<p>@Latichever
It’s highly unlikely that someone who took the IMO and Math 55 didn’t know how to apply basic integration (like how to apply integration by parts). It probably meant that the student wasn’t aware of the more theoretical side of calculus, like epsilon-delta arguments, proof of Cauchy’s Mean Value Theorem and Taylor’s Theorem, etc.</p>
<p>^Agreed: most students in top math competitions do understand material well beyond the regular combinatorics, number theory, algebra, geometry, etc. covered in high school. I’ve heard accounts of IMOers bashing inequalities with Lagrange when it could have easily been done with Muirhead’s/Holder’s/etc. (not saying this is elegant, but they are well aware of tools past elementary mathematics).</p>
<p>I don’t think Chicago’s honors analysis uses Rudin. I’m pretty sure it does Lebesgue theory and functional analysis throughout the course instead of sticking it in the last chapter like Rudin. I’ve heard that it’s basically a typical graduate level analysis course.</p>
<p>Here’s a decent thread discussing Honors Analysis and 55, with links to other threads, and a link to a Math 207 mid-term:
<a href=“http://talk.collegeconfidential.com/university-chicago/551878-math-uchicago.html?highlight=55”>http://talk.collegeconfidential.com/university-chicago/551878-math-uchicago.html?highlight=55</a> </p>
<p>Here’s a link to some first quarter Honors Analysis problem sets: [Index</a> of /~ryzhik/MATH207-07](<a href=“http://www.math.uchicago.edu/~ryzhik/MATH207-07/]Index”>http://www.math.uchicago.edu/~ryzhik/MATH207-07/)</p>
<p>And here’s a couple of fairly concise summaries phuriku wrote a few years ago:</p>
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</p>
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</p>
<p>Is the hardest freshman math course at MIT comparable to Honors Analysis or Math 55?</p>
<p>MIT doesn’t have “freshmen” math classes like Harvard or Chicago do instead students simply start at whatever level they are at. So instead of all the best freshmen in one math class designed for freshmen they will be spread out among the various undergrad and occasionally even grad classes offered by MIT. So although there’s no comparable course at MIT, it’s not like top math students won’t be challenged as they can take as advanced math classes as they desire.</p>
<p>I understand that in the past some MIT freshmen cross-registered to take Math 55 at Harvard, but I think more recently MIT discouraged such practice. Just hearsay.</p>
<p>Etondad, how about you updating this page: [Math</a> 55 - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Math_55]Math”>Math 55 - Wikipedia)</p>
<p>I have to say that it takes all of my computer expertise to manage posting on CC-- Wikipedia is a whole other league!! :-)</p>
<p>I think that there is an understanding (not sure if it formal or informal) that first year math courses at Harvard are for Harvard students and Harvard freshmen don’t take math courses at MIT-- I asked my S who told me that he hasn’t heard of any MIT kids in 55, 25 or 23 (he has no idea about 21 or other courses, but doubts that MIT students would want to take lower level Harvard courses…)</p>
<p>Back in 2004 apparently MIT students could take Math 55. (Not clear whether freshmen were allowed, however.)</p>
<p>[The</a> Harvard Crimson | Computer Courses Draw MIT Students](<a href=“Computer Courses Draw MIT Students | News | The Harvard Crimson”>Computer Courses Draw MIT Students | News | The Harvard Crimson)</p>
<p>^^ that’s interesting, again, I just know what I have been told by my S. He hadn’t heard of any MIT students even inquiring about the freshman courses and certainly hasn’t heard of any top math kids at Harvard going over to MIT as freshmen. </p>
<p>I think that in order to cross register the home institution has to be satisfied that a similar course or course work cannot be taken at the home institution-- again, I haven’t checked the Handbook, but I recall that from the old days as a residential tutor, I think…"</p>
<p>Well, MIT freshmen are not allowed to cross-register, and Math 55 is only open to freshmen. </p>
<p>I thought I saw something in connection with an earlier discussion of whether MIT students could take Math 55 that said clearly no, one or both institutions forbade it. But I can’t remember what it was I saw.</p>
<p>It’s not necessarily a great loss. Princeton, Stanford, and MIT are pretty good math schools. They don’t offer a Math 55-equivalent course. That’s not because their students or faculty aren’t smart enough, well-enough prepared, and willing to work; it’s because they don’t agree that you learn most that way. Math 55 is basically an amalgam of three different courses and some extra material. Princeton et al. would say, “Take the three courses. Take four. Learn carefully, and at a reasonable rate, and you will do better in the long term.”</p>
