<p>My son, who down the road might apply to MIT, will be taking AP calculus in the 9th grade. We were checking out the MIT open courseware and noticed an intro calculus course with videos of students filling a large lecture hall. I sort of imagined that most admittees would have taken calculus already and many may have gone significantly beyond so I was surprised to see so many in an intro course. Are there that many non-hard science, non math students? I was puzzled by this.</p>
<p>You only get credit for intro Calc if you get a 5 on the APBC Calc exam. Not everyone gets a 5, so they need a Calc class
Also, your son is very, very far ahead in math.</p>
<p>I guess that means you can get into MIT without getting a 5. But can you get placed beyond intro–getting credit for it aside–with, say, a 4? And how would MIT place you if you got a 4 on AP calc and then moved on to multivariate calculus and/or linear algebra.</p>
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<p>Most people do AP out of Calc I. Calc II is multi-variable calculus. Even if they took multi-variable, most people would take it again because you have to take an advanced standing exam to get out of it. There are 1000 freshman. It doesn’t take that many people to fill a large lecture hall (50-100).</p>
<p>Calc I is there for people coming from bad schools, who may have taken a very watered-down version of calc.</p>
<p>There are several different ways to get credit for math courses at MIT. AP credit is one. For students who took math courses at a university, it’s possible to apply for transfer credit. Finally, students who can’t get credit by those other two means can take an advanced standing exam, which is equivalent to the final examination in the MIT-level course. (More info at the math department website [here](<a href=“http://math.mit.edu/academics/undergrad/first/]here[/url]”>First Year Subjects)</a>.)</p>
<p>It’s not terribly unusual for math-interested freshmen to come in and get credit for single-variable, multi-variable, and/or linear algebra. The math department is perfectly happy to allow students to start in graduate-level courses first semester freshman year, if students are adequately prepared.</p>
<p>But to answer the question in the OP, MIT offers intro calculus because single-variable calc is a General Institute Requirement required of all students for graduation, and not everybody comes in with adequate calc preparation to skip it. Speaking for myself, my high school didn’t offer calculus, and although I had taken two quarters at the local community college, I didn’t feel that I was prepared enough to skip MIT-level calculus, or to take the accelerated course that reviews single-variable in six weeks and proceeds to multivariable.</p>
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<p>The answer to your question is very simple. The students you speak of who were overenthusiastic about mathematics coming in may have gone into mathematics, theoretical physics, highly mathematical aspects of electrical engineering, etc, which utilize that kind of mathematical sophistication.</p>
<p>However, MIT offers many sciences and subjects like economics at what I would imagine is much more mathematically rigorous a level than most schools would. And it is imperative to have calculus thoroughly down for a foundation to excel in these areas. It is actually really easy to get a 5 on the AP exam for a properly prepared students, but most high school courses in calculus do offer too little. Taking limits and derivatives is probably not going to cut it. </p>
<p>Knowing something about calculus and being very comfortable in using it are two different stories. Would your son actually excel in an MIT economics course after his AP calculus experience at his school? Maybe. It’s hard to say, but the maturity required is great - the ideas presented in the courses will be hard independent of calculus, and if you’re lagging at the basics, you’re quite screwed.</p>
<p>For a lot of people, mathematics is ultimately a tool - and even for a lot of people who come in knowing more, ultimately if they decide not to be at the frontiers of mathematics research, it is ultimately just a tool and a side passion perhaps.</p>
<p>It is possible to have taken a schedule in high school like AP Biology, AP Chem, AP Calc AB, and done physics using mainly algebra and trigonometry, and still be quite sharp in many of the sciences and economics, but just not well acquainted with machinery assumed in the modern study.</p>
<p>I presume MIT offers introductory courses just so these things don’t bring students down later on, and so they have time to adjust.</p>
<p>Ok, let me phrase this answer slightly differently, perhaps to be more helpful. I think a lot of people have this idea that mathematics is a linear pathway of learning: go from level 1 to level 2 to level 3 to … level k. </p>
<p>It doesn’t work that way. Eventually people figure out what interests them, and they just need to get what they need to do that effectively very solid.</p>
<p>Often calculus is not one step prior to 20 others - it’s sometimes just one tiny piece of a puzzle which may be a mix of statistics, algorithms, biology, psychology, … who the heck knows. </p>
<p>Basic point is that a lot of fields really have their own language of which calculus plays just one small part. Someone could have deep interest in an area after barely having a basic limits, derivatives, integrals level familiarity with calculus.</p>