Math 55

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Discus: Ivy League Schools: Harvard University: 2004 Archive: Math 55
By Scorpsjl (Scorpsjl) on Sunday, May 02, 2004 - 02:00 pm: Edit

Who here thinks they're gonna take math 55 next year? personally, i'm pretty sure i'll opt for it over 25, tho i also want to take physics 16, and i dunno if i'll be able to deal with the work from both (can anyone say how much work 55 REALLY gives? I know it depends on the prof-does anyone know who's gonna teach it next year?)

By Vecter (Vecter) on Sunday, May 02, 2004 - 05:41 pm: Edit

i'm guessing ur a MOPer?

By Nifty101 (Nifty101) on Monday, May 03, 2004 - 09:22 pm: Edit

what is math 55, anyone like to explain please?

By Vecter (Vecter) on Monday, May 03, 2004 - 10:17 pm: Edit

math 55 is the hardest freshman undergraduate math class in the country. basically kids on the national math team (a.k.a. MOP-Math Olympiad Program) and the International Math Olympiad team (IMO) take it

for math geniuses :/

By Eurostar (Eurostar) on Tuesday, May 04, 2004 - 05:11 am: Edit

I am taking 21 or possibly 23

There is no way I would take 55. Don't torture yourself right away..

Everyone take Physics 16, though!

By El_Diablo (El_Diablo) on Tuesday, May 04, 2004 - 01:02 pm: Edit

how do u know the courses?

By Monekit (Monekit) on Tuesday, May 04, 2004 - 06:24 pm: Edit

By Kenenisa (Kenenisa) on Tuesday, May 04, 2004 - 08:06 pm: Edit

At the risk of sounding like a jerk (sorry in advance):
Yeah, I'm sure a school like Caltech doesn't offer anything even close to as challenging as Math 55, which according to the site is basically an accelerated math class covering the first couple of years of college math.

I know someone indirectly who is finished with undergraduate math, and he is still in high school.

By Scorpsjl (Scorpsjl) on Wednesday, May 05, 2004 - 09:15 pm: Edit

Kenenisa, i'm assuming that was sarcasitc. Indeed Math 55 has been heralded by many sources as the hardest undergrad math class in the country. This isn't to say that Caltech doesn't have a very hard honors class, or maybe even (hypothetically) a harder one, but Math 55's reputation is pretty respected. It covers Single and multivariable calculus, differential equations, linear algebra, and some topology (basically, the first 3 years of college math for a 'normal' math major, though i say that in quotes because many math majors, not only at harvard, are accelerated). The only topics left in normal undergrad math are analysis, and possibly some algebra. And to address the second point about your friend, many (most?) 55'ers have already seen all or most of the topics covered by the class. What's different about 55 is the level of depth and abstractness at which the topics are covered. The class is very intensive and proof based, as well as fast moving. what proof based means is that unlike in hs math, where you have to apply a theorem or algorithm that was already proved in class to examples, you will have to first prove that theorem or algorithm yourself, given the background from class. math 25 and i think 23 are proof-based also, but nowhere near as intense as 55. anyway , i think i'm gonna take it-will be insane, but an awesome experience. anyone else with me?

By Uncchlocalmayor (Uncchlocalmayor) on Thursday, May 06, 2004 - 04:32 am: Edit

Kenensia, are you talking about Anders Kaseorg who finished out the undergrad. math classes at uncc by his junior year in hs? yeah, i was in the same mathcounts group w/ the kid back when i homeschooled. anywho, later.

-UNC c/o 2006, hava'd sucks

By Corny (Corny) on Thursday, May 06, 2004 - 01:02 pm: Edit

Math 55 is definitely not for everyone. Even if you received a 5 on your AP Calc test, don't take Math 55 unless you already know how to write proofs very well or you'll regret it.

Most of the people in that class have been doing proofs for years and you'll never have time to catch up. Math 25 would be a safer bet but that class is no piece of cake either. At least in Math 25 you'll have fellow students who have never done real math proofs before and will suffer along with you.

By Kenenisa (Kenenisa) on Thursday, May 06, 2004 - 05:36 pm: Edit

It definitely was not sarcastic. To say that any class is the hardest undergraduate math class is absurd. What is an "undergraduate math class?" The person earlier said that it's the "hardest freshman math class" - what the heck is a freshman math class? Some people start with college algebra or calculus, for some people all of the topics you said would be review as a freshman, which you acknowledged. So basically, if your freshman year is the hardest, you're saying a year of review is the hardest year you have in college as a math major? I just find that hard to believe. I have a friend who is a junior in HS and he will be done with everything you said is in Math 55 by the time he is out of HS, and he just isn't that smart. If that's seriously as hard as math gets, then math is an easy major, and I really doubt that's the case. I have huge respect for math. I'm no math whiz compared to these math team guys (although I did make an 800 on IIC and I did just rock the BC calc exam), so maybe I'm barking up the wrong tree, but when I see someone coming onto a forum saying "my freshman math class at Harvard is the hardest math class in the nation," I feel like he is probably full of it, especially considering some people are DONE with undergrad math before they even finish HS... it's a moot point anyway.