<p>^^^ Definitely something to be said for that: for some students, the Math 55 approach is simply not the best. The trick, once you have Math 55 around, is to make sure that those who take the course are those rare learners for whom the course is optimal, and those for whom an alternative route is better are not enduring Math 55 just out of peer pressure or self-challenge.</p>
<p>The former Dean of the College, Benedict Gross, is a professor of mathematics. He has stated that he was concerned that some students would try to take 55 because it was iconic not because that was the best course for them. However, as the professor and the CA (a sophomore who took it the year prior) decide prior to add/drop if students are right for the course (and they can go to 25 w/o missing a beat as the two course track somewhat until that point), those students who are believed not right for the course in terms of comfort with proofs, the level of abstraction or preparation to handle the speed and are advised to take 25 instead . Also the amount of work is so so enormous and requires so much prior knowledge that it would be the rare odd duck indeed, who wanted to take it merely for the “bragging rights” (and I highly doubt that it is a social “boon” to say that one is in 55, even in nerd heaven).<br>
The math department makes it very clear in all of their materials that 55 is NOT necessary to be a top concentrator – that 25 is very very good preparation for upper level courses.</p>
<p>Now, of course, there will always be a student now and again who is taking it and gets over his or her (almost always his in 55) head because it is the wrong class and somehow escapes the notice of the CA or the professor until after add/drop. But the student doesn’t stay for 55b (there was one who had the “chops” but not the preparation recently and thought he could backfill-- he made it through to December but was known to the rest of the class as the “Gray Man” because he hadn’t slept in weeks. The others strongly suggested that he try 25b, that it was no reflection on his mathematical abilities-- he did and has done great. He will be doing upper level math next year). So I think if anything peer pressure is just the opposite than keeping someone in, but being supportive for those who feel they should leave.</p>
<p>I’m sure that many students at MIT, Princeton, or Stanford would like a very fast-paced course like Math 55, and have the necessary background/work ethic to do well.</p>
<p>Granted at MIT you’re constrained by the credit limit your first semester but it’s not obvious that 55 is much superior than grad level classes in analysis and algebra that a freshmen could take at MIT. This also had the added advantage of flexibility as students can focus on what interests them. Perhaps 55 is a unique experience but it’s less clear if it’s pedagogically superior.</p>
<p>^^^ This is allowed at Harvard too.</p>
<p>[Meet</a> Evan O?Dorney, high school math whiz](<a href=“http://www.thecalifornianpaper.com/news/1603-meet-evan-odorney-high-school-math-whiz.html]Meet”>http://www.thecalifornianpaper.com/news/1603-meet-evan-odorney-high-school-math-whiz.html)</p>
<p>[Freshman</a> O?Dorney Juggles Math and Music | News | The Harvard Crimson](<a href=“http://www.thecrimson.com/article/2012/1/27/Freshman-Math-Profile/]Freshman”>Freshman O’Dorney Juggles Math and Music | News | The Harvard Crimson)</p>
<p>Evan decided against taking 55 and did upper level courses but another student who while not as famous as Evan was also given the option of bypassing 55 but decided to take 55. Several students in addition to 55b took upper level algebra courses in the spring. </p>
<p>As noted perviously an examination of Siu’s graduate seminar in complex analysis proved vitally identical to his teaching in 55b this past year.</p>
<p>Ok I guess you can do that at Harvard too it’s just not as common. Maybe I’m mistaken but I got the impression from the website that it was frowned upon in most cases as well.</p>
<p>As a parent, I find it noteworthy that Evan didn’t enter college until he was 17.</p>
<p>I wonder if there is any record, anecdotal or otherwise, of accomplishments and distinguished careers among those who didn’t take 55. I mean, can the academic advisors say something like, “Look at Dr X. He washed out of 55 and went on to win the Fields.”</p>
<p>Humm, this thread has now become “Harvard Math 55”.</p>