<p>I'm wondering, hypothetically speaking i get accepted into harvard next year, how would one go about registering for Math 55. My school doesn't offer multivariable calculus but i think i might be able to take it at a local university along with linear algebra. Are you selected for this program or do you select it? I know it's the hardest freshman math course in the country but i don't think i would mind the 30-40 hour problem sets or any other challenges the course might present.</p>
<p>Harvard students begin their semesters by attending classes during "shopping period," which allows them to try out a lot of different classes and see which ones are a good fit to register for. Most would-be math students at Harvard who want really challenging math courses shop at both Math 25 and Math 55, which coordinate their syllabuses at the beginning of the semester. Math 55 has always been legendarily hard, and this year it is harder than ever. All of the top Harvard math courses have been upgraded significantly in difficulty and prerequisite background, because Harvard is faring very well in enrolling very well prepared would-be math majors. A first course in multivariable calculus with linear algebra at your friendly local university would likely get you ready for Math 23, and possibly get you ready for Math 25 if you supplemented it with a lot of outside reading, but would only be the beginning of getting you ready for Math 55. You will be allowed to shop at any of the courses, I'm pretty sure, if you are admitted to Harvard. Once you see the first problem set for each course you will be able to gauge what you are ready for. </p>
<p><a href="http://math.harvard.edu/courses/index.html%5B/url%5D">http://math.harvard.edu/courses/index.html</a> </p>
<p><a href="http://math.harvard.edu/pamphlets/freshmenguide.html%5B/url%5D">http://math.harvard.edu/pamphlets/freshmenguide.html</a> </p>
<p>(The pamphlet about the four Harvard courses on multivariable calculus and linear algebra has not been updated to reflect the recent curriculum changes, which are more apparent in the course list.) </p>
<p>Best wishes in your preparation.</p>
<p>I heard they were covering Lp spaces in math 55 this year. Uh....that's pretty advanced for freshmen, especially since peer math majors I know of at Princeton , Stanford etc don' really touch on that until junior year analysis. </p>
<p>Chaotic, unless you are really talented at mathematics (as in IMO caliber) I think you would be at a severe disadvantage taking math 55 without at least taking some sort of proof based linear algebra and multivariable calculus. </p>
<p>But hey, I've heard stories of Asian/Eastern Europeans without much exposure to calculus at all excelling in that course. But obviously, they have a comprehensive mastery of problem solving skills and critical thinking abilities/proof writing.</p>
<p>Best thing for you to do is to sit in during shopping period and see for yourself.</p>
<p>so actually, apparently over 100 people shop 55 every year just to see what it is like, although only about 10 actually end up taking it. </p>
<p>for 55, you have to have exceptional math abilities, and they assume a ton of prior knowledge, or so people I know who have taken the class say.</p>
<p>if you haven't done that much math but are looking for an very hard challenge, i would say that you could try 25. from what i hear from students and profs, 21, 23 and 25 all start out at the same point, and don't assume you know any of the material - even with respect to writing proofs. everything is taught in the course itself. but the higher the number the faster the course moves and the more theoretical and abstract it gets, so for 25, if you don't have a prior background you have to work very fast to keep up, as many people in the course do have a background. </p>
<p>but.....i think that math 25 is achievable, even for one with very little background, if you are willing to work extremely hard.</p>
<p>My favorite story from AoPS a few years ago is about a Bulgarian student who, according to the story, first learned to integrate in Math 55. He was, of course, a math olympiad competitor with a lot of experience in writing proofs. I don't know the storied student's name.</p>
<p>"problem sets can take anywhere from 24 to 60 hours to complete"</p>
<p>60 hours, that's more than many people who have a full-time job work in an entire week, and just for the HOMEWORK of ONE course, that's incredible! I'll definitely check it out in the shopping period if I get accepted :D</p>
<p>I'm pretty sure the 'storied' Bulgarian kid actually lived in my dorm freshman year. None of us really knew him very well though, and I literally have not seen him since we all moved up to upperclassmen houses. Would the time-frame for this kid popping up on AoPS be around 2005-2006?</p>
<p>If I get accepted, I just want to sit in on the course for the day, maybe try to catch some of the brilliance radiating from the people serious about the course. I mean, I'm waaay accelerated in math at my school, but not nearly ready for that.</p>
<p>As a side-note, this is a perfect example of the kind of attitude adjustment that is needed upon entering Harvard. Being good at ___ in HS doesn't necessarily translate into being good at ___ at Harvard (because, let's face it, we were all pretty good at everything). The highest level of something at Harvard is usually pretty equivalent to the highest national level of said activity/subject (math, debate, a cappella, etc). </p>
<p>This is not to say that you shouldn't try lot's of different stuff at Harvard (b/c that's half the fun), just that you should definitely realize that unless you truly excelled at something in HS (aka, on the state/national level, not just got A's or in-house awards for it) you probably won't be ready to jump right into the advanced or highest-level equivalent right off the bat. One of the coolest parts about Harvard though, is that you can make serious progress in getting to that level just by being around so many super-talented people and learning from them.</p>
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Would the time-frame for this kid popping up on AoPS be around 2005-2006?