Anyway, I am definitely jealous of you guys who will be in a class like that. I wish I had used more opportunities to take college math in HS. Best of luck to you in that class, I'm sure it is definitely difficult :)

Oh, and I understand the difference in applying rules and writing your own proofs, but like I've said a hundred times, I just don't see how a year of what for many people is review could possibly be the hardest undergrad math course in the nation when there's crap like chaos math (I don't even know what that is, I just heard the name from Good Will Hunting!).

By Vecter (Vecter) on Thursday, May 06, 2004 - 05:49 pm: Edit

i know someone taking 55 next year, he did a research project on de Sitter space. in case you don't know what de Sitter space is (and I still don't haha), here's a definition I found online:

I think it's funny how almost EVERY WORD in that definition requires a definition in itself

that's 55 for ya :-P

(btw i'm just a high school BC-er who bows down to MOP/IMOers)

i also saw a copy of his paper, more equations than words lol

tho it's interesting b/c he never did MOP or IMO, i guess he's just a closet genius who doesn't do those sorts of competition, but I can definitely see him doing decently in 55, if not well

By Fprescott54 (Fprescott54) on Thursday, May 06, 2004 - 07:27 pm: Edit

Vecter I agree :) I also bow down to IMO/ MOPpers

Kenenisa, you obviously have not heard about 55. I have a friend who is a former MOPper and struggling in 55. I don't think it is hard b/c of its set curriculum, its considered to be incredibly hard b/c they gather the BEST freshman mathematications in the country and put them in a proof-based class determined to study as much obscure math as possible. It is a class only offered to freshmen and is known for 30-page problem sets. I don't think "upperlevel" math classes like abstract algebra are necesarily "harder", but math 55 is definately "harder" b/c you are not just learning about new topics like for example taking Calc 2 after taking Calc 1, you are probing the entire reasoning behind Calc 1 and trying to really understand what math is about.

By Kenenisa (Kenenisa) on Thursday, May 06, 2004 - 08:11 pm: Edit

Ok, so be it. If a freshman course that basically covers from calc through linear algebra is the most difficult math course in America, then the future of math is disheartening. However, I will shut up because I freely admit I do not know what I'm talking about, it just surprises me greatly (and I still think it's probably very wrong, but like I said I have no facts to back it up so I won't keep arguing).

By Corny (Corny) on Thursday, May 06, 2004 - 08:29 pm: Edit


The best analogy is learning a language.

If somebody told you that they were going to cram four years of language learning into a single year, would you think that was difficult? Yes, of course, because you'll be learning the material at such a fast rate.

And then if they told you that you would have to study that language with gifted language learners, would that make the class even harder? Yes, because the faster people learn, the faster the teacher can teach the class. That means there is no time for review because you have to move on to the next topic.

Math 55 is that type of experience.

By Scorpsjl (Scorpsjl) on Friday, May 07, 2004 - 12:39 am: Edit

corny-pretty good analogy

kenenisa- first of all, if you reread your first post, you 'were' being sarcastic-"yeah, i'm sure that caltech doesn't etc.. etc"...that was just how you were making your point ( you even prefaced it with "i dont wann be a jerk, etc" and i was just making sure thats what you meant.

secondly, what you don't seem to understand is that math 55 doesn't cover the HARDEST topics in mathematics, it's just that it's the hardest class. And by that we mean the most intensive, and most time-consuming, not necessarilly the most intelligence-demanding. For example, (although linear algebra and calculus can be very difficult and deep if one considers them in enough detail), there are many fields of mathematics that are more complicated than those covered in 55 that, in a normal math progression, come in the upperclass years of undergrad and in grad school. However, these classes are taught much more slowly than 55, and the students have more time to go over what they have learned, do problems, and really understand what is going on. Yes, these topics are "harder", as you say, and presumably there are some people who just won't get them, ever, although these same people might be able to get calc and linear algebra if they try hard enough. But these same people would crackle and burn in 55. do you see the point? and all of your arguments about "really smart undergrads who take all sorts of math in hs" don't really make sense, because, though i won't get into an argument of overall quality of school or even department, it is hard to argue with the statement that harvard gets practically all the best pure math students in the country (even over MIT, which really has a much better engineering program than pure math, tho must people aren't aware of this). And all of these best math students, the steven byrnes and the gabriel carrols, etc. etc, the smartest math majors in the country, take 55 (instead of skipping it and going into grad classes as freshman). and are challenged by it, and have a lot of fun in it. Our assertions are definitely correct, and i still don't understand why you find it so hard to believe, tho as you 'freely admit', you have no idea what you're talking about (i.e. the 'inside' math game), and so i'll excuse you.

vecter- with respect to your friend, he doesn't necesarilly have to be a "closet" geniuses. there are many mathematicians who are very good researchers, great at grasping concepts and coming up with new ideas, but these same people are not great at math competitions, which utilize different skills than research (fast thinking, quick problem solving, resourcefulness). although many people are good at both, many awesome mathematicians are good at research but not at competitions (the opposite isn't really true -- it's hard to say that many awesome mathematicians are good at competitions but not at research, because, ultimately, it is research that is important).

aaah can't wait for 55. it's why i chose harvard over stanford. both have great depts (even heard stanford's was friendlier) - but like all of you are saying, it's the students (all the MOP'ers, intel finalists, semifinalists and isef winners in math, etc...) who go to harvard that make it the best.

