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college math vs olympiad math
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#1
college math vs olympiad math
how useful is an olympiad math backround for studying math seriously?
hello, i am looking for some advise regarding studying math. i have finished one year of undergraduate math and i plan to continue studying math. One thing that is starting to bother me is that till recently i have never seen and attempted olympiad level problems. i was wondering if this will hinder my progression in learning math or, by doing undergraduate level courses i will learn much of the mathematical thinking that i have missing from not practicing olympiad problem solving skills. i have a feeling that without doing olympiad math im at an eternal disadvantage to those who do/did.. so i would like to know what you people think?

PostPosted: Tue Feb 24, 2009 6:34 pm  Back to top 
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gauss202
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You are not at a significant disadvantage. I've known many great mathematicians who did not participate in (or did not do exceptionally well in) High School Olympiads.

PostPosted: Wed Feb 25, 2009 7:13 am  Back to top 
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#3
i actually really feel it does disadvantage me... beacuse olympiad math builds a sort of core of mathematical thinking and knowledge. coming to college with this more developed mind will enable a student to effectively absorb more content then a regular student will. i would compare this to having so called 'good fundamentals' which enable you to achieve more then someone who is already building on flawed fundamental techniques. you know... the tower is only as good as its base kind of analogy..
do you all agree?

p.s to gauss202: im not talking about participating in an actual olympiad im talking about learning olympiad problem solving skills and material.. if your friends might have not done well (whatever your standard of well is...) in olympiads but if they participated i would imagine they would have studied some olympiad problem solving in preparation/selection.

PostPosted: Wed Feb 25, 2009 4:22 pm  Back to top 
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#4
gauss202 wrote:
You are not at a significant disadvantage. I've known many great mathematicians who did not participate in (or did not do exceptionally well in) High School Olympiads.


Conversely, I seem to find out fairly frequently that various graduate students/faculty at my university or top researchers in my subfield were IMO medalists or Putnam high scorers/fellows. And it's a bit disconcerting (if completely unsurprising) that they are the ones who come off as being really, really smart.

I mean, I scored in the top 200 on the Putnam as an undergraduate and graduated at the age of 20, and now that I've completed almost two years of graduate school, I feel like I knew nothing as an undergrad. In comparison to most of my graduate school peers I feel like my problem solving skills are quite good. But all of the olympiad superstars and whatever that I know are just scary smart, and it's hard not to feel like they are in another league from you, and that you just don't have the intellectual capacity to accomplish the things that they will or that they have.

On the other hand, unless your happiness or sense of self-worth is predicated on being one of the top x mathematicians in the world, all of this doesn't matter that much. You can be a good mathematician without being terry tao, after all. So if you are disadvantaged by not having an IQ of 180 like some olympiad superstars or because you picked up math later than others, well, accept it and go on with your life.

PostPosted: Sat Mar 14, 2009 9:55 pm  Back to top 
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ghjk
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#5
blahblahblah wrote:


Conversely, I seem to find out fairly frequently that various graduate students/faculty at my university or top researchers in my subfield were IMO medalists or Putnam high scorers/fellows. And it's a bit disconcerting (if completely unsurprising) that they are the ones who come off as being really, really smart.

I mean, I scored in the top 200 on the Putnam as an undergraduate and graduated at the age of 20, and now that I've completed almost two years of graduate school, I feel like I knew nothing as an undergrad. In comparison to most of my graduate school peers I feel like my problem solving skills are quite good. But all of the olympiad superstars and whatever that I know are just scary smart, and it's hard not to feel like they are in another league from you, and that you just don't have the intellectual capacity to accomplish the things that they will or that they have.

On the other hand, unless your happiness or sense of self-worth is predicated on being one of the top x mathematicians in the world, all of this doesn't matter that much. You can be a good mathematician without being terry tao, after all. So if you are disadvantaged by not having an IQ of 180 like some olympiad superstars or because you picked up math later than others, well, accept it and go on with your life.

Does John Conway get IMO anytime in his life?No(?). Is he one of the best mathematicians compared to Terry Tao? Absolutely! But we don't need to always mention Terry Tao though. He's a genius and everyone knows that. However, I believe we already knew many such "genius" people in this forum(Vasc, Harazi, or Iurie Boreico(5 times IMO medalist). We should note that each mathematician has his/her own strength, and h/she only works on the fields that he/she is an expert on it. I agree that Terry Tao discovers the significant proof for Green-Tao theorem, but Ngo Bao Chau-a Vietnamese mathematician who improved the Fermat's last theorem further and got a prize(don't remember whether it's a Field Medal or not)- is not well-known as Terry is. It's okay because that's life and sometimes people don't know your work until you die! If you consider the world of inequality, Vasc and Harazi should be the "Mozart" in that world. Will Terry Tao can beat them in this field? I suspect that possibility despite the fact that he's the greatest mathematician in our time. Like Bill Gate versus Steve Jobs in the entertainment, who wins?Steve Jobs is leading even though Bill Gate is a genius and beat Steve Jobs in computer field easily
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PostPosted: Sat Mar 14, 2009 10:11 pm  Back to top 
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#6
I'm not sure why you decided to fly off the handle just because I mentioned Terry Tao. My point was that your decision to study math, or your happiness, or whatever, should not be dependent on your ability to be one of the top x mathematicians in the world. I mentioned Terry Tao because as long as x>1, he is probably among those top x mathematicians.

ghjk wrote:

Does John Conway get IMO anytime in his life?No(?). Is he one of the best mathematicians compared to Terry Tao? Absolutely! But we don't need to always mention Terry Tao though. He's a genius and everyone knows that. However, I believe we already knew many such "genius" people in this forum(Vasc, Harazi, or Iurie Boreico(5 times IMO medalist).


