<p>At least at Rice, the stated policy is exactly the opposite of what you suggest – they want you to take the most advanced course you can.</p>
<p>Here’s the policy at Rice:
- Basic principle:  If you want to take calculus, you should enroll in a course as
 advanced as you can possibly handle.  If you find you are in over your head, you
 may easily drop down to a more elementary course.  (A transition in the other
 direction is obviously much more difficult to manage.)
- No calculus background at all:  You should begin with MATH 101 or 111.
- Advanced placement credit:
 a. Grade of 4 or 5 on AB test.  You have credit for MATH 101 and you
 may start with MATH 102.
 b. Grade of 4 or 5 on BC test:  You have credit for MATH 101-102 and you
 may start with MATH 211 or 212. You should consider MATH 221 if you
 love math.
- No advanced placement credit:  You may have taken some calculus, however,
 and probably should enroll in a course beyond MATH 101.  Consult with a
 Mathematics professor for advice.
- Transfer credit from another university: Consult with Prof. Jones for advice.
- Have taken Multivariable calculus (but might not have credit): Talk to a MATH
 advisor. You should strongly consider MATH 221-222 (see the discussion on the
 first page).
 Math 101 – Calc I
 Math 102 – Calc II
 Math 211 – ODE & Linear
 Math 212 – Multi-variable
 Math 221-222 – Honors Calculus (multivariable plus problem solving)</p>
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<p>At MIT, my daughter’s friends take 18.024 their first semester, which is Calc II with theory.</p>
<p>The placement page at MIT doesn’t seem to express a preference either way (start from the beginning in Calc I or go on with the highest placement), just noting that if you have credit for 18.01 (due to AP, usually) and choose to re-take 18.01 then you lose 12 units of math but gain 3 units of elective.</p>
<p>However, they offer 3 levels of Calc I (18.01, 18.01a for repeaters, and 18.014 with theory) and 5 levels of Calc II (18.02, 18.02a for repeaters, 18.022 with a math focus, 18.023 with applications, and 18.024 with theory).</p>
<hr>
<p>At Harvard, the advice on the website [Harvard</a> Mathematics Department : 21, 23, 25, or 55?](<a href=“http://www.math.harvard.edu/pamphlets/freshmenguide.html]Harvard”>http://www.math.harvard.edu/pamphlets/freshmenguide.html) seems to imply that a 4 or a 5 in AP Calc BC plus sufficient math placement score means you should NOT repeat. There are, however, 4 levels of classes to choose from next, including what is considered the hardest math class in the nation (Math 55).</p>
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<p>Williams College has a flow chart that seems to direct students to skip forward in the sequence if you’ve had any experience at all with calculus.</p>
<p>[Williams</a> College Registrar’s Office](<a href=“Williams College”>Williams College)
Note the two levels of Multi, based on BC scores.</p>