Just how hard is Math 55?

Colleges and Universities A-Z Harvard University
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<p>I am a senior who applied to Harvard early, interested in majoring in Math. I have qualified to the AIME 3x and got an 8 on the 2010 AIME II. I have also taken Linear Algebra and Ordinary Differential Equations through EPGY. Neither of those courses covered the entire textbook so I studied the non-covered portions on my own. I also supplemented both with MIT's OCW, and studied Partial Differential Equations on OCW and from a textbook as well. I have taken a couple courses on Art Of Problem Solving and done pretty well on them. 800s on SAT 1 math and Math II, A+'s in all math classes (including calculus BC, multivariate calc, discrete mathematics @ community college) and 5s on all the math AP tests (and perfect scores on all the other science tests I've taken). COSMOS Math @ UC Davis sophomore year and PROMYS last summer. However, I heard from someone currently at Harvard but not in Math 55 that most of the kids in Math 55 will be people who consistently do well at USAMO (at least 80th percentile+) or have equivalent-level ability. I don't rate my math ability nearly that high but I think that I am nevertheless good at math and would be at an advantage having already studied advanced algebra and calculus (although obviously not all the content of Math 55). Is anyone currently in math 55 that can tell me how hard it is? Obviously this is all hypothetical since admission decisions aren't out, but I would like to know.</p>

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<p>Lol, if I didn’t know any better, I’d say this thread was an opportunity for you to boast about your math ability XD</p>

<p>One of my sister’s friends took 55, and when he asked my sister for help, she took one look and went:
<a href=“http://cdn3.knowyourmeme.com/i/000/101/781/original/Y0UJC.png?1298581940[/url]”>http://cdn3.knowyourmeme.com/i/000/101/781/original/Y0UJC.png?1298581940&lt;/a&gt;&lt;/p&gt;

<p>Calculus of manifolds, man…</p>

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<p>If you get in, enroll! But about half drop after officially enrolling, which is gonna be one of the highest drop rates you see. Be willing to be one of them.</p>

<p>[Burden</a> of Proof | FM | The Harvard Crimson](<a href=“http://www.thecrimson.com/article/2006/12/6/burden-of-proof-at-1002-am/]Burden”>The Harvard Crimson)</p>

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<p>With your background, it is entirely possible for you to succeed in math 55. But it depends on how hard you want to work. You should prepare this year with some algebra or analysis or both.</p>

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<p>I’m gonna guess and say that a lot of Math 55 is problem solving, as in having to prove all of the theorems which are taught by yourself - so if you’re not used to proofs and working on problems which can take you hours and hours to work through, I don’t think it’s for you. I can’t really say for sure, but given it’s reputation, it’s not going to be the content which is most difficult, it’s how you learn it and how deeply you learn it.</p>

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<p>This article scares me, since a kid who ranked in the top 12 in USAMO in his sophomore year (and took AP calc in 9th grade, like I did) dropped the class. Maybe it was more because of the insane workload than that he didn’t understand the material, though.</p>

<p>Is this course for freshmen?</p>

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<p>I’m pretty sure Math 55 is limited to freshmen. There is a very similar course at the University of Chicago that they will let some sophomores take, too, if they have aced Honors Calculus. </p>

<p>Before you get too nuts about Math 55 (or its equivalent anywhere else), however, you should recognize that: (a) Lots of people who could take the class don’t, or try it and leave, and it’s not always because they are too stupid for it. It’s one way to learn math, not the only way, and not necessarily the best way for everyone. (b) Many universities with excellent math departments, on a par with Harvard and Chicago, choose not to offer a Math 55-style course. I don’t think Princeton or MIT has one. And it’s not because the faculty is less competent there, or because every year Harvard has 10-20 freshman math students who are better than everyone at Princeton and MIT. It’s because Math 55 isn’t necessarily the best way to learn math. (c) Worry about Math 55 when you get into Harvard.</p>

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<p>There is also Math 25, which is pretty respectable in its own right, also open to freshmen only. Many people “drop down” from Math 55 to Math 25. Recently the textbook was Baby Rudin, plus a Linear Algebra book (don’t know about now), and the first problem set had a question that amounted to having you prove the Cantor-Bernstein-Schroeder Theorem (without naming it of course).</p>

<p>Not clear to me whether that UChicago course is more like Math 55 or Math 25, actually.</p>

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<p>I went to Math 55 for a while and decided to drop to 25. My school never competed outside of state-level math, so I can’t par my own abilities against AMC rankings and beyond (never knew these existed), but I will give input:</p>

<p>Quite honestly, AMC/AIME/USAMO aren’t really good indicators of whether or not you’ll succeed here. Most of those competitions rely on clever problem-solving vs. manipulating abstract concepts to logically define phenomena (proofs). Some mathematicians are great at one of these things but not the other; the two categories seem to use different skills.</p>

