<p>Perhaps OP can provide more detail about his math and other academic accomplishments and why he feels so confident about being able to study theoretical math at institutions like Princeton or MIT. My son took Calc BC in middle school and was in a math circle where some of the kids were light years ahead of him. Two of them went on to Princeton and Yale to study math (theoretical and applied, respectively) but what they were able to accomplish in HS would make your jaw drop. </p>
<p>Even at top-end math departments, the typical undergraduate pure math major is not a super-prodigy who completed calculus in middle school.</p>
<p>My son is not a prodigy but there were certainly kids who were in his math circle. You cannot take Math 55 at a place like Harvard (my daughter is there so I have a point of reference and I also attended and taught at other Ivies) and not have been a super gifted HS math student. If you don’t have an extensive background in doing proofs, you aren’t even allowed to enroll in the course.</p>
<p>Someone who takes calculus in middle school (5 years ahead of normal level) is a prodigy in math by US standards.</p>
<p>Harvard’s Math 55a-55b is the third honors level of the math sequence (the other honors levels are 25a-25b and 23a-23b, and the normal level is 21a-21b). Harvard’s math concentration does not require the student to take any of the honors versions of 21a-21b, although students can do so.</p>
<p><a href=“http://www.math.harvard.edu/pamphlets/concentration.pdf”>http://www.math.harvard.edu/pamphlets/concentration.pdf</a>
<a href=“http://www.math.harvard.edu/pamphlets/prepair.html”>http://www.math.harvard.edu/pamphlets/prepair.html</a>
<a href=“http://www.math.harvard.edu/pamphlets/freshmenguide.html”>http://www.math.harvard.edu/pamphlets/freshmenguide.html</a></p>
<p>I’m not sure what your point is in listing the courses out. My point was simply that the OP was searching for the most rigorous programs where he could take theoretical math and I was simply questioning if he had the background to take theoretical math at the most rigorous programs or if not what made him believe that he could be successful doing so. He may very well have both the background and the super-intellect to do so, I don’t know. I just didn’t see anyhting in his posts so I asked the question. I wish him well.</p>
<p>I am pretty sure that many HS students who have completed calculus through linear algebra cannot solve the problems in the following URL. But some middle and HS students who have not taken calculus can.</p>
<p><a href=“http://www.bamo.org/archives[/url]”>http://www.bamo.org/archives</a> </p>
<p>With respect to whether my son is a prodigy or not, I agree that just from the optics of the situation one might assume he is a prodigy. I wonder how much can be attributed to intellect and how much is just a matter of exposure. My son will be first one to tell you that most of the other kids in his math group were mathematically superior to him whether they were older, younger, ahead of or behind him in coursework. Now, even after having taken much more advanced courses in math he can still say with certainty that the kids who are now studying theoretical math at Princeton and Harvard and even the one studying applied math at Yale are a lot more talented in math than he will ever be.</p>
<p>Falcon - You explained very well.</p>
<p>Thanks @coolweather!</p>
<p>However, Falcon1’s son is a math prodigy. The fact that some of his friends are even better at math than he is does not mean that he is not an extreme outlier in math ability compared to the overall population (even if you narrow the overall to college students or math majors in college).</p>
<p>I don’t know, @Falcon1, you’re probably no math slouch yourself. That your child was in a school where there were math wizards brighter than him doesn’t come as much of a surprise if you were teaching at an ivy at the time. Your son’s peers probably had parents who were teaching at the ivy, too, and expected a great deal of their children and the middle schools where their children were enrolled. I tend to think that a kid doing BC in middle school is a very intelligent kid with a very high math capability. I’ve met very few of them in thirty years of college teaching, none of those years at an ivy. There’s a lot of rare intelligence on those ivy campuses and in the local schools. I’m seldom unimpressed by my colleagues who teach at ivies.</p>
<p>@jkeil911 That’s a fine piece of deductive reasoning that, although plausible, was not actually the case. My son’s math group met at local university (non-Ivy) and consisted of kids in the region who’s parents came from all walks of life. The only common threads about them that I noticed were that they valued education for their kids whom they felt were gifted in math and they were willing to give up a chunk of their Saturdays driving them to the meetings.</p>
<p>Perhaps you are right @ucbalumnus and my son is an extreme outlier (at least compared to the general population). I’m not quite sure then how to characterize the other kids who’s shadows he walked in (extreme outliers ^2 ?) </p>
<p>Anyway, in the Princeton forum, OP very thoughtfully addressed my questions for which I thanked him and wished him the best of luck.</p>
<p>Thanks all!</p>