By Vecter (Vecter) on Friday, May 07, 2004 - 10:08 am: Edit

lol yeah i think there are at least 11 intel finalists going to harvard this year, but among them only two are doing math, the kid I mentioned before and another one from NY.

mit has 8 grr, but we got boris ;)

By Ambitiousyokel (Ambitiousyokel) on Friday, May 07, 2004 - 10:24 am: Edit

Awesome. That kid whipped my ass in a chess tournament in sixth or seventh grade. B*tch-slapped me, as it were.

By Corny (Corny) on Friday, May 07, 2004 - 02:36 pm: Edit

I'm not sure if the process has changed but a few years ago, Math 25 and Math 55 met together for the first few weeks and then only those who did extremely well on the homework assignments were asked to join Math 55. The rest remained in Math 25. I guess it was a way to weed out those who weren't good yet at writing proofs and solving abstract problems.

Does anyone know if that is still the case or can a student go directly into Math 55 now?

By Vecter (Vecter) on Friday, May 07, 2004 - 02:56 pm: Edit

hehe ambitiousyokel are you talking about amos lubin? i didn't know he played chess. how do you know him?

By Kenenisa (Kenenisa) on Friday, May 07, 2004 - 06:00 pm: Edit

You're right about the sarcasm - I misunderstood what you were saying. I had forgotten exactly what I posted, and I thought I had just said "there's no way Math 55 is that hard" and then you asked "are you being sarcastic." Sorry about that.

And anyway yes I can understand that perhaps it has the most "work" of any class, I was just very taken aback by "hardest." In a way I was partially correct in that, in my opinion, most people when they think about "hard" math classes think of stuff that is difficult to comprehend. At least I do, and that was my entire point, but basically I will concede that perhaps it has the most work of any traditional undergrad math course (although, of course, the real super geniuses as seniors probably are doing independent studies where they are creating new theorems working 8 hours a day, but anyway I'll just leave it at that :) )

Good luck in math 55.

By Almostdead (Almostdead) on Saturday, May 08, 2004 - 04:19 pm: Edit

math 25 and 55 are taught separately to give the students the opportunity to shop both.

math 55 is NOT simply cramming 3 or 4 math classes into one. While the book says it's on differential equations, mv calc, etc... it's NOT. DEFINITELY NOT. It goes waaaaaaaaaay beyond normal calculus into algebra, Lie algebra, real/complex analysis, Fourier analysis, and... well I don't exactly know what they've done, but even IMO winners have trouble in that class. A lot of trouble. I've heard only one other math class offered for undergrads at Harvard can match 55's difficulty. Even the other classes in the 100s or 200s aren't as hard. Or so they say. professor in that class will expect you to have already learned everything, so he can just go straight to the really really really theoretical stuff.

Hmm what else... oh yeah... 25 (which I am taking). Also do NOT take this class if you haven't done any proofs before. Well, I don't know who's teaching it next year.... but this year we had a really demanding professor... and well, 16 students dropped after the first semester, making 25 an even smaller class (10 studnets) than 55 (18 students).

By Scorpsjl (Scorpsjl) on Saturday, May 08, 2004 - 10:10 pm: Edit

Almostdead- are you taking 25 this year? Is there only one section? If so, I must have seen you... I sat in on the monday 25 class during prefrosh weekend. Are you in the class with all of the stuy people (alex ellis, joel lewis, alex levin), and the french guy? It seemed like a good class, but i still want to try for 55. i know a few people who are in it, and although i don't know how they're doing, they aren't godly at math. tho joel lewis is, and he's not taking it, which depresses me a little... how much work a week do you get from 25?

Are you a math major? If so, i'll probably run into you next year...

By Scorpsjl (Scorpsjl) on Saturday, May 08, 2004 - 10:12 pm: Edit

vecter-is amos the tall, quiet, sort of oddball guy?

I might have gone to HCSSiM with him

By Vecter (Vecter) on Saturday, May 08, 2004 - 10:21 pm: Edit

yeah Scorpsjl, very shy guy lol, took me a week to be able to get him to talk in a normal conversation

what's HCSSiM?

By Almostdead (Almostdead) on Saturday, May 08, 2004 - 11:14 pm: Edit

scorpsjl: lol yeah, exactly that class. are you from stuy? good luck on shopping 55 next year... heh... i was there for two days and then i realized it was impossible for me to follow. (i hadn't had any math beyond calc BC....)
i'm definitely NOT a math major... prolly physics... math 25 showed me that i am horrible at math in a most efficient way. =(

By Scorpsjl (Scorpsjl) on Saturday, May 08, 2004 - 11:20 pm: Edit

HCSSiM is the hampshire college summer studies in mathematics, a math summer program at hampshire college in amherst, mass. It's not super well known and super rich like RSI (nor is it focused on research like RSI)-it's more like PROMYS for (in my opinion) smarter people. (Though i really have no idea what they do at promys so i dunno). The director is a new-age mathematician named David Kelly, and he and all the other teachers there are incredibly smart. google it to get their website (

vecter-are you going to ISEF?