There are lots of great mathematicians (especially older ones!) who never participated in the IMO or on the Putnam, and some who have managed to be great without having a skill-set suited to success on olympiads and the like. I'm just observing that most of the people who have been very successful in competition math often seem almost 'untouchably' smart in person. So are you at a disadvantage because you didn't do olympiad math per se? No. But you probably are at a significant comparative disadvantage because they have probably put much more time into math than you, have received specialized training than you haven't, and are inherently more capable than you. But math isn't a competitive sport, and life isn't fair, so this isn't something you should waste much time thinking about.

ghjk wrote:

We should note that each mathematician has his/her own strength, and h/she only works on the fields that he/she is an expert on it. I agree that Terry Tao discovers the significant proof for Green-Tao theorem, but Ngo Bao Chau-a Vietnamese mathematician who improved the Fermat's last theorem further and got a prize(don't remember whether it's a Field Medal or not)- is not well-known as Terry is. It's okay because that's life and sometimes people don't know your work until you die!


So what are you trying to argue here? Ngo Bao Chau is certainly a very very good mathematician. He's also a multiple IMO medalist. By any reasonable measure he's not as good of a mathematician as Terry Tao is. That, too, is life.

ghjk wrote:

If you consider the world of inequality, Vasc and Harazi should be the "Mozart" in that world. Will Terry Tao can beat them in this field? I suspect that possibility despite the fact that he's the greatest mathematician in our time. Like Bill Gate versus Steve Jobs in the entertainment, who wins?Steve Jobs is leading even though Bill Gate is a genius and beat Steve Jobs in computer field easily


This is pretty nonsensical and irrelevant. The fact is that there are very few mathematicians who have any sort of interest in proving 3-variable polynomial inequalities. It's stupid to compare work done in a subfield that virtually no one studies seriously to the kind of things Terry Tao does (harmonic analysis and arithmetic combinatorics are among the most active subfields of mathematics today). Basically you have no clue what you're talking about.

PostPosted: Sat Mar 14, 2009 10:42 pm  Back to top 
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Gen8
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#7
I was perusing through this section of AoPS, and I accidentally managed to stumble upon this thread, it seems an interesting discussion is going on. I apologize for reviving this thread again.

Quote:
You are not at a significant disadvantage. I've known many great mathematicians who did not participate in (or did not do exceptionally well in) High School Olympiads.


I wholly second this post, an instance for the above 'quote' is - Ramanujan. (Though, I would like to concede that IMO and Putnam didn't exist when he was there, but he would have easily won many IMO medals for sure).

Quote:
i actually really feel it does disadvantage me... because Olympiad math builds a sort of core of mathematical thinking and knowledge. coming to college with this more developed mind will enable a student to effectively absorb more content then a regular student will. i would compare this to having so called 'good fundamentals' which enable you to achieve more then someone who is already building on flawed fundamental techniques. you know... the tower is only as good as its base kind of analogy..
do you all agree?


I agree with this post, though I hadn't competed at the Olympiads, I have interacted with people who had competed; If you manage to solve Olympiad level problems it deeply strengthens your understanding of Mathematics, because 'some of the research problems in Math' (I mean some) seem pretty much like Olympiad problems (but they require more patience and perseverance). If you managed to compete at the IMO and also managed to get a medal, you're at a significant advantage than your peers at your undergraduate institution both in terms of mathematical ability, and proficiency.


Quote:
You can be a good mathematician without being terry tao, after all.



Quote:
So what are you trying to argue here? Ngo Bao Chau is certainly a very very good mathematician. He's also a multiple IMO medalist. By any reasonable measure he's not as good of a mathematician as Terry Tao is. That, too, is life.


So, you seem to greatly concur with your delusional notion that 'Terry Tao' is the greatest mathematician of our time (or whatever). I bet Ramanujan, and as well as Perelman, Grothendieck, Charles Fefferman are as good as Tao if not better. It is unfortunate that some people with as much talent and ability don't get fame like Tao does. (But I acknowledge that Tao is a great mathematician).

PostPosted: Wed May 20, 2009 1:41 pm  Back to top 
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#8
Gen8 wrote:
So, you seem to greatly concur with your delusional notion that 'Terry Tao' (I respect him greatly) is the greatest mathematician of our time (or whatever). I bet Ramanujan, and as well as Perelman, Grothendieck, Charles Fefferman are as good as Tao if not better.


no, that's not what I said. i said that terry tao was probably a better mathematician than ngo bao chau. tao is younger, has proved more important results (slightly subjective), and been awarded more prestigious prizes by his fellow mathematicians. both of them are easily in the top 1% of research mathematicians. just for my own personal amusement, i'd like to hear why calling terry tao the best mathematician of our time (which I never did) would be 'delusional', though.

