<p>I think I was over-thinking this—something that should not even be on my mind unless I am actually making a decision to enroll, not debating whether to apply—and was just upset with myself over nonsense.…</p>
<p>I actually did more thorough research than reading sensational Crimson stories and looked at the syllabi, textbooks used, course notes, and problem sets from past years for Math 55. I found that I have worked through on my own about half the texts covered in most years (Axler’s Linear Algebra Done Right, Artin Algebra, Baby Rudin, Spivak Calculus on Manifolds—and almost a text of an equivalent level—and actually remember a good number of the problems pulled to be used in the homework, so even if the curriculum is meant to go far beyond what is covered in the texts, I still have a chance at dealing this course or at least Math 25 after filling out gaps by taking a complex analysis course and continuing independent study. </p>
<p>Maybe it’s good that I get personal issues with this and inferiority complexes out of the way now and understand that no matter where I end studying, I will find some path to follow even if it’s not ideal or entirely respectable.</p>
<p>I am really tempted to say that anyone who seriously believes, at 17, that he or she is so far behind in an academic discipline that it’s not worth pursuing, is categorically too stupid and/or intimidated to go to Harvard.</p>
<p>Ditto for anyone who believes it’s not worth studying a field in which he or she is not demonstrably a genius before starting the first college class.</p>
<p>It’s just a ridiculous attitude, a complete misunderstanding of what scholarship means and what scholars do. Both anti-intellectual and self-destructive.</p>
<p>I know that what I am talking about is essentially irrelevant to my potential to be productive in academia. There seems to be something inherently anti-intellectual about introductory undergraduate courses and how they determine whether a person is on track to work in academia based solely on their prior knowledge of a subject and the demonstration of ability in it. At the same time, though, if you don’t show any genius but have great interest in a subject, what more aptitude for a subject could you have than anyone else? My guess would be likely less than that of the average Harvard student or one anywhere else who has no interest in that field. </p>
<p>Nevertheless, I think that you are right: I am either not intelligent enough or too unwilling to accept my place as a second-rate student to go to a school like Harvard. I am not sure what I can do with this fact other than change my goals, look elsewhere for study, or just hope for the best at a top school and accept my place.</p>
<p>That’s not what’s going on. I started the thread by stating how ridiculous that notion is. I am generalizing based off what seems a fairly representative case to determine whether or not I stand a chance in math departments at top universities.</p>
<p>You are completely missing the point, though. Math 55 is just one pathway into high-level math. It’s not the only pathway, or even necessarily the best one. Relatively few colleges offer anything like it, and not always because they wouldn’t have anyone to place into it. Princeton’s math faculty is not outshone by Harvard’s, and Princeton deliberately does not offer a stunt class like Math 55. Nor, I believe, does MIT. Chicago has a similar course, but unlike Harvard it fills half of the class with second-year students who performed really well in Honors Calculus their first year (and Honors Calculus there, if I understand things correctly, is equivalent to Math 23 at Harvard). And I know of at least one student who placed into Chicago’s version of Math 55 as a first-year and, after talking about it with the faculty, decided with their full support to give it a pass and to take other advanced math courses.</p>
<p>Harvard does NOT have some kind of a monopoly on high-level math education, and even at Harvard there are more ways than one to skin a cat. Have you read what the Harvard math department says about Math 25?:</p>
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<p>Doesn’t that sound like you? Do you think they are lying when they say you can catch up? </p>
<p>In fact, maybe you can’t completely catch up to the Math 55 guys (and they are overwhelmingly guys), at least while you are an undergraduate. But do you really think the 10-15 people who complete Math 55 each year grab all of the desirable math grad school slots in the world? Some of them drop out of college and start companies (like You-Know-Who). Some of them make it through Math 55, but barely, hardly covered with glory (I know one of those). Some of them burn out on math and get interested in other things. Some, like many of their classmates, go for the big bucks in financial industry jobs (I know one of those, too). And the handful that are left? By the time you and they are 25, barely into your adult careers, no one will be able to tell you apart based on what you know, and whether any of you have the stuff for a brilliant math career will just be beginning to be shown.</p>