By Scorpsjl (Scorpsjl) on Saturday, May 08, 2004 - 11:28 pm: Edit

almostdead- yeah from stuy...

physics major? so you're like alex ellis, physics and math? he told me the physics majors, and espeically the math/physics people, were all pretty tight-knit. sounds cool. With no math beyond calc, it's probably pretty impressive that you're still in 25 right? I guess i just don't like people quitting on math, (usually it's because they think they're bad when they're really not) because it's so much fun! But it does get so esoteric sometimes, i might end up doing somethign applied too. i was thinking biology maybe instead of physics tho. how's your physics class?

By Vecter (Vecter) on Sunday, May 09, 2004 - 12:46 am: Edit

naw i got shafted by regionals, gl there (i guess you did a math proj?). i saw a commercial for isef, looked really cool esp. @ the end @ the awards ceremony

i dunno how much freedom they give you there, but milk every ounce of it lol

By Jab93 (Jab93) on Sunday, May 09, 2004 - 03:40 am: Edit

I graduated Harvard in 1993 with a degree in Physics and Astrophysics... then, there was only 3 options for the multivariable calculus/linear algebra track: 21 (regular), 22 (physics oriented), 25 (theoretical math oriented)...

For those who are physics/chemistry/engineering oriented, Math 21 is probably the best choice...
it is a very practical, problem-solving oriented track that is incredibly useleful in solving actual physics problems that you will encounter in your science courses...
The vast, vast majority of physics, astro, chem, geo, bio, etc concentrators take math 21.

Math 22 is more theoretical physics oriented... the funny thing is... my friends who took it didn't learn any practical techniques in solving actual problems... you learn math that you won't need until you get to graduate level physics, but in the meantime, you learn nothing of practical value for the physics courses you take as an undergrad.... my physics major friends who took this course regretted it...

Math 25 (and I guess now 55) is truly only for hardcore theoretical math types and physics people who want to focus on theoretical mathematical physics.... you won't learn anything of use whatsoever in solving real-world math problems that you will encounter in science or engineering...

By the way... most physics majors follow math 21 with the Applied Math 105ab sequence (complex variable analysis, partial differential equations, and fourier analysis)... which is by far the absolute most useful math sequence I have ever taken... I went on to get a PhD in astrophysics and I am now a astrophysicist... and I use the applied math I learned in those two courses every single day of my career.

By Cosmology2020 (Cosmology2020) on Saturday, May 22, 2004 - 12:39 pm: Edit

do any other colleges offer a class similar to math 55 or math 25?

By Corny (Corny) on Sunday, May 23, 2004 - 01:24 am: Edit

A lot of top schools (princeton, columbia,etc) offer honors math courses like math 25 but not math 55. At least, I don't know of a school that does.

By Irock1ce (Irock1ce) on Sunday, May 23, 2004 - 04:14 pm: Edit

Berkeley's 53/54H maybe? Probably not.. but it definitely isnt TOO far behind in difficulty.. especially when you get a professor who speaks broken english.

By Vecter (Vecter) on Monday, May 24, 2004 - 02:55 pm: Edit

lol Irock1ce, I doubt Math 55 is difficult b/c the professor is a poor communicator ;)

if that were the case then I took a VERY hard multivariable course

By Corny (Corny) on Monday, May 24, 2004 - 09:43 pm: Edit

Believe me, we've all been there and we completely sympathize. I don't know how many times I couldn't understand a professor because english was not his or her native tongue. The worst is when you ask them to repeat something and you still can't understand.

My other pet peeve: why the hell can't math and physics professors stick to using a few greek letters that everybody knows (alpha, beta, gamma, delta, psi, phi). Xi and See are NOT easy to draw without practice so I end up with notes that look like wavy line doodling.

By Corny (Corny) on Monday, May 24, 2004 - 09:56 pm: Edit


I just checked Berkeley's Math H53/H54 website. The books those classes use are the standard second year multivariable calc/linear algebra books (not necessarily books for math majors).

Math 25 tends to use third-year level books used by math majors like Principles of Mathematical Analysis by Rudin. The proofs in that book are harder just because of the amount of math background it assumes the student has. I just checked the Math 25 website and they're using a graduate-level textbook Real and Functional Analysis by Lang.

So the Berkeley honors courses H53/H54 are not equivalent.

By Irock1ce (Irock1ce) on Thursday, May 27, 2004 - 12:07 am: Edit

eh. i know. but im just saying that the amount of cutthroat asians from china, japan and korea in there makes it 100000000 times harder.. for example... i know some students that came here as china's elite math program.. (we're talking finishing high school when they're 10) and they are just simply amazing in math... the tihng is.. most of these kids end up at UC Berkeley... UCB is cheaper, closer to home and more famous (in Asia) for engineering. Thats what i meant by math 53/54H being super hard.

By Corny (Corny) on Thursday, May 27, 2004 - 09:43 pm: Edit

I guess it depends on the class. Some math classes don't grade on a curve so there isn't that much competition. But, you're right, if there is a curve, any class with super smart people would be extremely hard--no matter what the topic.

