest, it’s always good to learn more.</p>
<p>Wanted to add, if you are not already involved in competitive math, you might like to look into that. There are sites such as Art of problem solving which have lots of information and educational materials on this. If you haven’t been doing it for a while, you aren’t likely to do particularly well in competitions, but it can offer you some worthwhile exposure to many topics which aren’t part of the usual rush through calculus sequence, as well as an emphasis on solving more difficult problems rather than the more cookbook type of math you get in classes.</p>
<p>@ucbalumnus Thanks! @mathyone I would be able to complete the calculus sequence (Calc III over the summer and Calc IV in the fall term) and then take differential equations during the winter term and do some linear algebra in the spring. Also, for math competitions and just higher level math in general, is mental math really important? Are the kids able to calculate huge numbers in their head extremely fast? Or is it more about the process which is facilitated with the use of a calculator to do the number crunching? I’ve always wondered that because I’ve never been a super fast mental-math magician or anything. </p>
<p>Math competitions and junior/senior/graduate level math in college are typically more about proving theorems and such than calculating huge numbers in your head.</p>
<p>Note: calculus 3/4 (presuming a quarter system college), differential equations, and linear algebra are typical college sophomore level math. In most cases, they are not particularly proof-oriented. Some colleges have a proof techniques course to help students transition to college junior level math; others combine instruction in proof techniques with another course, such as a discrete math course or certain junior level courses that they recommend as the first junior level math course.</p>
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<p>I’m not saying they’ll be ahead of every other student in the world. I’m saying that they will be ahead of the typical college math sequence, which begins with Calculus. Presumably, they will have completed at least Calc I and II by the time college students, leaving them to begin with multivariable calculus, which is ahead of the typical math sequence. They can go on to take multivarabile, differential equations, and/or linear algebra has a high school student, and that’s fine. More power to them. But they may find that the quality of the course they took at a local community college is not the same as the course they would have taken at a “top school.” They may find that they would like to re-take the course (or that they’re college requires them to do so) before moving on to more advanced topics. But they are NOT “behind in math.” They’re just… not. You can complete a math major at a top school on time coming in with no calculus (or re-taking calculus courses already completed).</p>