<p>Look at the people who have faculty positions in math departments you respect. How many took Math 55, or anything like it, when they were 18? A few, sure, but certainly not all of them. Certainly not most of them. Some of them may well have started college in the equivalent of Math 1a, or not even that. Where people start in college reflects their past, not their potential.</p>
<p>And, anyway, if you love math and want to learn more of it, and to do it well, what other choices do you have? Go to a university with good mathematicians. Take as much math as you can. Get to know the faculty, and follow the advice of the ones you respect and trust. Work like a dog. What you achieve, ultimately, will likely be everything you are capable of achieving, and which freshman math course you took at which university will have absolutely nothing to do with anything.</p>
<p>I have seen the description, and it bothers me that this is the only alternative to people who aren’t Math 55 level or beyond. </p>
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<p>I would like that to be possible, but I don’t believe that class covering Axler’s linear algebra text and Rudin’s Principles of Mathematical Analysis can catch you up with people who cover several times the quantity and do work on a higher level. How can you catch up to people ahead of you by going slower than them? </p>
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<p>I have done these courses at a university and supplemented them with proof-based texts on my own. I don’t want to be walked through this again.</p>
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<p>Isn’t that what Math 55 is for? Real analysis, basic topology and linear algebra are not going to “patch up knowledge.” The material is limited in breadth, and Math 25 does not go into the depth that Math 55 does. Math 25 seems like a gentle way of letting people have fun for a year before letting them know that they have no future in mathematics at a major university. I could see how it could be perfect for physics and computer science students, but not pure math students.</p>
<p>Maybe this just means that Harvard and selective schools in general are just a fit for me.</p>
<p>“I have done these courses at a university and supplemented them with proof-based texts on my own. I don’t want to be walked through this again.”</p>
<p>So essentially you feel that you are too good for Math 25 but not good enough for math 55, without experiencing a single day in either course, or, heck, even before being accepted to Harvard…</p>
<p>Back to the main question you had though, which JHS answered perfectly, do you really think that the 15 or so kids that finish math 55 at Harvard are the only students with math futures in the entire nation? Really? As he mentioned, Princeton, MIT, and other top universities do not offer anything similar to Math 55. Are you suggesting that their math student populations all go off without any future in mathematical academia?</p>
<p>If you’re concerned about your entire future being determined by a math class you take freshman year at Harvard, before you’ve gotten into Harvard, then I’m not sure you have the maturity to handle Harvard.</p>
<p>“Do you really think that the 15 or so kids that finish math 55 at Harvard are the only students with math futures in the entire nation?”</p>
<p>No, but they are the only ones at Harvard who do, and when I don’t have legacy status at Princeton, what goes on there, even if it seems ideal to me from what I have read on their math department’s website, is not even relevant. I have one chance at finagling my way into what I want to do, and it seems to involve Harvard.</p>
<p>It’s not that I am “too good” for Math 25—most people in there would probably have more coursework and done more research than I have—but rather that the course shouldn’t be good enough for anyone who ever wants to go anywhere.</p>
<p>You don’t need to be a legacy to get into Princeton. I assume that you instead think that a legacy status at Harvard will get you in? It will help a bit at both schools, but Princeton won’t say “lol this kid’s not even a legacy; auto-REJECTION.” nor will Harvard automatically accept you.</p>
<p>After reading through Harvard’s math dept. website, they sync up Math 25 and 55 for the first few weeks so that you can sample both and move up and down as you see fit. You could use that to your advantage. Honestly if you can’t get past the fact that you might not get in to math 55 and think that this will rule out math research for you, you might want to consider taking a class in logic.</p>
<p>The people that take math 55 and/or end up succeeding are those that work as hard as they possibly can at something they are truly passionate about. If you end up failing, its because you spent your time comparing yourself to others and trying to convince strangers on a forum that you aren’t good enough to handle a particular class, not because you were unable to handle the coursework. </p>
<p>Fix your inferiority complex(“I am either not intelligent enough or too unwilling to accept my place as a second-rate student to go to a school like Harvard”) and get off your high horse (“the course shouldn’t be good enough for anyone who ever wants to go anywhere”) before going any further in your education.</p>