By Norm (Norm) on Friday, May 28, 2004 - 04:33 pm: Edit

Irock1ce, cutthroat asians compared to IMO participants...hmm I think 55 has much smarter people that could take any of the people in H53/54 anytime.

By Irock1ce (Irock1ce) on Saturday, May 29, 2004 - 02:39 am: Edit

oh u just dont know cutthroat Asians do you? As i said, there are the creme of the crop asian math geniuses here.... (btw, im pretty sure that Taiwan, China, Japan or South Korea could all kick our asses in Math). But if you dont believe me, you should come over here and check it out. UCB is cheaper, and its in a more convenient location. Thats why it attracts a good amount of Asian Math geniuses.

By Irock1ce (Irock1ce) on Saturday, May 29, 2004 - 02:48 am: Edit

heres an interesting stat: in 2001, all 6 of China's IMO members won gold. Same in 2002. 2003, 5/6 won gold. 6th one won silver. This is #1 in the world. Another thing.. I actually know 2 former IMO gold medalists from China (well my dad does.. he fixes their car. they're doin their graduate studies right now.. one of them did undergrad here. other one at XingHua(china's MIT).

So, you can take math with Chinese IMO team... or U.S. IMO team... Chinese IMO team > U.S. IMO team. Thats one way that Math 53/54H could be super super tough. Have random asian people come over and turn your curve super hard (UCB doesnt have grade inflation either.).

By Norm (Norm) on Saturday, May 29, 2004 - 11:49 am: Edit

Most Chinese IMO team doesn't go to UCB. More IMO students have gone to Harvard, or MIT, than UCB. Besides, if UCB top students are better than Harvard's top students, why don't I see them EVER beating Harvard in Putnam...

By Irock1ce (Irock1ce) on Saturday, May 29, 2004 - 03:00 pm: Edit

lol yeah i know. im just saying random stuff. but im just saying that i have known chinese IMO people at UCB.

By Vecter (Vecter) on Saturday, May 29, 2004 - 05:18 pm: Edit

on average, Chinese IMO > USA IMO,

but in 2001 USA got 2 perfect scores (Gabe Carroll @ Harvard and Reid Barton @ MIT) and so did China

By Norm (Norm) on Saturday, May 29, 2004 - 05:59 pm: Edit

of course it is...they have a billion people to choose from.

By Godis (Godis) on Sunday, May 30, 2004 - 02:39 am: Edit

not necessarily. the laws that limit families to having one children reduce the number of high school kids.

By Irock1ce (Irock1ce) on Sunday, May 30, 2004 - 01:29 pm: Edit

yeah nowadays its a bit different. they have one billion people to choose from... if you count the old, the middle aged, the babies and everyone else. Sure. But wouldnt it make sense that a place like India would be #1 since they have no birth control laws and its next generation probably outnumber the next generation of chinese?

By Vecter (Vecter) on Sunday, May 30, 2004 - 02:35 pm: Edit

Chinese people just accelerate their children in math

what's considered "accelerated" here in the US is standard in China

By Norm (Norm) on Sunday, May 30, 2004 - 03:01 pm: Edit

china has tons of special programs geared specifically toward the IMO. We realize the IMO isn't life...we win anyway.

By Scorpsjl (Scorpsjl) on Monday, May 31, 2004 - 01:43 pm: Edit

yea i agree with those last 2 posts, in a lot of different endeavors, there is an intersting pattern when comparing the west (usually the US) and the east (often china, and japan),. Japan and China tend to be superior at younger ages, to reach certain levels faster, and to be better trained/more disciplined at things. However, at higher levels, i.e. the professional level, etc, the US often wins, showing greater levels of creativity and risk taking, all importnat things for novel discoveries. THe same comment has been often made about baseball to explain why Japanese little-leaguers kick our ass, but why professional japanese players are nowhere near as gooda as ours. At the little league level, japanese-style is more honed and thus beats our kids. However, at the highest levels, the American MLB'ers can figure out the japanese style and beat them, and show more originality/creativity on the field. Of course these are all generalizaitons and not always true, but they make sense. In other words, china might do better at IMO than us without indicating that they are better than us at math. As vecter pointed out before i think, some really good US math students don't even do IMO. They are more intersted in researching, even at the high school level.

By Rtkysg (Rtkysg) on Monday, May 31, 2004 - 02:57 pm: Edit


I am inclined to agree with you, however I think you need to limit this 'Western adult trophy' only to pure science and sports. The reason why many of the chinese/korean IMO kids are not so famous in mathematics is because many of them knows that math field is not productive (in term of money) and hence they would often go for Engineering and Business and leave all those weird math stuff.

Many of them join the competition just for the sake to get scholarship to a prestigious university in US and have a bright promising career afterwards.

In case of sports, a good US baseball player is much much much wealthier than a top-notch Japanese player. Sports, frankly speaking, is not as highly respected as academics in Asia, and hence less people commit themselves to become a pro.