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<p>That sounds about right. I thought it was funny that there is someone in the world who first learned integration as Legesgue integration.</p>
<p>Yea, you can PM me if you want his actual identity.</p>
<p>"As a side-note, this is a perfect example of the kind of attitude adjustment that is needed upon entering Harvard. Being good at ___ in HS doesn't necessarily translate into being good at ___ at Harvard (because, let's face it, we were all pretty good at everything). The highest level of something at Harvard is usually pretty equivalent to the highest national level of said activity/subject (math, debate, a cappella, etc)."</p>
<p>Actually, that was my point exactly. I suppose my facetiousness didn't come through. The fact is, I'd be perfectly content settling for a lower-level math class, especially since I don't even plan to major in math. :P</p>
<p>Haha, no worries at all. My post wasn't aimed at you at all, it was more of a general note for the soon-to-be-accepted. I actually posted it as an addendum to my note on the Bulgarian kid, I didn't even read your post until afterwards. Anyways, I'm sure you'll have great success wherever you end up and whatever you choose to pursue (you're good enough to apply to Harvard, after all)</p>
<p>Oh a side note, what is the primary difference between math 23 and math 25? What kinds of people are in those two classes and what is the main source of division?</p>
<p>The main difference is that 23 still considers some applied problems, 25 is 100% pure math. Other than that, pretty much what previous posters have said. Both start with linear algebra, which excludes movement between those tracks and the 21 track.</p>
<p>23a: A rigorous, integrated treatment of linear algebra and multivariable differential calculus, emphasizing topics that are relevant to fields such as physics and economics. Topics: fields, vector spaces and linear transformations, scalar and vector products, elementary topology of Euclidean space, limits, continuity, and differentiation in n dimensions, eigenvectors and eigenvalues, inverse and implicit functions, manifolds, and Lagrange multipliers. Students are expected to master twenty important proofs.</p>
<p>25a: A rigorous treatment of linear algebra. Topics include: Construction of number systems; fields, vector spaces and linear transformations; eigenvalues and eigenvectors, determinants and inner products. Metric spaces, compactness and connectedness.</p>
<p>My friend is in Math 55. When we went to a Boston Symphony Orchestra concert, he was doing his homework through the entire performance...</p>
<p>Well they do say that classical music helps with those math problem sets...... haha</p>
<p>Does anyone have any experience with Physics 16? I've been skimming through David Morin's book, it seems awfully challenging though :p</p>
<p>I know anecdotally that the curve for it is supposed to be absolutely hysterical. 90% of the grades are B+ or higher and then the curve drops straight down and the rest get Cs or fail. No one thinks to call it grade inflation though, b/c the attrition rate is high enough that most people assume all the kids who care about grades but would have gotten Bs or lower dropped, leaving the kids who are rocking the class and the kids who are interested and don't care about grades anyways. I have absolutely nothing hard to support this though, just what I've heard...</p>
<p>Hmm, though i am more advanced than my peers at school, i don't think i've done near enough outside studying for that- i just started doing number theory on my own which is pretty easy but useful. I think i might sign up-if i get in- in math 23, maybe math 25 but definitely not math55, thanks for the information! In addition i'm not close to the IMO level, more around the AIME level which is way below the supossed math 55 standard maybe by the end of my senior year i will be at the USAMO level!
Thanks again for enlightening me on the rigor and the expectations of this course.</p>