<p>What you have to realize is that 25 and 55 have only one purpose, from the department’s point of view: to keep irritating freshmen out of upper-level courses. Sweating over which one you get into is like sweating over which line you wait in at airport security. There’s no use in it, because it’s mainly a time-wasting exercise and the stuff you really want is on the other end.</p>
<p>I had a few friends in each of the classes, two of whom I have more or less kept in touch with. Both did PhD’s, the 25er at a slightly higher-ranked program, the 55er at a more prestigious overall institution. Neither one landed a TT job. The 25er is in now industrial research, the 55er teaches high school. </p>
<p>Admit rates for both classes to prestige graduate programs are very high? How high? I don’t know. Ask the department, which is really what you should be doing anyways rather than making stories up in your mind and hyperventilating about them.</p>
<p>On another note, you have a real talent for eliciting negative reactions from people. It’s kind of impressive. If you found a way to channel that talent rather than exercising it randomly because you were bored or depressed or whatever, it could be a real asset to you. Have you seen any of Andy Kaufman’s stuff?</p>
<p>"I am generalizing based off what seems a fairly representative case to determine whether or not I stand a chance in math departments at top universities. "</p>
<p>Harvard does not admit math majors. They admit undergrads.</p>
<p>So you are a HS student who has taken five advanced math classes beyond Calc BC and you are already washed up for a career in mathematics? That is certainly a shame. Are there any other careers that you have no future in or have you not had the time to mentally project yourself failing in them yet?</p>
<p>Geez, worry about getting a place like Harvard first and then worry about where the road will take you. Einstein was a patent clerk and it didn’t seem to hold him back (but then again if he’d taken Math 25, he probably wouldn’t have had any good ideas after that).</p>
<p>You know, I saw a homeless guy on the street yesterday, and I asked him what first-year math course he took in college. Turns out it wasn’t Math 55 at Harvard. Coincidence? I think not. OP, there is no hope…</p>
<p>You have to do competitive math to become a top math major, but, believing this, you opted not to participate?
Math 25 is way too easy for you but you are clearly underqualified to take Math 55?<br>
Only students who take Math 55 can get into a top grad program or be successful at math? </p>
<p>Here are my suggestions:
Stop wringing your hands about it and participate in competitive math this year. And don’t freak out when you don’t do as well as the kids who have been living and breathing it for the past 10 years.
<em>If</em> you get in to Harvard, then consult directly with them about your math placement. Don’t rely on potential misinformation from kids on the internet.
Do some actual research instead of jumping to conclusions about what grad school opportunities are available to which Harvard students.</p>
<p>Since this post is still fairly recent, I figured I’d chime in with my $0.02 cents after reading this fairly hilarious thread. </p>
<p>OP, I am a math major at a <em>crappy</em> state university. My high school offered Calc AB for the first time my senior year and I had effectively zero University-level mathematics experience when I arrived here. Three years later, I have a Goldwater, a standing offer to attend graduate school at Yale, and am halfway through my school’s graduate curriculum. </p>
<p>Am I a “math mind”? No! There are at least two people in my class (HERE at <em>crappy</em> state university!) that are markedly more advanced in the classical sense. They know “more” math. However, I jumped on the most advanced research opportunities I could find at every step and quickly found myself surpassing the kids that were at your level exiting high school plus or minus an olympiad. </p>
<p>Math is not a rat race. If you think you’re behind that just means that you know enough about what’s out there to take the next step. There will always be people that look smarter than you, faster than you,… that has nothing to do with how good of a researcher YOU will be. You’re more than prepared enough to jump into undergrad at Harvard, so just do it and quit being such a b***h.</p>
<p>P.S. My first undergraduate math course was Calculus II. (At the level of the Calc BC test).</p>
<p>well, @clandarkfire, you certainly are showing your school in its best light. Where would Yale be without people like you to spread FUD on potential Harvard applicants? Why are you trolling the Harvard boards anyway, and particularly in math?</p>
<p>Anyway, OP - I don’t think you know what will make you successful in any given field or not. But to answer your question, Harvard 25 and even (gasp) 21 math majors can still go to top graduate schools. The primary factors are overall academic performance, quality/quantity of research performed, and recommendations.</p>