I believe in term of trading and business, the chinese/japanese/korean professionals will be as good as the western ones

By 301aish (301aish) on Wednesday, June 02, 2004 - 12:50 am: Edit

Why does eveyone make such a big deal about Math Team...i'm on math team, and once you've seen a certain question type enough times it's just reflexive and not really a matter of skill...isn't "outside the box" thinking actually tested much better in doing actual resarch...Things like USAMO and AIME are so arbitrary...the only people I know who have been able to do both with success are Joel Louis (The MAN!) and Gabe Carrol

By Rtkysg (Rtkysg) on Wednesday, June 02, 2004 - 07:31 am: Edit

301aish, I agree with you, but Putnam is an exception i guess ...

By Vecter (Vecter) on Wednesday, June 02, 2004 - 08:39 pm: Edit

301aish i miss your point.

how are AIME and USAMO arbitrary? People who do well on these (and then advance to MOP/IMO) often do great on Putnam also, not to mention college math in general...

you make it sound so easy ("reflexive"), but unless you can actually do it and make MOP/IMO (are you?? that would be VERY impressive), i wouldn't talk it down. I know that I certainly can't do AIME/USAMO, but I don't dismiss them as foolish just because I'm not good enough for them.

By Pimpdaddy (Pimpdaddy) on Wednesday, June 02, 2004 - 10:46 pm: Edit

"Joel Louis"
wow, small world

By Vecter (Vecter) on Wednesday, June 02, 2004 - 11:25 pm: Edit

I thought it was "Joel Lewis" (stuyvesant?)

By 301aish (301aish) on Wednesday, June 02, 2004 - 11:38 pm: Edit

My big "point" (not trying to be arrogant) is that I don't see the big deal with these "geniuses" from Bulgaria, China, or whatever (although they are all VERY smart) I mean, they have been doing this stuff for years more than their American counterparts...It doesn't make them smarter, it just means that they've seen these problems dozens of more times and practiced, practiced, practiced. At that point, it becomes less intelligence and more test prep, albeit at a very high level.
At the same time, can you prepare like this for math/physics/biology research? of cousse, your dad or mom can be a doctor, but at some point you have to understand it for yourself, and make your own connections
Also, isn't the impact that research has more important than isolated math questions that don't have context?

By 301aish (301aish) on Wednesday, June 02, 2004 - 11:38 pm: Edit

Pimpdaddy: You know Joel? From where? why "small world?"

By Vecter (Vecter) on Thursday, June 03, 2004 - 01:22 pm: Edit

301, i think that getting a gold at IMO DOES mean that you're "smarter" (however that relative clause is used...).

have you seen Gabe Carroll's writing? I was browsing his website and looked on his "thoughts on harvard" and omg I could tell by reading his few sentences that his level of intellect was vastly superior to most people's i've seen. his language is so abstract and almost beautiful, just a reflection of the thought processes he learned through his math studies.

and remember that math is the foundation for most sciences. Try writing a scientific paper without manipulating numbers.

also, showing your proficiency in math proves that you're capable of learning basically anything you want to. Michael Lander (MIT prof, MacArthur fellowship winner, IMO gold, Westinghouse STS 1st place winner) basically ran the human genome project @ the whitehead institute. Math prodigy gone to bio.

sorry i guess i'm ranting, but my point is these math geniuses had to work for their skills ("natural" prodigies like Gauss aside) and spend countless hours studying writing doing working etc. while you and I were hanging out w/friends or focusing on something different (say research!). Being success in a math competition (or any competition for that matter) just shows that you're capable, so it's not fair to downplay USAMO/MOP/IMO. Saying that doing well in math is reflexive is the same as saying that doing well in the national biology olympiad is reflexive. of course! but you had to spend years learning all that "reflexive" stuff!

And doing well in research? Well that's a combination of luck, intelligence, and innovation. Like you said, you can't prepare per se for research, but you can in the sense that the more you know, the more you can possibly do. How can you possibly expect to do an advanced physics project if you don't know the math to handle maxwell's equations?

As an aside, I don't think that AIME/USAMO are arbitrary--people who REALLY know math do well on them consistently year after year. Of course you can get lucky.

By Rtkysg (Rtkysg) on Saturday, June 05, 2004 - 01:22 am: Edit


It is true that AIME/USAMO is not arbitrary, but for those already in the field (Engineers, Scientist, Prof) it doesn't look as great anymore. The reason because in your college year, and even more in graduate school, many of these AIME/USAMO/IMO competitors does not exhibit better capability.

An easy illustration would be like this, John Nash try to compete in Putnam (Putnam by far is harder than AIME/USAM/IMO/IPhO/etc) 2 times and lost. Richard Feynman was a Putnam 1st winner. However, John Nash produce a brilliant Math Game Theory at the age of 22 (and yet still cannot win the Putnam). Feynman, get intimidated by abstract math at graduate school, and choose to go to Physics (he's definitely no less smart :)).