Gen8 wrote:
I bet Ramanujan, and as well as Perelman, Grothendieck, Charles Fefferman are as good as Tao if not better.


you know so little mathematics that this opinion is completely worthless. your understanding of mathematics is so rudimentary that it is unlikely that you could follow a single important paper of tao, grothendieck, or fefferman, so why do you think you could correctly judge which of them is the better mathematician (if, indeed, there is even a well-ordering on mathematicians of this type)?

PostPosted: Wed May 20, 2009 1:58 pm  Back to top 
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#9
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you know so little mathematics that this opinion is completely worthless. your understanding of mathematics is so rudimentary that it is unlikely that you could follow a single important paper of tao, grothendieck, or fefferman, so why do you think you could correctly judge which of them is the better mathematician (if, indeed, there is even a well-ordering on mathematicians of this type)?


I am a major in computer science (and not Mathematics!); I had taken just 3 courses in Math in my under-grad school (I'm not from the U.S.A.) so it might be that I have a rudimentary level of proficiency in Math. I also don't know LATEX (I'm learning it though).

Those links that you had cited were- in specific, some doubts I had , (I committed a mistake in one of the arithmetic progression problems, it is quite natural to commit mistakes and have doubts).

Quote:
you know so little mathematics that this opinion is completely worthless. your understanding of mathematics is so rudimentary that it is unlikely that you could follow a single important paper of tao, grothendieck, or fefferman, so why do you think you could correctly judge which of them is the better mathematician (if, indeed, there is even a well-ordering on mathematicians of this type)?


Well, As I have reiterated my major is in CS and not Math! So, you can't expect me to know math as you do, similarly I can't expect you to know CS as I do. I bet your understanding or proficiency in CS is similar to what I have in Math.

I never said that I correctly judged any of them (or my opinion was correct), it was an opinion of mine (just as you had regarding Tao), given the fact that fefferman won a fields medal at 28, and Perelman solved an 'very difficult open problem in Math' and Tao didn't.

I hope you get it into your head that these are highly subjective opinions based upon achievements (like solving open problems).

P.S.: With due respect, your posts almost always (I mean non-technical posts) exhibit characteristics of a 'troll'. Very Happy I think you delight in 'flame wars' in your pastime.

PostPosted: Wed May 20, 2009 2:15 pm  Back to top 
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#10
Gen8 wrote:
Well, As I have reiterated my major is in CS and not Math! So, you can't expect me to know math as you do, similarly I can't expect you to know CS as I do. I bet your understanding or proficiency in CS is similar to what I have in Math.


i think being able to turn on a computer would indicate a proficiency in CS roughly equal to your proficiency in mathematics.

Gen8 wrote:
and Perelman solved an 'very difficult open problem in Math' and Tao didn't.


the question resolved by the green-tao theorem was asked over a hundred years before the [url=http://en.wikipedia.org/wiki/Poincaré_conjecture]poincare conjecture[/url] was ever posed. you're just embarassing yourself (that is, more than usual) now.

PostPosted: Wed May 20, 2009 2:27 pm  Back to top 
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#11
Back to the original topic: a few observations.

1. You don't have to be good at solving Olympiad problems to be good at research mathematics. They occur on very different time scales - being good at solving Olympiad problems requires that you can solve difficult problems on the scale of hours, whereas being good at research mathematics takes place on a scale of days, weeks, months, or years, and with very different resources available to you. They're not necessarily comparable activities; it is possible to be good at one and not the other.

2. Nevertheless, there is a strong correlation between the two. Why? As Kiran Kedlaya puts it, if you like Olympiad math that probably means you prefer to solve problems that take hours instead of minutes (as in high school), so it's likely that you prefer to solve problems that take weeks instead of hours. How interested (as opposed to how good) you are in Olympiad mathematics is a good indicator of how interested you will be in a professional mathematics career, although it is by no means a foolproof indicator.

3. I also think that a second advantage in having done a lot of Olympiad mathematics is that you become acquainted with a wide variety of elementary (and not so elementary) problem-solving tools; having many tools in your toolbox will of course make it easier to do research math. It is possible, however, that the rise of the Tricki will make this less of an issue.

So, short answer: it is not necessary, but it can be useful.
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PostPosted: Wed May 20, 2009 2:30 pm  Back to top 
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#12
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i think being able to turn on a computer would indicate a proficiency in CS roughly equal to your proficiency in mathematics.


So, you mean you can only turn on a computer? Rotfl Since my proficiency in Math is similar to your proficiency in CS.

Since I'm a graduate in CS, I would be much better off in comprehending abstruse concepts of CS than learning elementary/advanced Math (or whatever); But I like to dabble in Math ( and also comment on Math-related topics).

PostPosted: Wed May 20, 2009 2:44 pm  Back to top 
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