<p>I’m not sure which part of your experiences have involved writing proofs, but that’s the only way to gauge success in that class. I have met people who aced many math hurdles but struggle in math 55 and 25, and I have met people who suddenly realized that proof-writing was their thing. There’s no need to list your accomplishments here, I’m guessing most hold very little weight in your ability to do the coursework (though I can’t be sure, I haven’t even heard of most of the things you listed). I would re-recommend the advice that you should worry about it after you get in. Good luck.</p>

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<p>My S is in 55. The key is not what courses you have taken as that is the table stakes to do the course, or even if you are an IMO’er (about 1/2 are Olympiad and 1/2 are college course background). The questions you should ask yourself is how well do you do with writing proofs from scratch with deep rigour? And what level of abstraction are you comfortable with? </p>

<p>This week’s Pset involves establishing the fundamental proof of Galois theory. Prof Siu gave out Galois’ final writings that he scribbled before he died in a duel (very cool) but alas the paper is in French–pretty sure Siu didn’t even realize that. Last week was Lie Algebra and the class seems convinced that next semester is going to lead to calculus of manifolds in analysis --which is even terrifying them–(lots of crashing on extra reading during J term…). The work load is no joke-- he spent 17 hours on one proof alone last week and he and his friends average over 40 hours a week on the Psets. </p>

<p>That being said he is absolutely in love with the course…he has never felt more challenged and he can’t believe how much he has learned–not merely in material but in a whole approach to math. He now delves into original math papers as they work on proofs and his ability to demand rigour from his work has changed enormously.</p>

<p>Now the joke is that the class could all get easy As in 25 but that they are willing to chance a worse grade for the chance to see how much they can learn. But to repeat_–I haven’t ever seen him so excited about a course in his life (again, of course he was also so happy that Vet Day had no classes bc he had his first non all-nighter Thursday (Psets due at 5pm Friday). </p>

<p>It is a fraternity. If you take the class your best friends will come from the class both because you and they will spend hours and hours together, no one else can understand what you are going through and frankly lots of Harvard folks think 55’ers are the class nerds (yeah, even at Harvard there is a hierarchy of nerd-dom). So take it if that is the the type of freshman (collegiate) experience you want. </p>

<p>Don’t take it to impress people --you, your folks, your old math teacher back home, your Olympiad teammates. That wears off every quickly. You have to LOVE math. It has to be your passion. That is the only reason to take it.</p>

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<p>When my S was in Math 55 one of his friends tracked the drop out rate day by day. I think the first day of shopping period there were over sixty in the class, they ended up with around twenty. A few of those did not stick around for 55b. I believe Math 25 is scheduled at the same time to make it easy to switch if you need to.</p>

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<p>Do not forget kids who as a freshman by pass the Math 55 and take courses that are beyond Math 55.</p>

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<p>You will get a B or a C in that class, based off your level of math and the success you have had in math competitions.</p>

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<p>Well I do love math, that’s why I want to major in it. I do have proof experience, because a lot of my higher math courses have been proof based.</p>

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They might actually be easier than Math 55, even though they’re later.</p>

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<p>Is the grading scale really that hard? I have heard that Harvard has grade inflation.</p>

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<p>There were two members of the Class of '15 who were given the option to take 55 or go straight to 100 level classes. One did and one is taking 55. The 100 level courses are “easier” in terms of work load but if one doesn’t have 55 then there will be holes in one’s preparation unless one is very exceptional in the work done prior to Harvard. </p>

<p>This year’s 55 is gearing up (so my S and his friends say) for a kick ass 2nd semester analysis course which will be at an advanced graduate level. He has been told they will start with calculus of manifolds and then they fun will begin after that. (Siu is an analysis scholar and this terms algebra has been really to develop the tools for the second semester.</p>

<p>A number of the kids in his class chose Harvard specifically to take 55-- And these are kids from around the world (every continent but Antarctica is represented). My S says that what makes 55 terrific is equally the material and the chance to join with kids like them. </p>

<p>Go for it–you an always drop down to 25 if it seems not to be the right fit. (They call it “voting your self off the island.”)</p>

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<p>As for grade inflation in 55–no one is taking it “for a grade” per se-- because if one was concerned about GPA first and foremost that person would have opted for 25 where an A is practically assured (there is a huge gap in the level of rigour and amount of content between the two classes). So if you take 55 --again do it to learn math, not for the grade.</p>

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<p>Of course I would not do it just to get an A, but on the other hand I don’t want to jeopardize myself by getting a C.</p>

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<p>If you do the work, and don’t hang on stubbornly to the class if it is beyond you, you won’t get a C. And even if you did…if you got enough out of it it would be worth it.</p>