Now would you judge John Nash is less smart than Feynman in Math ?? No. Nash > Feynman in mathematics. So don't get humbled by your incapability of doing USAMO/AIME. It does not mean you have a less great potential capability. It's just that you are not well-trained for that kind of competition. That's all no big deal :)

By Buckojack (Buckojack) on Saturday, June 05, 2004 - 02:46 am: Edit

I don't know what the hell any of you are talking about with the math 55/53 /54/ h/24/25325//325/235235/32325, but as for the baseball thing, American's are better at baseball then the Japanese simply because our people on average are much bigger and stronger. Hideki Matsui was considered to be an enormous player in Japan, and he is simply average compared to American sluggers.

By Vecter (Vecter) on Saturday, June 05, 2004 - 04:26 pm: Edit

I believe Nash got honorable mentions, which is still very respectable. I didn't know about Feynmann, but in hindsight it's not too surprising (hey, they both went on to win nobels!).

I understand you're point about not looking too far up on MOP/IMO people, but I was just replying to 301 that at the same time, they should not simply be dismissed.

ahh I just wish I were good @ math...

By Aycaramba799 (Aycaramba799) on Saturday, June 05, 2004 - 11:28 pm: Edit

As impressed as I am with math geniuses, i think there is a certain level of unfairness. I think a great number of people could be amazing at those competitions if they were taught "competition math" at a young age. By that I mean, going into several of these competitions with the algorithms under your fingers helps alot.
For someone like me, who is an ok math guy, but not amazing, I would have loved to have the oppurtunity to distinguish my self in something that im actually good at, like history or english. Unfourtanetly, there are no real competitions that recognize those students (cept for maybe history day).
pardon my rambling

By 301aish (301aish) on Sunday, June 06, 2004 - 07:35 pm: Edit

Vecter: do you get my drift now?

By Vecter (Vecter) on Sunday, June 06, 2004 - 09:42 pm: Edit

sorta, it just seems like you were casting off the math geniuses as "reflexive", which I thought was an unfair assesment that took away from their accomplishments.

By 301aish (301aish) on Monday, June 07, 2004 - 09:33 pm: Edit

For example, some of my friends just got back from ARML. One of them was like "i missed a medal because i wrote '64' instead of '64i' as the answer." Who cares if you had a moment of forgetfullness and wrote down the wrong thing--that's just like the SAT's--things like that don't happen in research. It's not petty and stupid in that sense. In research you have time to look over what you have done and THINK, not just spit out answers to randomly assigned questions of increasing difficulty. As a great math team coach and math teacher once told me, "It is always preferable to write your own problems than solve someone else's." I think that is the crux of the matter. Math team can SOMETIMEs (Not always) be people who are smart but like their challanges in recognizable, bite sized dosages. In that sense, they are more like puzzles, which are fun but ultimately , what is their point? That is the exact reason why i don't think math team is reflective of "math skills" and people who are good at math team are "geniuses." What are they really demonstrating in the end? This is very unlike the kind of abstract thinking and reasoning, and teamwork, that is necessary in a real research project. Kind of ranting here. Math team people, please don't be offended

By Z00b (Z00b) on Tuesday, June 08, 2004 - 12:57 am: Edit

Heh, just read an interview with Bill Gates somewhere... I can't exactly recall... I think it might have been Forbes, The Week or PC Magazine and he was asked something like "I was always told that no matter how smart you are, there is always someone smarter than you. How do you feel about that? He referenced Math 55, saying everyone had 800s on their Sats and 5 on their APs, saying it gave him a reality check. Let me see if I can find it...

By Vecter (Vecter) on Tuesday, June 08, 2004 - 04:07 am: Edit

Z00b I remember that also, I think it was BusinessWeek.

Yeah, he was asked about smart people and he said something along the lines of "There was this one class Math 55..." yada yada yada. I didn't realize Bill Gates was a math genius until then.

By Mattlord (Mattlord) on Friday, June 18, 2004 - 03:19 am: Edit

what's gabe carroll's website?

By Vecter (Vecter) on Friday, June 18, 2004 - 10:53 am: Edit

5 seconds on google answers questions faster than almost any forum can ;)

By 2bad4u (2bad4u) on Sunday, June 20, 2004 - 03:00 pm: Edit

USAMO people are a million times more talented than 800M or 1600 , although at times it is true exposing oneself to competition math is part of doing great, I would hold more respect for someone who got honorable mention in putnam's without ever being exposed to comp math than someone who has been around it all their life and only gets in the top 5-20 in putnam

By Serdu (Serdu) on Sunday, July 18, 2004 - 07:39 pm: Edit

One of my classmates (08'er) will go directly into Math 55 this fall. He is a math genius though. He was telling me about how he's already finished last year's problem sets.

By Mruncleramos (Mruncleramos) on Wednesday, July 28, 2004 - 02:12 pm: Edit

I agree with Scorpsjl.
The topics covered in Math 55 are not really that hard... They use Principles of Mathematical Analysis by Walter Rudin and some other linear algebra book. I've finished the principles of mathematical analysis book and I can understand why even some extremely talented competition mathematicians would falter on the material. I don't consider myself a genius. I'm just another sophmore who finished Calc BC. In addition to that my competition math is mediocre. But all that the book really requires is hard work and some mathematical intuitiveness. On the other hand, doing well in the class requires alot of hard work. Honestly, they don't cover that many topics as it may seem.

By Ali_Liu (Ali_Liu) on Thursday, July 29, 2004 - 05:58 pm: Edit

Does anyone know how IB Further Math compares to these courses?

By Mruncleramos (Mruncleramos) on Friday, July 30, 2004 - 06:08 pm: Edit

IB Further Math barely pales in comparison to Math 55. It also is no match for Math 25 many other classes. IB Further Math is a toned down Introductory Analysis Course with other topics.

By The_Brain9 (The_Brain9) on Saturday, August 07, 2004 - 02:51 am: Edit

What book would one use to become proficient enough at writing proofs to take Math 55? I am student who has done very well in calculus (easy 5 on BC) however, my school did not offer anything in the way of proofs. I have already checked out the website: so is there anything else? Any help is greatly appreciated and no I don't need anybody saying just to give up because it's too hard. Thanks.

By Corny (Corny) on Saturday, August 07, 2004 - 10:45 am: Edit

Since you got a 5 on BC, you should get a book on calculus that is proof-based and work through the proofs. Make sure you understand the thought process.

One unusually good book (usually used in honors single variable calc courses) is

Calculus by Michael Spivak

Make sure to get the solutions manual for detailed explanation of proofs in the exercises.

Answer Book for Calculus by Michael Spivak

Look on Amazon to see the reviews. Yes, Math 55 will be much harder but at least you will have practice with writing proofs.

By The_Brain9 (The_Brain9) on Saturday, August 07, 2004 - 12:20 pm: Edit

Corny, it's funny that you mention that book because I have it - I just haven't started working through it yet. Yeah, I picked it up because of the good reviews on Amazon...

Edit: I also have the solutions manual too!

By Ubercollegeman (Ubercollegeman) on Saturday, August 07, 2004 - 04:03 pm: Edit

Spivak's Calculus is one of the best I've ever seen. It is a newer text than most of the classics by the masters, so the notation and stuff is all good, and I highly recommend it too.

It is rather difficult though. Don't be surprised if you can't do many of his problems.

If you think Spivak's book is too easy for you (highly unlikely, I think Spivak is only suited for the top 0.5% of high school math students if even that), I can recommend others that are even harder.

By The_Brain9 (The_Brain9) on Saturday, August 07, 2004 - 05:44 pm: Edit

Ubercollegeman, Spivak is the perfect difficulty right now however I do want to hear some of your recommendations because Spivak doens't go into multi-var proofs.....

By Mruncleramos (Mruncleramos) on Saturday, August 07, 2004 - 08:16 pm: Edit

Holy crap, how many people here can do Spivak's Calculus on Manifolds... I was underestimating you guys, that book is pretty terse. I would recommend Analysis on Manifolds or Rudin's Principles of Mathematical Analysis. If you work through them line by line and don't get frustrated.

By Ubercollegeman (Ubercollegeman) on Saturday, August 07, 2004 - 09:16 pm: Edit

Not Spivak's Calculus on Manifolds. Just Spivak's Calculus. He has two books.

Some books that are a bit harder or about the same as Spivak's are:

Apostol - Calculus Vols. I and II (I is single-variable, II is multivariable + other stuff)

Courant - Differential and Integral Calculus Vols. I and II (see above note about Apostol)

Hardy - A Course of Pure Mathematics (no multivariable or beyond)*

*: This book is especially difficult, and Hardy was one of the greatest mathematicians of the 20th century (and arguably when combined with Littlewood the greatest mathematical team ever). The book is written very clearly, yet "rigor" cannot be overstated. If you want to take mathematics seriously, start with this book.

Books to avoid are basically any main-stream types like Stewart's, Thomas', and Larson's that have reduced calculus to a system of plugging and chugging. No beauty can be found in those books.

WARNING: I would look at Spivak's more closely. If Spivak's is "just right" for you, I would work with that a little bit before jumping into Hardy's. That book is a classic among classics for a reason: it may be the most difficult elementary calculus book ever written.

Also note that if you want books that match the AP curriculum, don't look into these. These are far more difficult than anything the AP test can offer, and the topics get far more abstruse.

By Corny (Corny) on Sunday, August 08, 2004 - 12:27 am: Edit

Spivak's Calculus is a superb book so you definitely made a good choice.

I hesitated mentioning Apostol's book just because I've heard there aren't as many detailed explanations of the proofs and at this stage you need to understand the underlying thought process. I haven't read Hardy so I can't comment on that one.

Believe me, you don't need to have studied multivar calc beforehand. The proof writing process is the most important thing right now. Once you get that down pat, any new topic will be relatively easy.

If, however, you're looking for a proof-based multivar calc book, there is Vector Calculus, Linear Algebra and Differential Forms by John H. Hubbard. But it is difficult and probably would be helpful once you're in Math 55. It is probably the best example of the type of proofs Math 55 will deal with.

By The_Brain9 (The_Brain9) on Sunday, August 08, 2004 - 02:03 am: Edit

Thanks for all of your responses. I did about 3 hours of Spivak's Calculus today and hopefully will go cover to cover. I got to get some sleep right now but please - if anybody has any recommendations for intro proof based mathematics - I am willing to listen. Goodnight!

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